(%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, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < 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 - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc 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 : false, if (not found) 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 : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) 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 > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, 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"))),
if (not found) 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 : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, 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"))),
if (not found) 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, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found 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")),
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, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < 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 - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc 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 : false, if (not found) 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 : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) 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 > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, 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"))),
if (not found) 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 : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, 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"))),
if (not found) 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, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found 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")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_0D1 array_x ,
1 1 1
array_tmp2 : array_const_0D2 + array_tmp1 , array_tmp3 : exp(array_tmp2 ),
1 1 1 1 1
array_tmp4 : array_tmp3 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp3 array_tmp2
1 2
array_tmp3 : -----------------------, array_tmp4 : array_tmp3 ,
2 1 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp4 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_tmp3 array_tmp2
2 2
array_tmp3 : -----------------------, array_tmp4 : array_tmp3 ,
3 2 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp4 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_tmp3 array_tmp2
3 2
array_tmp3 : -----------------------, array_tmp4 : array_tmp3 ,
4 3 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp4 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_tmp3 array_tmp2
4 2
array_tmp3 : -----------------------, array_tmp4 : array_tmp3 ,
5 4 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp4 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_tmp3 :
kkk
array_tmp3 array_tmp2
kkk - 1 2
-----------------------------, array_tmp4 : array_tmp3 , order_d : 1,
kkk - 1 kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp4 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_0D1 array_x ,
1 1 1
array_tmp2 : array_const_0D2 + array_tmp1 , array_tmp3 : exp(array_tmp2 ),
1 1 1 1 1
array_tmp4 : array_tmp3 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp3 array_tmp2
1 2
array_tmp3 : -----------------------, array_tmp4 : array_tmp3 ,
2 1 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp4 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_tmp3 array_tmp2
2 2
array_tmp3 : -----------------------, array_tmp4 : array_tmp3 ,
3 2 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp4 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_tmp3 array_tmp2
3 2
array_tmp3 : -----------------------, array_tmp4 : array_tmp3 ,
4 3 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp4 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_tmp3 array_tmp2
4 2
array_tmp3 : -----------------------, array_tmp4 : array_tmp3 ,
5 4 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp4 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_tmp3 :
kkk
array_tmp3 array_tmp2
kkk - 1 2
-----------------------------, array_tmp4 : array_tmp3 , order_d : 1,
kkk - 1 kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp4 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole() := 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
(%o27) 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
(%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i31) 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, " | "))
(%o31) 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, " | "))
(%i32) log_revs(file, revs) := printf(file, revs)
(%o32) log_revs(file, revs) := printf(file, revs)
(%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i34) 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, " | "))
(%o34) 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, " | "))
(%i35) logstart(file) := printf(file, "")
(%o35) logstart(file) := printf(file, "
")
(%i36) logend(file) := printf(file, "
~%")
(%o36) logend(file) := printf(file, "~%")
(%i37) 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())
(%o37) 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())
(%i38) 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
(%o38) 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
(%i39) 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
(%o39) 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
(%i40) factorial_2(nnn) := nnn!
(%o40) factorial_2(nnn) := nnn!
(%i41) 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
(%o41) 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
(%i42) 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)
(%o42) 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)
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i46) Si(x) := 0.0
(%o46) Si(x) := 0.0
(%i47) Ci(x) := 0.0
(%o47) Ci(x) := 0.0
(%i48) ln(x) := log(x)
(%o48) ln(x) := log(x)
(%i49) arcsin(x) := asin(x)
(%o49) arcsin(x) := asin(x)
(%i50) arccos(x) := acos(x)
(%o50) arccos(x) := acos(x)
(%i51) arctan(x) := atan(x)
(%o51) arctan(x) := atan(x)
(%i52) omniabs(x) := abs(x)
(%o52) omniabs(x) := abs(x)
(%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i54) 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)
(%o54) 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)
(%i55) exact_soln_y(x) := block(10.0 exp(0.2 + 0.1 x))
(%o55) exact_soln_y(x) := block(10.0 exp(0.2 + 0.1 x))
(%i56) 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, log10norm,
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_log10normmin, 0.1, float),
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_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, 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_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
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-51, 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_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/lin_exppostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp (0.1 * x + 0.2 ) ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms:30,"),
omniout_str(ALWAYS, "Digits:32,"), 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:10.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.00001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (10.0 * exp(0.1 * x + 0.2)) "),
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, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, max_terms : 30, Digits : 32,
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_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_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term),
term
array_const_0D2 : 0.2, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 1.0,
iiif, jjjf
x_end : 10.0, array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5,
1 + 0
glob_look_poles : true, glob_max_iter : 10, glob_desired_digits_correct : 10,
glob_display_interval : 0.001, glob_look_poles : true,
glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, 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_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), 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 ) = exp (0.1 * x + 0.2 ) ;"),
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,
"2013-01-12T23:55:58-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_exp"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = exp (0.1 * x + 0.2 ) ;"),
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, " 156 | "), logitem_str(html_log_file, "lin_exp diffeq.max"),
logitem_str(html_log_file,
"lin_exp maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%o56) 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, log10norm,
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_log10normmin, 0.1, float),
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_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, 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_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
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-51, 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_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/lin_exppostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp (0.1 * x + 0.2 ) ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms:30,"),
omniout_str(ALWAYS, "Digits:32,"), 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:10.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.00001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (10.0 * exp(0.1 * x + 0.2)) "),
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, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, max_terms : 30, Digits : 32,
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_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_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term),
term
array_const_0D2 : 0.2, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 1.0,
iiif, jjjf
x_end : 10.0, array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5,
1 + 0
glob_look_poles : true, glob_max_iter : 10, glob_desired_digits_correct : 10,
glob_display_interval : 0.001, glob_look_poles : true,
glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, 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_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), 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 ) = exp (0.1 * x + 0.2 ) ;"),
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,
"2013-01-12T23:55:58-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_exp"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = exp (0.1 * x + 0.2 ) ;"),
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, " 156 | "), logitem_str(html_log_file, "lin_exp diffeq.max"),
logitem_str(html_log_file,
"lin_exp maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i57) main()
"##############ECHO OF PROBLEM#################"
"##############temp/lin_exppostode.ode#################"
"diff ( y , x , 1 ) = exp (0.1 * x + 0.2 ) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"max_terms:30,"
"Digits:32,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:1.0,"
"x_end:10.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.00001,"
"glob_look_poles:true,"
"glob_max_iter:10,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (10.0 * exp(0.1 * x + 0.2)) "
"));"
""
"/* 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 = 9. ""
estimated_steps = 9000. ""
step_error = 1.111111111111111200000000000000E-14 ""
est_needed_step_err = 1.111111111111111200000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 3.3471110534999350000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-130 ""
max_value3 = 3.3471110534999350000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-130 ""
value3 = 3.3471110534999350000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-130 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = 1. " "
y[1] (analytic) = 13.498588075760033 " "
y[1] (numeric) = 13.498588075760033 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1. " "
y[1] (analytic) = 13.498588075760033 " "
y[1] (numeric) = 13.498588075760033 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.001 " "
y[1] (analytic) = 13.499938002062796 " "
y[1] (numeric) = 13.499938002062798 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.315825923888555800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0019999999999998 " "
y[1] (analytic) = 13.501288063364944 " "
y[1] (numeric) = 13.501288063364944 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0029999999999997 " "
y[1] (analytic) = 13.502638259679971 " "
y[1] (numeric) = 13.502638259679971 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0039999999999996 " "
y[1] (analytic) = 13.50398859102138 " "
y[1] (numeric) = 13.50398859102138 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0049999999999994 " "
y[1] (analytic) = 13.505339057402677 " "
y[1] (numeric) = 13.505339057402677 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0059999999999993 " "
y[1] (analytic) = 13.506689658837363 " "
y[1] (numeric) = 13.506689658837365 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.315168175377442500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0069999999999992 " "
y[1] (analytic) = 13.508040395338945 " "
y[1] (numeric) = 13.508040395338949 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.63007333027105300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0079999999999991 " "
y[1] (analytic) = 13.509391266920934 " "
y[1] (numeric) = 13.509391266920936 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.31490516804397700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.008999999999999 " "
y[1] (analytic) = 13.510742273596833 " "
y[1] (numeric) = 13.510742273596836 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.629547368202958500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.009999999999999 " "
y[1] (analytic) = 13.512093415380155 " "
y[1] (numeric) = 13.512093415380159 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.62928442661343700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0109999999999988 " "
y[1] (analytic) = 13.513444692284413 " "
y[1] (numeric) = 13.513444692284416 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.629021511316760000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0119999999999987 " "
y[1] (analytic) = 13.514796104323118 " "
y[1] (numeric) = 13.514796104323121 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.628758622310297000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0129999999999986 " "
y[1] (analytic) = 13.516147651509783 " "
y[1] (numeric) = 13.516147651509787 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.628495759591421000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0139999999999985 " "
y[1] (analytic) = 13.517499333857923 " "
y[1] (numeric) = 13.517499333857929 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 3.942349384736254500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0149999999999983 " "
y[1] (analytic) = 13.51885115138106 " "
y[1] (numeric) = 13.518851151381064 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.627970113005913500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741884.5 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0159999999999982 " "
y[1] (analytic) = 13.520203104092705 " "
y[1] (numeric) = 13.520203104092712 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.25541465826805200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0169999999999981 " "
y[1] (analytic) = 13.521555192006383 " "
y[1] (numeric) = 13.52155519200639 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.25488914307842200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.017999999999998 " "
y[1] (analytic) = 13.522907415135615 " "
y[1] (numeric) = 13.52290741513562 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 3.94077276032826330000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.018999999999998 " "
y[1] (analytic) = 13.524259773493919 " "
y[1] (numeric) = 13.524259773493924 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 3.940378702755437700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0199999999999978 " "
y[1] (analytic) = 13.52561226709482 " "
y[1] (numeric) = 13.525612267094827 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.253312912781866000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0209999999999977 " "
y[1] (analytic) = 13.526964895951846 " "
y[1] (numeric) = 13.526964895951853 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.25278760775627600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0219999999999976 " "
y[1] (analytic) = 13.52831766007852 " "
y[1] (numeric) = 13.528317660078526 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.25226235525856300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0229999999999975 " "
y[1] (analytic) = 13.52967055948837 " "
y[1] (numeric) = 13.529670559488377 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.25173715528347400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0239999999999974 " "
y[1] (analytic) = 13.531023594194927 " "
y[1] (numeric) = 13.531023594194933 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 3.93840900586931700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0249999999999972 " "
y[1] (analytic) = 13.53237676421172 " "
y[1] (numeric) = 13.532376764211726 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 3.938015184660118600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0259999999999971 " "
y[1] (analytic) = 13.533730069552279 " "
y[1] (numeric) = 13.533730069552286 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.2501618704414300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.026999999999997 " "
y[1] (analytic) = 13.535083510230141 " "
y[1] (numeric) = 13.535083510230148 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.2496368805043200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.027999999999997 " "
y[1] (analytic) = 13.536437086258838 " "
y[1] (numeric) = 13.536437086258845 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.24911194306357900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0289999999999968 " "
y[1] (analytic) = 13.537790797651905 " "
y[1] (numeric) = 13.537790797651912 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.248587058113958000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0299999999999967 " "
y[1] (analytic) = 13.53914464442288 " "
y[1] (numeric) = 13.539144644422887 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.24806222565020700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0309999999999966 " "
y[1] (analytic) = 13.540498626585302 " "
y[1] (numeric) = 13.54049862658531 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.247537445667079000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0319999999999965 " "
y[1] (analytic) = 13.54185274415271 " "
y[1] (numeric) = 13.541852744152719 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.55876589769915500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0329999999999964 " "
y[1] (analytic) = 13.543206997138647 " "
y[1] (numeric) = 13.543206997138654 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.24648804312169800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 687194767359986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0339999999999963 " "
y[1] (analytic) = 13.544561385556653 " "
y[1] (numeric) = 13.54456138555666 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.24596342054895000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0349999999999961 " "
y[1] (analytic) = 13.545915909420271 " "
y[1] (numeric) = 13.54591590942028 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.556798563044800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.035999999999996 " "
y[1] (analytic) = 13.54727056874305 " "
y[1] (numeric) = 13.547270568743059 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.55614291597139600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.036999999999996 " "
y[1] (analytic) = 13.548625363538536 " "
y[1] (numeric) = 13.548625363538545 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.5554873344594200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0379999999999958 " "
y[1] (analytic) = 13.549980293820274 " "
y[1] (numeric) = 13.549980293820283 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.55483181850231800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0389999999999957 " "
y[1] (analytic) = 13.551335359601817 " "
y[1] (numeric) = 13.551335359601826 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.55417636809353400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0399999999999956 " "
y[1] (analytic) = 13.552690560896712 " "
y[1] (numeric) = 13.552690560896721 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.55352098322651400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0409999999999955 " "
y[1] (analytic) = 13.554045897718511 " "
y[1] (numeric) = 13.554045897718522 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 7.86343879667364700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0419999999999954 " "
y[1] (analytic) = 13.555401370080773 " "
y[1] (numeric) = 13.555401370080782 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.55221041009155100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0429999999999953 " "
y[1] (analytic) = 13.556756977997047 " "
y[1] (numeric) = 13.556756977997056 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.55155522181050200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0439999999999952 " "
y[1] (analytic) = 13.55811272148089 " "
y[1] (numeric) = 13.5581127214809 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.55090009904500600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.044999999999995 " "
y[1] (analytic) = 13.559468600545863 " "
y[1] (numeric) = 13.559468600545872 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.5502450417885100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.045999999999995 " "
y[1] (analytic) = 13.56082461520552 " "
y[1] (numeric) = 13.56082461520553 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.54959005003446400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0469999999999948 " "
y[1] (analytic) = 13.562180765473425 " "
y[1] (numeric) = 13.562180765473434 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.5489351237763190000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0479999999999947 " "
y[1] (analytic) = 13.563537051363134 " "
y[1] (numeric) = 13.563537051363145 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 7.85793631560903300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0489999999999946 " "
y[1] (analytic) = 13.564893472888217 " "
y[1] (numeric) = 13.564893472888228 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 7.85715056126584300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999945 " "
y[1] (analytic) = 13.566250030062236 " "
y[1] (numeric) = 13.566250030062244 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.54697073791179900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 687194767359986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0509999999999944 " "
y[1] (analytic) = 13.56760672289875 " "
y[1] (numeric) = 13.567606722898763 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.1648425030004800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 768307106.7995584 " "
Order of pole = 68719476735987.625 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0519999999999943 " "
y[1] (analytic) = 13.568963551411334 " "
y[1] (numeric) = 13.568963551411347 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.16392606457286700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0529999999999942 " "
y[1] (analytic) = 13.570320515613556 " "
y[1] (numeric) = 13.570320515613567 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 7.85400832952958000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.053999999999994 " "
y[1] (analytic) = 13.571677615518983 " "
y[1] (numeric) = 13.571677615518992 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.54435247330446800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.054999999999994 " "
y[1] (analytic) = 13.573034851141184 " "
y[1] (numeric) = 13.573034851141193 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.54369807077780800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0559999999999938 " "
y[1] (analytic) = 13.574392222493735 " "
y[1] (numeric) = 13.574392222493744 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.5430437336881310000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0569999999999937 " "
y[1] (analytic) = 13.575749729590207 " "
y[1] (numeric) = 13.575749729590218 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 7.85086735443466900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0579999999999936 " "
y[1] (analytic) = 13.577107372444177 " "
y[1] (numeric) = 13.577107372444187 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 7.85008230695225300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 687194767359986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0589999999999935 " "
y[1] (analytic) = 13.57846515106922 " "
y[1] (numeric) = 13.578465151069231 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 7.84929733797066100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0599999999999934 " "
y[1] (analytic) = 13.579823065478918 " "
y[1] (numeric) = 13.579823065478926 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.54042703956836800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0609999999999933 " "
y[1] (analytic) = 13.581181115686842 " "
y[1] (numeric) = 13.581181115686853 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 7.84772763547855000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0619999999999932 " "
y[1] (analytic) = 13.58253930170658 " "
y[1] (numeric) = 13.582539301706591 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 7.84694290195233100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.062999999999993 " "
y[1] (analytic) = 13.58389762355171 " "
y[1] (numeric) = 13.583897623551723 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.15385128804480100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 343597383679986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.063999999999993 " "
y[1] (analytic) = 13.58525608123582 " "
y[1] (numeric) = 13.58525608123583 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 7.84537367030033700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741884.5 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0649999999999928 " "
y[1] (analytic) = 13.586614674772486 " "
y[1] (numeric) = 13.586614674772498 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.15202070085201300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0659999999999927 " "
y[1] (analytic) = 13.587973404175303 " "
y[1] (numeric) = 13.587973404175314 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 7.8438047524632900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0669999999999926 " "
y[1] (analytic) = 13.58933226945785 " "
y[1] (numeric) = 13.589332269457863 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.15019047974005500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0679999999999925 " "
y[1] (analytic) = 13.590691270633723 " "
y[1] (numeric) = 13.590691270633735 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.14927550644150800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 343597383679986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0689999999999924 " "
y[1] (analytic) = 13.592050407716508 " "
y[1] (numeric) = 13.59205040771652 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.14836062463571600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0699999999999923 " "
y[1] (analytic) = 13.593409680719796 " "
y[1] (numeric) = 13.593409680719809 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.14744583431353100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0709999999999922 " "
y[1] (analytic) = 13.594769089657182 " "
y[1] (numeric) = 13.594769089657195 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.14653113546580500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.071999999999992 " "
y[1] (analytic) = 13.596128634542259 " "
y[1] (numeric) = 13.596128634542271 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.1456165280833900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 465854610.9187168 " "
Order of pole = 30317416207047.875 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.072999999999992 " "
y[1] (analytic) = 13.597488315388622 " "
y[1] (numeric) = 13.597488315388635 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.1447020121571400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0739999999999919 " "
y[1] (analytic) = 13.598848132209868 " "
y[1] (numeric) = 13.59884813220988 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.14378758767791100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0749999999999917 " "
y[1] (analytic) = 13.600208085019599 " "
y[1] (numeric) = 13.60020808501961 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 7.83674850397419000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0759999999999916 " "
y[1] (analytic) = 13.601568173831406 " "
y[1] (numeric) = 13.601568173831419 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.14195901302393500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 343597383679986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0769999999999915 " "
y[1] (analytic) = 13.602928398658898 " "
y[1] (numeric) = 13.60292839865891 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.14104486283090400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0779999999999914 " "
y[1] (analytic) = 13.604288759515672 " "
y[1] (numeric) = 13.604288759515686 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.04458637760552250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 343597383679986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0789999999999913 " "
y[1] (analytic) = 13.605649256415335 " "
y[1] (numeric) = 13.605649256415349 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.04448192419051980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0799999999999912 " "
y[1] (analytic) = 13.607009889371492 " "
y[1] (numeric) = 13.607009889371504 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.13830296067794200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.080999999999991 " "
y[1] (analytic) = 13.608370658397744 " "
y[1] (numeric) = 13.608370658397758 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.04427304869392760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.081999999999991 " "
y[1] (analytic) = 13.609731563507706 " "
y[1] (numeric) = 13.609731563507719 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.13647548283968200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0829999999999909 " "
y[1] (analytic) = 13.611092604714983 " "
y[1] (numeric) = 13.611092604714996 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.13556188097225300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0839999999999907 " "
y[1] (analytic) = 13.612453782033185 " "
y[1] (numeric) = 13.6124537820332 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.04395981376690770000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0849999999999906 " "
y[1] (analytic) = 13.613815095475925 " "
y[1] (numeric) = 13.61381509547594 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.1743373508808010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 687194767359986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0859999999999905 " "
y[1] (analytic) = 13.615176545056817 " "
y[1] (numeric) = 13.615176545056833 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.17421992301720370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0869999999999904 " "
y[1] (analytic) = 13.616538130789476 " "
y[1] (numeric) = 13.616538130789491 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.1741025068958060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0879999999999903 " "
y[1] (analytic) = 13.617899852687515 " "
y[1] (numeric) = 13.61789985268753 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.17398510251543330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0889999999999902 " "
y[1] (analytic) = 13.619261710764553 " "
y[1] (numeric) = 13.619261710764569 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.17386770987491150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 768307106.7995597 " "
Order of pole = 34359738367989.5 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.08999999999999 " "
y[1] (analytic) = 13.620623705034207 " "
y[1] (numeric) = 13.620623705034223 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.1737503289730669000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.09099999999999 " "
y[1] (analytic) = 13.6219858355101 " "
y[1] (numeric) = 13.621985835510115 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.0432292976077560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0919999999999899 " "
y[1] (analytic) = 13.623348102205851 " "
y[1] (numeric) = 13.623348102205865 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.04312497989396790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0929999999999898 " "
y[1] (analytic) = 13.62471050513508 " "
y[1] (numeric) = 13.624710505135097 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.17339825668785830000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0939999999999896 " "
y[1] (analytic) = 13.626073044311418 " "
y[1] (numeric) = 13.626073044311434 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.17328092272898520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0949999999999895 " "
y[1] (analytic) = 13.627435719748485 " "
y[1] (numeric) = 13.627435719748501 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.17316360050292140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0959999999999894 " "
y[1] (analytic) = 13.628798531459909 " "
y[1] (numeric) = 13.628798531459926 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.3033847666761042000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0969999999999893 " "
y[1] (analytic) = 13.63016147945932 " "
y[1] (numeric) = 13.630161479459337 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.30325443471614320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0979999999999892 " "
y[1] (analytic) = 13.631524563760344 " "
y[1] (numeric) = 13.631524563760362 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.30312411578872660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 687194767359986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.098999999999989 " "
y[1] (analytic) = 13.632887784376615 " "
y[1] (numeric) = 13.632887784376633 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.3029938098925510000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.099999999999989 " "
y[1] (analytic) = 13.634251141321762 " "
y[1] (numeric) = 13.634251141321782 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.43314986872894540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1009999999999889 " "
y[1] (analytic) = 13.635614634609423 " "
y[1] (numeric) = 13.635614634609443 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.43300656090758260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1019999999999888 " "
y[1] (analytic) = 13.63697826425323 " "
y[1] (numeric) = 13.63697826425325 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.4328632674162858000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1029999999999887 " "
y[1] (analytic) = 13.63834203026682 " "
y[1] (numeric) = 13.63834203026684 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.43271998825362180000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1039999999999885 " "
y[1] (analytic) = 13.63970593266383 " "
y[1] (numeric) = 13.63970593266385 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.43257672341815740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 1030792151039986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1049999999999884 " "
y[1] (analytic) = 13.6410699714579 " "
y[1] (numeric) = 13.641069971457918 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.30221224809860040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1059999999999883 " "
y[1] (analytic) = 13.642434146662668 " "
y[1] (numeric) = 13.642434146662687 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.43229023672309860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1069999999999882 " "
y[1] (analytic) = 13.643798458291778 " "
y[1] (numeric) = 13.643798458291798 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.43214701486063860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.107999999999988 " "
y[1] (analytic) = 13.645162906358875 " "
y[1] (numeric) = 13.645162906358893 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.30182164301786280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.108999999999988 " "
y[1] (analytic) = 13.646527490877599 " "
y[1] (numeric) = 13.646527490877617 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.30169146736245220000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999879 " "
y[1] (analytic) = 13.647892211861599 " "
y[1] (numeric) = 13.647892211861617 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.30156130472395630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1109999999999878 " "
y[1] (analytic) = 13.649257069324518 " "
y[1] (numeric) = 13.64925706932454 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.56171738612128850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1119999999999877 " "
y[1] (analytic) = 13.65062206328001 " "
y[1] (numeric) = 13.650622063280032 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.56156122219100300000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1129999999999876 " "
y[1] (analytic) = 13.651987193741727 " "
y[1] (numeric) = 13.651987193741746 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.43128798438663520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1139999999999874 " "
y[1] (analytic) = 13.653352460723312 " "
y[1] (numeric) = 13.653352460723331 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.4311448627443982000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1149999999999873 " "
y[1] (analytic) = 13.654717864238421 " "
y[1] (numeric) = 13.654717864238442 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.56109282408757430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 687194767359986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1159999999999872 " "
y[1] (analytic) = 13.656083404300709 " "
y[1] (numeric) = 13.656083404300732 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 1.69101478282790040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1169999999999871 " "
y[1] (analytic) = 13.657449080923834 " "
y[1] (numeric) = 13.657449080923856 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.56078063674253140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.117999999999987 " "
y[1] (analytic) = 13.658814894121447 " "
y[1] (numeric) = 13.65881489412147 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 1.69067661368937560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.118999999999987 " "
y[1] (analytic) = 13.660180843907211 " "
y[1] (numeric) = 13.660180843907233 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.5604685118287150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999868 " "
y[1] (analytic) = 13.661546930294781 " "
y[1] (numeric) = 13.661546930294804 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 1.6903385121779160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1209999999999867 " "
y[1] (analytic) = 13.662913153297822 " "
y[1] (numeric) = 13.662913153297845 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 1.69016948677810920000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483794. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1219999999999866 " "
y[1] (analytic) = 13.664279512929996 " "
y[1] (numeric) = 13.664279512930017 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.56000044148922800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1229999999999865 " "
y[1] (analytic) = 13.665646009204965 " "
y[1] (numeric) = 13.665646009204986 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.55984444924482100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1239999999999863 " "
y[1] (analytic) = 13.667012642136392 " "
y[1] (numeric) = 13.667012642136415 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 1.68966251198209740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 343597383679986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1249999999999862 " "
y[1] (analytic) = 13.668379411737945 " "
y[1] (numeric) = 13.66837941173797 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.81945459680807890000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1259999999999861 " "
y[1] (analytic) = 13.669746318023295 " "
y[1] (numeric) = 13.66974631802332 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.81927266044536740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.126999999999986 " "
y[1] (analytic) = 13.671113361006107 " "
y[1] (numeric) = 13.671113361006132 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.81909074227538330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.127999999999986 " "
y[1] (analytic) = 13.672480540700052 " "
y[1] (numeric) = 13.672480540700077 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.81890884229630620000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 343597383679986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1289999999999858 " "
y[1] (analytic) = 13.673847857118805 " "
y[1] (numeric) = 13.673847857118828 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 1.68881789189872340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999857 " "
y[1] (analytic) = 13.675215310276034 " "
y[1] (numeric) = 13.675215310276059 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.81854509690359850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1309999999999856 " "
y[1] (analytic) = 13.676582900185418 " "
y[1] (numeric) = 13.676582900185442 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.81836325148633070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1319999999999855 " "
y[1] (analytic) = 13.677950626860628 " "
y[1] (numeric) = 13.677950626860655 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.94805152598503100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1329999999999854 " "
y[1] (analytic) = 13.67931849031535 " "
y[1] (numeric) = 13.679318490315374 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.8179996152008740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1339999999999852 " "
y[1] (analytic) = 13.680686490563252 " "
y[1] (numeric) = 13.680686490563279 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.9476619546382670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1349999999999851 " "
y[1] (analytic) = 13.68205462761802 " "
y[1] (numeric) = 13.682054627618047 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.94746719818078840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.135999999999985 " "
y[1] (analytic) = 13.683422901493337 " "
y[1] (numeric) = 13.683422901493362 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.81745429711811620000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.136999999999985 " "
y[1] (analytic) = 13.68479131220288 " "
y[1] (numeric) = 13.684791312202906 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.94707774368790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1379999999999848 " "
y[1] (analytic) = 13.68615985976034 " "
y[1] (numeric) = 13.686159859760364 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.81709084260535530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1389999999999847 " "
y[1] (analytic) = 13.687528544179395 " "
y[1] (numeric) = 13.68752854417942 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.81690914260624640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999846 " "
y[1] (analytic) = 13.688897365473736 " "
y[1] (numeric) = 13.688897365473762 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.94649370797453100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1409999999999845 " "
y[1] (analytic) = 13.690266323657053 " "
y[1] (numeric) = 13.690266323657077 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.81654579711348550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1419999999999844 " "
y[1] (analytic) = 13.691635418743031 " "
y[1] (numeric) = 13.691635418743056 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.81636415161620050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1429999999999843 " "
y[1] (analytic) = 13.693004650745364 " "
y[1] (numeric) = 13.69300465074539 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.94590984744559660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 701365222.4760818 " "
Order of pole = 114532461226654.87 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1439999999999841 " "
y[1] (analytic) = 13.694374019677744 " "
y[1] (numeric) = 13.69437401967777 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.9457152661900770000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.144999999999984 " "
y[1] (analytic) = 13.695743525553864 " "
y[1] (numeric) = 13.69574352555389 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.94552070439171030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 343597383679986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.145999999999984 " "
y[1] (analytic) = 13.697113168387418 " "
y[1] (numeric) = 13.697113168387446 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.07501457285178740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1469999999999838 " "
y[1] (analytic) = 13.698482948192106 " "
y[1] (numeric) = 13.698482948192133 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.9451316391586520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1479999999999837 " "
y[1] (analytic) = 13.699852864981624 " "
y[1] (numeric) = 13.69985286498165 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.94493713572007040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 795273410.100515 " "
Order of pole = 98170681051416.69 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1489999999999836 " "
y[1] (analytic) = 13.70122291876967 " "
y[1] (numeric) = 13.701222918769696 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.94474265173085970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999835 " "
y[1] (analytic) = 13.702593109569944 " "
y[1] (numeric) = 13.702593109569971 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.94454818718907570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1509999999999834 " "
y[1] (analytic) = 13.70396343739615 " "
y[1] (numeric) = 13.703963437396178 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.07397732489895880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1519999999999833 " "
y[1] (analytic) = 13.70533390226199 " "
y[1] (numeric) = 13.70533390226202 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.073769937536010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1529999999999831 " "
y[1] (analytic) = 13.706704504181172 " "
y[1] (numeric) = 13.7067045041812 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.07356257091076020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.153999999999983 " "
y[1] (analytic) = 13.708075243167396 " "
y[1] (numeric) = 13.708075243167425 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.07335522502113650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.154999999999983 " "
y[1] (analytic) = 13.709446119234375 " "
y[1] (numeric) = 13.709446119234402 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.94357615612349820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 743910157.3518739 " "
Order of pole = 21474836479989.125 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1559999999999828 " "
y[1] (analytic) = 13.710817132395812 " "
y[1] (numeric) = 13.71081713239584 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.07294059544047250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1569999999999827 " "
y[1] (analytic) = 13.712188282665423 " "
y[1] (numeric) = 13.712188282665451 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.0727333117452860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1579999999999826 " "
y[1] (analytic) = 13.713559570056917 " "
y[1] (numeric) = 13.713559570056944 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.9429931707288428000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1589999999999825 " "
y[1] (analytic) = 13.714930994584005 " "
y[1] (numeric) = 13.714930994584034 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.07231880653483970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1599999999999824 " "
y[1] (analytic) = 13.716302556260406 " "
y[1] (numeric) = 13.716302556260432 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.942604610951969800000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1609999999999823 " "
y[1] (analytic) = 13.717674255099828 " "
y[1] (numeric) = 13.717674255099856 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.0719043842171458000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1619999999999822 " "
y[1] (analytic) = 13.719046091115997 " "
y[1] (numeric) = 13.719046091116024 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.9422161288792820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.162999999999982 " "
y[1] (analytic) = 13.720418064322624 " "
y[1] (numeric) = 13.720418064322653 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.0714900447756280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.163999999999982 " "
y[1] (analytic) = 13.721790174733435 " "
y[1] (numeric) = 13.721790174733462 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.9418277244952392000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1649999999999818 " "
y[1] (analytic) = 13.723162422362146 " "
y[1] (numeric) = 13.723162422362172 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.94163355143160470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1659999999999817 " "
y[1] (analytic) = 13.72453480722248 " "
y[1] (numeric) = 13.724534807222508 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.07086869096992640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1669999999999816 " "
y[1] (analytic) = 13.725907329328164 " "
y[1] (numeric) = 13.72590732932819 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.9412452635514010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1679999999999815 " "
y[1] (analytic) = 13.727279988692922 " "
y[1] (numeric) = 13.727279988692947 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.8116477388155520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1689999999999814 " "
y[1] (analytic) = 13.728652785330478 " "
y[1] (numeric) = 13.728652785330505 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.94085705332100760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1699999999999813 " "
y[1] (analytic) = 13.730025719254565 " "
y[1] (numeric) = 13.73002571925459 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.8112854454983282000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1709999999999812 " "
y[1] (analytic) = 13.731398790478906 " "
y[1] (numeric) = 13.731398790478933 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.9404689207248970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.171999999999981 " "
y[1] (analytic) = 13.732771999017235 " "
y[1] (numeric) = 13.732771999017263 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.0696265424371690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.172999999999981 " "
y[1] (analytic) = 13.734145344883286 " "
y[1] (numeric) = 13.734145344883315 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.0694195901307130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1739999999999808 " "
y[1] (analytic) = 13.73551882809079 " "
y[1] (numeric) = 13.735518828090818 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.06921265851845280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1749999999999807 " "
y[1] (analytic) = 13.736892448653482 " "
y[1] (numeric) = 13.73689244865351 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.06900574759831950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1759999999999806 " "
y[1] (analytic) = 13.738266206585099 " "
y[1] (numeric) = 13.738266206585127 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.06879885736824360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1769999999999805 " "
y[1] (analytic) = 13.739640101899377 " "
y[1] (numeric) = 13.739640101899406 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.06859198782615630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1779999999999804 " "
y[1] (analytic) = 13.74101413461006 " "
y[1] (numeric) = 13.741014134610086 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.93911106778436450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1789999999999803 " "
y[1] (analytic) = 13.742388304730882 " "
y[1] (numeric) = 13.742388304730909 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.93891716637281800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1799999999999802 " "
y[1] (analytic) = 13.743762612275585 " "
y[1] (numeric) = 13.743762612275614 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.067971503307140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.18099999999998 " "
y[1] (analytic) = 13.745137057257917 " "
y[1] (numeric) = 13.745137057257946 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.0677647164963220000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.18199999999998 " "
y[1] (analytic) = 13.746511639691619 " "
y[1] (numeric) = 13.746511639691647 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.06755795036315140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1829999999999798 " "
y[1] (analytic) = 13.747886359590439 " "
y[1] (numeric) = 13.747886359590465 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.93814175459896270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1839999999999797 " "
y[1] (analytic) = 13.749261216968119 " "
y[1] (numeric) = 13.749261216968147 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.06714448012148100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1849999999999796 " "
y[1] (analytic) = 13.750636211838414 " "
y[1] (numeric) = 13.750636211838442 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.06693777600884730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1859999999999795 " "
y[1] (analytic) = 13.75201134421507 " "
y[1] (numeric) = 13.752011344215099 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.06673109256559050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1869999999999794 " "
y[1] (analytic) = 13.75338661411184 " "
y[1] (numeric) = 13.75338661411187 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 2.1956822066514980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1879999999999793 " "
y[1] (analytic) = 13.754762021542478 " "
y[1] (numeric) = 13.754762021542506 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.06631778767894380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1889999999999792 " "
y[1] (analytic) = 13.756137566520731 " "
y[1] (numeric) = 13.756137566520763 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 2.32437506201034820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.189999999999979 " "
y[1] (analytic) = 13.757513249060365 " "
y[1] (numeric) = 13.757513249060397 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 2.32414263612563540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.190999999999979 " "
y[1] (analytic) = 13.758889069175131 " "
y[1] (numeric) = 13.758889069175162 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 2.19480410939999570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1919999999999789 " "
y[1] (analytic) = 13.760265026878786 " "
y[1] (numeric) = 13.760265026878818 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 2.3236778540781640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 687194767359986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1929999999999787 " "
y[1] (analytic) = 13.761641122185093 " "
y[1] (numeric) = 13.761641122185125 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 2.3234454979107580000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1939999999999786 " "
y[1] (analytic) = 13.76301735510781 " "
y[1] (numeric) = 13.763017355107843 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 2.45228056303213040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1949999999999785 " "
y[1] (analytic) = 13.764393725660701 " "
y[1] (numeric) = 13.764393725660735 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 2.4520353472368210000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1959999999999784 " "
y[1] (analytic) = 13.76577023385753 " "
y[1] (numeric) = 13.765770233857564 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 2.4517901559618652000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 795273410.100515 " "
Order of pole = 98170681051416.69 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1969999999999783 " "
y[1] (analytic) = 13.767146879712062 " "
y[1] (numeric) = 13.767146879712095 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 2.45154498920481130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 743910157.3518739 " "
Order of pole = 21474836479989.125 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1979999999999782 " "
y[1] (analytic) = 13.768523663238062 " "
y[1] (numeric) = 13.768523663238096 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 2.4512998469632072000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.198999999999978 " "
y[1] (analytic) = 13.7699005844493 " "
y[1] (numeric) = 13.769900584449333 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 2.4510547292346020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.199999999999978 " "
y[1] (analytic) = 13.771277643359541 " "
y[1] (numeric) = 13.771277643359577 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 2.57979961685951940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2009999999999779 " "
y[1] (analytic) = 13.772654839982561 " "
y[1] (numeric) = 13.772654839982597 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 2.57954164979640130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2019999999999778 " "
y[1] (analytic) = 13.77403217433213 " "
y[1] (numeric) = 13.774032174332165 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 2.57928370852870000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 343597383679986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2029999999999776 " "
y[1] (analytic) = 13.77540964642202 " "
y[1] (numeric) = 13.775409646422055 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 2.57902579305383600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2039999999999775 " "
y[1] (analytic) = 13.776787256266003 " "
y[1] (numeric) = 13.776787256266042 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.8366446937061530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 343597383679986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2049999999999774 " "
y[1] (analytic) = 13.778165003877863 " "
y[1] (numeric) = 13.7781650038779 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.7074355414459180000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2059999999999773 " "
y[1] (analytic) = 13.779542889271372 " "
y[1] (numeric) = 13.77954288927141 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.70716481142849960000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2069999999999772 " "
y[1] (analytic) = 13.78092091246031 " "
y[1] (numeric) = 13.780920912460347 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.706894108482729700000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.207999999999977 " "
y[1] (analytic) = 13.782299073458457 " "
y[1] (numeric) = 13.782299073458494 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.7066234326059013000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.208999999999977 " "
y[1] (analytic) = 13.783677372279595 " "
y[1] (numeric) = 13.783677372279632 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.70635278379530660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999769 " "
y[1] (analytic) = 13.785055808937507 " "
y[1] (numeric) = 13.785055808937544 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.706082162048240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2109999999999768 " "
y[1] (analytic) = 13.786434383445979 " "
y[1] (numeric) = 13.786434383446014 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 2.5769633974876140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2119999999999767 " "
y[1] (analytic) = 13.787813095818793 " "
y[1] (numeric) = 13.787813095818828 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 2.5767057140322530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2129999999999765 " "
y[1] (analytic) = 13.789191946069737 " "
y[1] (numeric) = 13.789191946069774 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.7052704591611465000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2139999999999764 " "
y[1] (analytic) = 13.790570934212603 " "
y[1] (numeric) = 13.790570934212639 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 2.57619042442012560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2149999999999763 " "
y[1] (analytic) = 13.791950060261176 " "
y[1] (numeric) = 13.791950060261213 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.70472945917111700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 343597383679986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2159999999999762 " "
y[1] (analytic) = 13.793329324229251 " "
y[1] (numeric) = 13.793329324229289 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.7044589997483960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.216999999999976 " "
y[1] (analytic) = 13.79470872613062 " "
y[1] (numeric) = 13.794708726130658 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.70418856737026540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.217999999999976 " "
y[1] (analytic) = 13.796088265979076 " "
y[1] (numeric) = 13.796088265979114 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.70391816203402100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2189999999999759 " "
y[1] (analytic) = 13.797467943788414 " "
y[1] (numeric) = 13.797467943788453 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.832392916295860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999758 " "
y[1] (analytic) = 13.798847759572432 " "
y[1] (numeric) = 13.798847759572471 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.8321096911657230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 768307106.7995597 " "
Order of pole = 34359738367989.5 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2209999999999757 " "
y[1] (analytic) = 13.800227713344928 " "
y[1] (numeric) = 13.800227713344967 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.8318264943566834000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2219999999999756 " "
y[1] (analytic) = 13.8016078051197 " "
y[1] (numeric) = 13.80160780511974 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 2.96024984067799500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2229999999999754 " "
y[1] (analytic) = 13.802988034910554 " "
y[1] (numeric) = 13.802988034910591 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.7025665408864490000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2239999999999753 " "
y[1] (analytic) = 13.804368402731285 " "
y[1] (numeric) = 13.804368402731322 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.70229629774474300000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2249999999999752 " "
y[1] (analytic) = 13.8057489085957 " "
y[1] (numeric) = 13.805748908595739 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.8306939902748570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.225999999999975 " "
y[1] (analytic) = 13.807129552517605 " "
y[1] (numeric) = 13.807129552517644 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.83041093502882760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.226999999999975 " "
y[1] (analytic) = 13.808510334510805 " "
y[1] (numeric) = 13.808510334510844 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.83012790808690740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.227999999999975 " "
y[1] (analytic) = 13.80989125458911 " "
y[1] (numeric) = 13.809891254589148 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.8298449094462670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2289999999999748 " "
y[1] (analytic) = 13.811272312766325 " "
y[1] (numeric) = 13.811272312766365 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.8295619391040750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999747 " "
y[1] (analytic) = 13.812653509056265 " "
y[1] (numeric) = 13.812653509056304 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.8292789970575033000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 687194767359986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2309999999999746 " "
y[1] (analytic) = 13.81403484347274 " "
y[1] (numeric) = 13.814034843472779 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.8289960833037210000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2319999999999744 " "
y[1] (analytic) = 13.815416316029566 " "
y[1] (numeric) = 13.815416316029603 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.70013532521081230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2329999999999743 " "
y[1] (analytic) = 13.816797926740552 " "
y[1] (numeric) = 13.816797926740591 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.828430340663210000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2339999999999742 " "
y[1] (analytic) = 13.818179675619518 " "
y[1] (numeric) = 13.818179675619557 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.8281475117708240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2349999999999741 " "
y[1] (analytic) = 13.819561562680281 " "
y[1] (numeric) = 13.81956156268032 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.8278647111599130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.235999999999974 " "
y[1] (analytic) = 13.820943587936661 " "
y[1] (numeric) = 13.8209435879367 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.82758193882764900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.236999999999974 " "
y[1] (analytic) = 13.822325751402476 " "
y[1] (numeric) = 13.822325751402515 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.8272991947712050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2379999999999738 " "
y[1] (analytic) = 13.823708053091549 " "
y[1] (numeric) = 13.823708053091588 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.82701647898775200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2389999999999737 " "
y[1] (analytic) = 13.825090493017703 " "
y[1] (numeric) = 13.825090493017742 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.8267337914744650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999736 " "
y[1] (analytic) = 13.82647307119476 " "
y[1] (numeric) = 13.8264730711948 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.82645113222851600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2409999999999735 " "
y[1] (analytic) = 13.82785578763655 " "
y[1] (numeric) = 13.827855787636588 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.82616850124707700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2419999999999733 " "
y[1] (analytic) = 13.829238642356897 " "
y[1] (numeric) = 13.829238642356936 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.8258858985273240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2429999999999732 " "
y[1] (analytic) = 13.83062163536963 " "
y[1] (numeric) = 13.83062163536967 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 2.95403983879672260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2439999999999731 " "
y[1] (analytic) = 13.832004766688579 " "
y[1] (numeric) = 13.832004766688621 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 3.082168121303530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.244999999999973 " "
y[1] (analytic) = 13.833388036327579 " "
y[1] (numeric) = 13.83338803632762 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 2.95344908990582130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.245999999999973 " "
y[1] (analytic) = 13.834771444300456 " "
y[1] (numeric) = 13.834771444300499 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 3.08155174931852240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2469999999999728 " "
y[1] (analytic) = 13.836154990621049 " "
y[1] (numeric) = 13.836154990621091 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 3.0812436095508360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2479999999999727 " "
y[1] (analytic) = 13.837538675303191 " "
y[1] (numeric) = 13.837538675303234 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 3.08093550059558600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2489999999999726 " "
y[1] (analytic) = 13.838922498360722 " "
y[1] (numeric) = 13.838922498360764 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 3.080627422449690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999725 " "
y[1] (analytic) = 13.840306459807477 " "
y[1] (numeric) = 13.84030645980752 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 3.08031937511006800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2509999999999724 " "
y[1] (analytic) = 13.841690559657296 " "
y[1] (numeric) = 13.84169055965734 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 3.2083451651808764000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2519999999999722 " "
y[1] (analytic) = 13.843074797924022 " "
y[1] (numeric) = 13.843074797924066 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 3.2080243467055490000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2529999999999721 " "
y[1] (analytic) = 13.844459174621495 " "
y[1] (numeric) = 13.844459174621539 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 3.2077035603104660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.253999999999972 " "
y[1] (analytic) = 13.84584368976356 " "
y[1] (numeric) = 13.845843689763605 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 3.2073828059924175000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.254999999999972 " "
y[1] (analytic) = 13.847228343364062 " "
y[1] (numeric) = 13.847228343364108 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 3.33534456709812630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2559999999999718 " "
y[1] (analytic) = 13.84861313543685 " "
y[1] (numeric) = 13.848613135436894 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 3.2067413935745990000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2569999999999717 " "
y[1] (analytic) = 13.849998065995766 " "
y[1] (numeric) = 13.84999806599581 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 3.20642073546841430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2579999999999716 " "
y[1] (analytic) = 13.851383135054665 " "
y[1] (numeric) = 13.851383135054709 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 3.20610010942643700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2589999999999715 " "
y[1] (analytic) = 13.852768342627392 " "
y[1] (numeric) = 13.852768342627439 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 3.3340106960632790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2599999999999714 " "
y[1] (analytic) = 13.854153688727806 " "
y[1] (numeric) = 13.854153688727852 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 3.33367731166317070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2609999999999713 " "
y[1] (analytic) = 13.855539173369758 " "
y[1] (numeric) = 13.855539173369802 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 3.20513842365368730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2619999999999711 " "
y[1] (analytic) = 13.856924796567098 " "
y[1] (numeric) = 13.856924796567144 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 3.33301064286993960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.262999999999971 " "
y[1] (analytic) = 13.858310558333688 " "
y[1] (numeric) = 13.858310558333734 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 3.33267735847015100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 1030792151039986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.263999999999971 " "
y[1] (analytic) = 13.859696458683386 " "
y[1] (numeric) = 13.85969645868343 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 3.2041770263433983000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2649999999999708 " "
y[1] (analytic) = 13.861082497630047 " "
y[1] (numeric) = 13.861082497630091 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 3.20385662466111550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2659999999999707 " "
y[1] (analytic) = 13.862468675187532 " "
y[1] (numeric) = 13.862468675187577 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 3.20353625501739850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2669999999999706 " "
y[1] (analytic) = 13.863854991369704 " "
y[1] (numeric) = 13.863854991369749 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 3.2032159174090440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2679999999999705 " "
y[1] (analytic) = 13.865241446190426 " "
y[1] (numeric) = 13.865241446190472 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 3.3310114363061630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2689999999999704 " "
y[1] (analytic) = 13.866628039663562 " "
y[1] (numeric) = 13.86662803966361 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 3.45878136534845950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2699999999999703 " "
y[1] (analytic) = 13.868014771802981 " "
y[1] (numeric) = 13.868014771803027 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 3.3303453006346895000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2709999999999702 " "
y[1] (analytic) = 13.869401642622545 " "
y[1] (numeric) = 13.869401642622593 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 3.45808967824640550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.27199999999997 " "
y[1] (analytic) = 13.870788652136127 " "
y[1] (numeric) = 13.870788652136175 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 3.45774388656845300000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.27299999999997 " "
y[1] (analytic) = 13.872175800357596 " "
y[1] (numeric) = 13.872175800357644 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 3.4573981294679390000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2739999999999698 " "
y[1] (analytic) = 13.873563087300825 " "
y[1] (numeric) = 13.873563087300871 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 3.3290134289065390000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1402730444.952159 " "
Order of pole = 114532461226655.81 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2749999999999697 " "
y[1] (analytic) = 13.87495051297968 " "
y[1] (numeric) = 13.87495051297973 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 3.58473289376263550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2759999999999696 " "
y[1] (analytic) = 13.876338077408043 " "
y[1] (numeric) = 13.876338077408093 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 3.58437443839632660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2769999999999695 " "
y[1] (analytic) = 13.877725780599787 " "
y[1] (numeric) = 13.877725780599837 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 3.58401601887376130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2779999999999694 " "
y[1] (analytic) = 13.879113622568791 " "
y[1] (numeric) = 13.87911362256884 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 3.45566986250595070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2789999999999693 " "
y[1] (analytic) = 13.880501603328927 " "
y[1] (numeric) = 13.880501603328977 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 3.58329928734552800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999692 " "
y[1] (analytic) = 13.881889722894082 " "
y[1] (numeric) = 13.881889722894131 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 3.58294097533269350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 404933399.99680364 " "
Order of pole = 229064922453321. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.280999999999969 " "
y[1] (analytic) = 13.883277981278132 " "
y[1] (numeric) = 13.883277981278184 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 3.7105320812617420000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483794. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.281999999999969 " "
y[1] (analytic) = 13.884666378494966 " "
y[1] (numeric) = 13.884666378495016 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 3.5822244587916690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2829999999999688 " "
y[1] (analytic) = 13.88605491455846 " "
y[1] (numeric) = 13.886054914558512 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 3.70979004905118370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2839999999999687 " "
y[1] (analytic) = 13.887443589482505 " "
y[1] (numeric) = 13.887443589482556 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 3.70941908859461040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2849999999999686 " "
y[1] (analytic) = 13.888832403280986 " "
y[1] (numeric) = 13.888832403281038 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 3.70904816523222800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2859999999999685 " "
y[1] (analytic) = 13.89022135596779 " "
y[1] (numeric) = 13.890221355967842 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 3.7086772789603280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2869999999999684 " "
y[1] (analytic) = 13.891610447556808 " "
y[1] (numeric) = 13.891610447556861 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 3.83617906528469050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2879999999999683 " "
y[1] (analytic) = 13.892999678061933 " "
y[1] (numeric) = 13.892999678061985 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 3.7079356176731370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2889999999999682 " "
y[1] (analytic) = 13.894389047497052 " "
y[1] (numeric) = 13.894389047497105 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 3.83541190619010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.289999999999968 " "
y[1] (analytic) = 13.895778555876062 " "
y[1] (numeric) = 13.895778555876117 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 3.96286266364843150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.290999999999968 " "
y[1] (analytic) = 13.89716820321286 " "
y[1] (numeric) = 13.897168203212914 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 3.8346449005119860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2919999999999678 " "
y[1] (analytic) = 13.898557989521336 " "
y[1] (numeric) = 13.898557989521393 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 4.08987888554082250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 743910157.3518739 " "
Order of pole = 21474836479989.125 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2929999999999677 " "
y[1] (analytic) = 13.899947914815396 " "
y[1] (numeric) = 13.899947914815451 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 3.9616739831603254000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2939999999999676 " "
y[1] (analytic) = 13.901337979108934 " "
y[1] (numeric) = 13.90133797910899 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 3.96127783556971870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2949999999999675 " "
y[1] (analytic) = 13.902728182415851 " "
y[1] (numeric) = 13.902728182415906 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 3.96088172759189060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2959999999999674 " "
y[1] (analytic) = 13.904118524750052 " "
y[1] (numeric) = 13.904118524750105 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 3.83272805731246450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2969999999999673 " "
y[1] (analytic) = 13.905509006125436 " "
y[1] (numeric) = 13.90550900612549 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 3.83234480366973500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2979999999999672 " "
y[1] (analytic) = 13.90689962655591 " "
y[1] (numeric) = 13.906899626555965 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 3.95969364129546800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 687194767359986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.298999999999967 " "
y[1] (analytic) = 13.908290386055382 " "
y[1] (numeric) = 13.908290386055437 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 3.9592976917291467000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.299999999999967 " "
y[1] (analytic) = 13.909681284637758 " "
y[1] (numeric) = 13.909681284637813 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 3.9589017817558030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3009999999999668 " "
y[1] (analytic) = 13.911072322316947 " "
y[1] (numeric) = 13.911072322317 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 3.8308121722949773000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3019999999999667 " "
y[1] (analytic) = 13.912463499106858 " "
y[1] (numeric) = 13.912463499106913 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 3.95811008057220970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3029999999999666 " "
y[1] (analytic) = 13.913854815021406 " "
y[1] (numeric) = 13.91385481502146 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 3.95771428935404230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3039999999999665 " "
y[1] (analytic) = 13.9152462700745 " "
y[1] (numeric) = 13.915246270074556 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 4.0849739744134390000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3049999999999664 " "
y[1] (analytic) = 13.916637864280057 " "
y[1] (numeric) = 13.916637864280114 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 4.08456549744018740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3059999999999663 " "
y[1] (analytic) = 13.918029597651993 " "
y[1] (numeric) = 13.918029597652051 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 4.2117869694786090000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3069999999999662 " "
y[1] (analytic) = 13.919421470204227 " "
y[1] (numeric) = 13.919421470204284 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 4.0837486660265626000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 36893488147419104. " "
Order of pole = 3689348814741885. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.307999999999966 " "
y[1] (analytic) = 13.920813481950674 " "
y[1] (numeric) = 13.920813481950733 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 4.21094469631483670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.308999999999966 " "
y[1] (analytic) = 13.922205632905255 " "
y[1] (numeric) = 13.922205632905316 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 4.33811524783556700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 768307106.7995597 " "
Order of pole = 34359738367989.5 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999659 " "
y[1] (analytic) = 13.923597923081896 " "
y[1] (numeric) = 13.923597923081955 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 4.2101025915888535000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3109999999999657 " "
y[1] (analytic) = 13.924990352494515 " "
y[1] (numeric) = 13.924990352494573 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 4.20968160237950530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3119999999999656 " "
y[1] (analytic) = 13.926382921157037 " "
y[1] (numeric) = 13.926382921157096 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 4.2092606552669737000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 687194767359986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3129999999999655 " "
y[1] (analytic) = 13.927775629083389 " "
y[1] (numeric) = 13.927775629083447 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 4.2088397502470487000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3139999999999654 " "
y[1] (analytic) = 13.929168476287495 " "
y[1] (numeric) = 13.929168476287556 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 4.3359467323856893000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 940980188.7064694 " "
Order of pole = 68719476735988. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3149999999999653 " "
y[1] (analytic) = 13.930561462783288 " "
y[1] (numeric) = 13.930561462783349 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 4.3355131593914620000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 343597383679986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3159999999999652 " "
y[1] (analytic) = 13.931954588584695 " "
y[1] (numeric) = 13.931954588584755 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 4.3350796297523660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.316999999999965 " "
y[1] (analytic) = 13.93334785370565 " "
y[1] (numeric) = 13.933347853705708 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 4.20715655100924070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.317999999999965 " "
y[1] (analytic) = 13.934741258160079 " "
y[1] (numeric) = 13.934741258160141 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 4.46168954465523500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3189999999999649 " "
y[1] (analytic) = 13.936134801961925 " "
y[1] (numeric) = 13.936134801961986 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 4.3337793009225173000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999648 " "
y[1] (analytic) = 13.937528485125117 " "
y[1] (numeric) = 13.93752848512518 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 4.46079729597414650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3209999999999646 " "
y[1] (analytic) = 13.938922307663596 " "
y[1] (numeric) = 13.938922307663658 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 4.4603512385477917000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 343597383679986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3219999999999645 " "
y[1] (analytic) = 13.940316269591296 " "
y[1] (numeric) = 13.940316269591358 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 4.459905225724950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3229999999999644 " "
y[1] (analytic) = 13.941710370922161 " "
y[1] (numeric) = 13.941710370922221 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 4.332046135858270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3239999999999643 " "
y[1] (analytic) = 13.943104611670128 " "
y[1] (numeric) = 13.94310461167019 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 4.45901333387196340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3249999999999642 " "
y[1] (analytic) = 13.94449899184914 " "
y[1] (numeric) = 13.944498991849205 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 4.5859550963995540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.325999999999964 " "
y[1] (analytic) = 13.945893511473146 " "
y[1] (numeric) = 13.945893511473209 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 4.45812162037951040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.326999999999964 " "
y[1] (analytic) = 13.947288170556085 " "
y[1] (numeric) = 13.947288170556147 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 4.45767583050733800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3279999999999639 " "
y[1] (analytic) = 13.948682969111905 " "
y[1] (numeric) = 13.94868296911197 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 4.5845795162179780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3289999999999638 " "
y[1] (analytic) = 13.950077907154556 " "
y[1] (numeric) = 13.95007790715462 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 4.5841210811884910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999637 " "
y[1] (analytic) = 13.951472984697986 " "
y[1] (numeric) = 13.95147298469805 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 4.5836626920002127000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3309999999999635 " "
y[1] (analytic) = 13.952868201756147 " "
y[1] (numeric) = 13.95286820175621 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 4.5832043486485630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used"
Radius of convergence = 1214800199.9904199 " "
Order of pole = 687194767359986. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3319999999999634 " "
y[1] (analytic) = 13.954263558342987 " "
y[1] (numeric) = 13.954263558343053 " "
absolute error = 6.57252030578092700000000000000E-14 " "
relative error = 4.7100445525492046000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3329999999999633 " "
y[1] (analytic) = 13.955659054472465 " "
y[1] (numeric) = 13.95565905447253 " "
absolute error = 6.57252030578092700000000000000E-14 " "
relative error = 4.7095735716433873000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used"
Radius of convergence = 73786976294838210. " "
Order of pole = 7378697629483795. " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = exp (0.1 * x + 0.2 ) ;"
Iterations = 334
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds
"Expected Time Remaining "= 0 Years 0 Days 1 Hours 17 Minutes 42 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 1 Hours 17 Minutes 27 Seconds
"Expected Total Time "= 0 Years 0 Days 1 Hours 20 Minutes 27 Seconds
"Time to Timeout " Unknown
Percent Done = 3.7222222222218124 "%"
(%o57) true
(%o57) diffeq.max