(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m,
n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new,
ratio, term], n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m
1, m - 2
array_y_higher
1, m
: m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1,
array_y_higher
1, m - 2
if omniabs(hdrc) > glob_small_float glob_small_float
glob_h
then (rcs : ------, ord_no :
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
-----------------------------------------------------,
hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found_sing : 1,
1, 2 1, 2
array_type_pole : 2, if glob_display_flag
1
then (if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1"))),
if (1 # found_sing) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > - 1.0 glob_smallish_float)
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found_sing : 1, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE for equation 1")),
if (1 # found_sing) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole > - 1.0
1, 1 1, 2
glob_smallish_float))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2,
1, 2 1, 2 1
found_sing : 1, if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))),
if 1 # found_sing then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m,
n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new,
ratio, term], n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m
1, m - 2
array_y_higher
1, m
: m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1,
array_y_higher
1, m - 2
if omniabs(hdrc) > glob_small_float glob_small_float
glob_h
then (rcs : ------, ord_no :
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
-----------------------------------------------------,
hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found_sing : 1,
1, 2 1, 2
array_type_pole : 2, if glob_display_flag
1
then (if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1"))),
if (1 # found_sing) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > - 1.0 glob_smallish_float)
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found_sing : 1, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE for equation 1")),
if (1 # found_sing) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole > - 1.0
1, 1 1, 2
glob_smallish_float))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2,
1, 2 1, 2 1
found_sing : 1, if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))),
if 1 # found_sing then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : array_const_0D2 array_x ,
1 1 1
array_tmp1
1
array_tmp3 : array_const_0D3 + array_tmp2 , array_tmp4 : -----------,
1 1 1 1 array_tmp3
1
array_tmp5 : array_tmp4 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
array_tmp2 : array_const_0D2 array_x , array_tmp3 : array_tmp2 ,
2 1 2 2 2
array_tmp1 - array_tmp4 array_tmp3
2 1 2
array_tmp4 : -------------------------------------,
2 array_tmp3
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
array_tmp1 - array_tmp4 array_tmp3
3 2 2
array_tmp4 : -------------------------------------,
3 array_tmp3
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
array_tmp1 - array_tmp4 array_tmp3
4 3 2
array_tmp4 : -------------------------------------,
4 array_tmp3
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
array_tmp1 - array_tmp4 array_tmp3
5 4 2
array_tmp4 : -------------------------------------,
5 array_tmp3
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
array_tmp1_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------,
kkk kkk - 1
- ats(kkk, array_tmp3, array_tmp4, 2)
array_tmp4 : -------------------------------------,
kkk array_tmp3
1
array_tmp5 : array_tmp4 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp5 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : array_const_0D2 array_x ,
1 1 1
array_tmp1
1
array_tmp3 : array_const_0D3 + array_tmp2 , array_tmp4 : -----------,
1 1 1 1 array_tmp3
1
array_tmp5 : array_tmp4 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
array_tmp2 : array_const_0D2 array_x , array_tmp3 : array_tmp2 ,
2 1 2 2 2
array_tmp1 - array_tmp4 array_tmp3
2 1 2
array_tmp4 : -------------------------------------,
2 array_tmp3
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
array_tmp1 - array_tmp4 array_tmp3
3 2 2
array_tmp4 : -------------------------------------,
3 array_tmp3
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
array_tmp1 - array_tmp4 array_tmp3
4 3 2
array_tmp4 : -------------------------------------,
4 array_tmp3
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
array_tmp1 - array_tmp4 array_tmp3
5 4 2
array_tmp4 : -------------------------------------,
5 array_tmp3
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
array_tmp1_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------,
kkk kkk - 1
- ats(kkk, array_tmp3, array_tmp4, 2)
array_tmp4 : -------------------------------------,
kkk array_tmp3
1
array_tmp5 : array_tmp4 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp5 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole_debug(typ, radius, order2) :=
(if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS,
"DBG Radius of convergence ", 4, radius, 4, " "),
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " "))
(%o27) display_pole_debug(typ, radius, order2) :=
(if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS,
"DBG Radius of convergence ", 4, radius, 4, " "),
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " "))
(%i28) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o28) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i29) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o29) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i30) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o30) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i31) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o31) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i32) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o32) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i33) log_revs(file, revs) := printf(file, revs)
(%o33) log_revs(file, revs) := printf(file, revs)
(%i34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i35) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o35) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i36) logstart(file) := printf(file, "")
(%o36) logstart(file) := printf(file, "
")
(%i37) logend(file) := printf(file, "
~%")
(%o37) logend(file) := printf(file, "~%")
(%i38) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o38) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i40) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o40) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i41) factorial_2(nnn) := nnn!
(%o41) factorial_2(nnn) := nnn!
(%i42) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o42) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i43) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o43) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i44) convfp(mmm) := mmm
(%o44) convfp(mmm) := mmm
(%i45) convfloat(mmm) := mmm
(%o45) convfloat(mmm) := mmm
(%i46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i47) Si(x) := 0.0
(%o47) Si(x) := 0.0
(%i48) Ci(x) := 0.0
(%o48) Ci(x) := 0.0
(%i49) ln(x) := log(x)
(%o49) ln(x) := log(x)
(%i50) arcsin(x) := asin(x)
(%o50) arcsin(x) := asin(x)
(%i51) arccos(x) := acos(x)
(%o51) arccos(x) := acos(x)
(%i52) arctan(x) := atan(x)
(%o52) arctan(x) := atan(x)
(%i53) omniabs(x) := abs(x)
(%o53) omniabs(x) := abs(x)
(%i54) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o54) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i55) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%o55) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%i56) exact_soln_y(x) := block(.3536860083385145 Si(1.5 + x)
- 4.987474933020272 Ci(1.5 + x))
(%o56) exact_soln_y(x) := block(.3536860083385145 Si(1.5 + x)
- 4.987474933020272 Ci(1.5 + x))
(%i57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms,
opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer,
best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-201, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\
########temp/div_sin_linpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x) / (0.2 * x + 0.3);"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.0,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "glob_display_interval:0.1,"),
omniout_str(ALWAYS, "glob_max_minutes: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, " (0.3\
5368600833851455044094925717134 * Si(x + 1.5000000000000000000000000000000) \
- 4.9874749330202721547086168557074 * Ci(x + 1.50000000000000000000000000000\
00)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS,
"/* END USER DEF BLOCK */"), omniout_str(ALWAYS,
"#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0,
glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200,
glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100,
glob_almost_1 : 0.99, Digits : 32, max_terms : 30, glob_max_terms : max_terms,
glob_html_log : true, array(array_y_init, 1 + max_terms),
array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 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_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_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_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_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_const_0D3, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term),
term
array_const_0D3 : 0.3, 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 : 0.0,
iiif, jjjf
x_end : 5.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1,
glob_max_minutes : 10, glob_desired_digits_correct : 10,
glob_display_interval : 0.001, glob_look_poles : true,
glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, if glob_max_h < glob_h
then glob_h : glob_max_h, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0,
omniout_str(DEBUGL, " "), glob_reached_optimal_h : true,
glob_optimal_clock_start_sec : elapsed_time_seconds(),
while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = sin(x) / (0.2 * x + 0.3);"),
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,
"2013-01-28T13:43:05-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "div_sin_lin"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x) / (0.2 * x + 0.3);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 165 | "), logitem_str(html_log_file, "div_sin_lin diffeq.max"),
logitem_str(html_log_file,
"div_sin_lin maxima results"),
logitem_str(html_log_file, "All Tests - All Languages"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%o57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms,
opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer,
best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-201, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\
########temp/div_sin_linpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x) / (0.2 * x + 0.3);"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.0,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "glob_display_interval:0.1,"),
omniout_str(ALWAYS, "glob_max_minutes: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, " (0.3\
5368600833851455044094925717134 * Si(x + 1.5000000000000000000000000000000) \
- 4.9874749330202721547086168557074 * Ci(x + 1.50000000000000000000000000000\
00)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS,
"/* END USER DEF BLOCK */"), omniout_str(ALWAYS,
"#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0,
glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200,
glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100,
glob_almost_1 : 0.99, Digits : 32, max_terms : 30, glob_max_terms : max_terms,
glob_html_log : true, array(array_y_init, 1 + max_terms),
array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 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_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_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_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_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_const_0D3, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term),
term
array_const_0D3 : 0.3, 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 : 0.0,
iiif, jjjf
x_end : 5.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1,
glob_max_minutes : 10, glob_desired_digits_correct : 10,
glob_display_interval : 0.001, glob_look_poles : true,
glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, if glob_max_h < glob_h
then glob_h : glob_max_h, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0,
omniout_str(DEBUGL, " "), glob_reached_optimal_h : true,
glob_optimal_clock_start_sec : elapsed_time_seconds(),
while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = sin(x) / (0.2 * x + 0.3);"),
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,
"2013-01-28T13:43:05-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "div_sin_lin"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x) / (0.2 * x + 0.3);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 165 | "), logitem_str(html_log_file, "div_sin_lin diffeq.max"),
logitem_str(html_log_file,
"div_sin_lin maxima results"),
logitem_str(html_log_file, "All Tests - All Languages"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i58) main()
"##############ECHO OF PROBLEM#################"
"##############temp/div_sin_linpostode.ode#################"
"diff ( y , x , 1 ) = sin(x) / (0.2 * x + 0.3);"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.0,"
"x_end:5.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"glob_display_interval:0.1,"
"glob_max_minutes: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("
" (0.35368600833851455044094925717134 * Si(x + 1.5000000000000000000000000000000) - 4.9874749330202721547086168557074 * Ci(x + 1.5000000000000000000000000000000)) "
"));"
"/* 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 = 5. ""
estimated_steps = 5000. ""
step_error = 2.00000000000000E-14 ""
est_needed_step_err = 2.00000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 4.758343790157882300000000000000000000000000000000000000000000000000000000000000000000000000000000000E-84 ""
max_value3 = 4.758343790157882300000000000000000000000000000000000000000000000000000000000000000000000000000000000E-84 ""
value3 = 4.758343790157882300000000000000000000000000000000000000000000000000000000000000000000000000000000000E-84 ""
best_h = 1.000E-3 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.0 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.0 " "
absolute error = 0.0 " "
relative error = -1. "%"
Correct digits = -1
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.000E-3 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.6659261572840195000000E-6 " "
absolute error = 1.6659261572840195000000E-6 " "
relative error = -1. "%"
Correct digits = -1
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.000E-3 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.660744440498500000000E-6 " "
absolute error = 6.660744440498500000000E-6 " "
relative error = -1. "%"
Correct digits = -1
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.000E-3 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.49800187200532700000E-5 " "
absolute error = 1.49800187200532700000E-5 " "
relative error = -1. "%"
Correct digits = -1
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.000E-3 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.66193183923979600000E-5 " "
absolute error = 2.66193183923979600000E-5 " "
relative error = -1. "%"
Correct digits = -1
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.000E-3 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.15742183653382600000E-5 " "
absolute error = 4.15742183653382600000E-5 " "
relative error = -1. "%"
Correct digits = -1
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.000E-3 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.9840299043404300000E-5 " "
absolute error = 5.9840299043404300000E-5 " "
relative error = -1. "%"
Correct digits = -1
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 6.35788009792476800E-2 " "
Order of pole = 1.051247977557068200000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.2715760195849530000E-3 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.78421999040920200000E-5 " "
absolute error = 8.78421999040920200000E-5 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.6805806723393175 " "
Order of pole = 2.19131379708414900000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.543152039169909000E-3 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.21181767817468980000E-4 " "
absolute error = 1.21181767817468980000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.178940048962386000E-3 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.39850348711147270000E-4 " "
absolute error = 1.39850348711147270000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.045051606854734100E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.81179455726958320000E-4 " "
absolute error = 1.81179455726958320000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.108630407833981900E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.03837725047723880000E-4 " "
absolute error = 2.03837725047723880000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.235788009792477400E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.53136059935827700000E-4 " "
absolute error = 2.53136059935827700000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.36294561175097300E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.0773595292394510000E-4 " "
absolute error = 3.0773595292394510000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.426524412730220700E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.37021173164123330000E-4 " "
absolute error = 3.37021173164123330000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.21926354247713462 " "
Order of pole = 8.9528384705772620000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.553682014688716200E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.99556547720287540000E-4 " "
absolute error = 3.99556547720287540000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.61726081566796400E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.32804459291126700000E-4 " "
absolute error = 4.32804459291126700000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.744418417626459300E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.0325513069149840000E-4 " "
absolute error = 5.0325513069149840000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.807997218605707200E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.4045565299861050000E-4 " "
absolute error = 5.4045565299861050000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.935154820564202700E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.1880148352400470000E-4 " "
absolute error = 6.1880148352400470000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.288181346227988 " "
Order of pole = 3.06208391975815200000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.062312422522698300E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.0239958895010170000E-4 " "
absolute error = 7.0239958895010170000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.12589122350194610E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.4616545811747050000E-4 " "
absolute error = 7.4616545811747050000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.253048825460441400E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.376252636207630000E-4 " "
absolute error = 8.376252636207630000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.316627626439689300E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.8531697623440790000E-4 " "
absolute error = 8.8531697623440790000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.443785228398184800E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.8461846829729640000E-4 " "
absolute error = 9.8461846829729640000E-4 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 2.584581769186603 " "
Order of pole = 3.33955085807247100000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.507364029377432400E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.0362260291521379000E-3 " "
absolute error = 1.0362260291521379000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.2674312635786453 " "
Order of pole = 2.244782137950096500000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.63452163133592800E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.1433492404080267000E-3 " "
absolute error = 1.1433492404080267000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.761679233294423400E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.255675860831301000E-3 " "
absolute error = 1.255675860831301000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.825258034273671000E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.3137876863211975000E-3 " "
absolute error = 1.3137876863211975000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.95241563623216700E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.4339028489291533000E-3 " "
absolute error = 1.4339028489291533000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.015994437211414500E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.4959039810031155000E-3 " "
absolute error = 1.4959039810031155000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1431520391699100E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.623787840382209000E-3 " "
absolute error = 1.623787840382209000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.20673084014915800E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.689668367678579000E-3 " "
absolute error = 1.689668367678579000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.9592626335222432 " "
Order of pole = 5.513278722446557000000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.333888442107653000E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.8253011237333985000E-3 " "
absolute error = 1.8253011237333985000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.4440691219979493 " "
Order of pole = 1.259436999134777600000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.46104604406614900E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.9660888331304174000E-3 " "
absolute error = 1.9660888331304174000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.52462484504539650E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.038413055223229000E-3 " "
absolute error = 2.038413055223229000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.65178244700389230E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.1869167612372425000E-3 " "
absolute error = 2.1869167612372425000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6683905398750578 " "
Order of pole = 3.29816174371444500000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7153612479831400E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.263094058456226200E-3 " "
absolute error = 2.263094058456226200E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.842518849941635000E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.419294080750997000E-3 " "
absolute error = 2.419294080750997000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.90609765092088330E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.4993146240696057000E-3 " "
absolute error = 2.4993146240696057000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.03325525287937860E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.663191326814371000E-3 " "
absolute error = 2.663191326814371000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.16041285483787440E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.8321749296101284000E-3 " "
absolute error = 2.8321749296101284000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.22399165581712200E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.9185791010554235000E-3 " "
absolute error = 2.9185791010554235000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.351149257775617000E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.095206756225656000E-3 " "
absolute error = 3.095206756225656000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.41472805875486540E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.1854280712621025000E-3 " "
absolute error = 3.1854280712621025000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.54188566071336060E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.3696802605945164000E-3 " "
absolute error = 3.3696802605945164000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.605464461692609000E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.4637089710589253000E-3 " "
absolute error = 3.4637089710589253000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.73262206365110400E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.655566220053719000E-3 " "
absolute error = 3.655566220053719000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859779665609599300E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.8524827111468630000E-3 " "
absolute error = 3.8524827111468630000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.92335846658884750E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.952835477242756000E-3 " "
absolute error = 3.952835477242756000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.05051606854734300E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.157324667059802000E-3 " "
absolute error = 4.157324667059802000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.114094869526591000E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.261458939785977600E-3 " "
absolute error = 4.261458939785977600E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.24125247148508600E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.473501469356632000E-3 " "
absolute error = 4.473501469356632000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 9.453265509414848 " "
Order of pole = 1.0271943295947494000000000E-9 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.30483127246433400E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.581407579977082000E-3 " "
absolute error = 4.581407579977082000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1425904795424566 " "
Order of pole = 2.373923280174494700000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.431988874422830000E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.800984133269695000E-3 " "
absolute error = 4.800984133269695000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 2.9502978071171775 " "
Order of pole = 7.46247508232045200000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.55914647638132500E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.0255726590250840000E-3 " "
absolute error = 5.0255726590250840000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.622725277360573000E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.139743738179462000E-3 " "
absolute error = 5.139743738179462000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.6265576381060085 " "
Order of pole = 6.934897101018578000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.74988287931906800E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.371834189126178000E-3 " "
absolute error = 5.371834189126178000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.81346168029831600E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.489751427304558000E-3 " "
absolute error = 5.489751427304558000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.940619282256812000E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.729324600901853000E-3 " "
absolute error = 5.729324600901853000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.00419808323605900E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.850978407393845000E-3 " "
absolute error = 5.850978407393845000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.13135568519455500E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.098015143284395000E-3 " "
absolute error = 6.098015143284395000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.2585132871530500E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.35001696346697000E-3 " "
absolute error = 6.35001696346697000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.32209208813229700E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.477877128227642000E-3 " "
absolute error = 6.477877128227642000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.44924969009079100E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.7373106699653360000E-3 " "
absolute error = 6.7373106699653360000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5732818375567281 " "
Order of pole = 1.23421273201529400000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.51282849107003800E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.868881930404442000E-3 " "
absolute error = 6.868881930404442000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 2.533683163227741 " "
Order of pole = 9.54347711967784600000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.63998609302853300E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.135728144841232000E-3 " "
absolute error = 7.135728144841232000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.7035648940077800E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.271000986906138000E-3 " "
absolute error = 7.271000986906138000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.83072249596627400E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.545240866632342000E-3 " "
absolute error = 7.545240866632342000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.95788009792476800E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.824399317257128000E-3 " "
absolute error = 7.824399317257128000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.02145889890401500E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.965820375798339000E-3 " "
absolute error = 7.965820375798339000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 2.0526168736901997 " "
Order of pole = 3.018740812876785600000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.14861650086250900E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.25234090426235000E-3 " "
absolute error = 8.25234090426235000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.21219530184175600E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.397438274425609000E-3 " "
absolute error = 8.397438274425609000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.3393529038002500E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.691301982878566000E-3 " "
absolute error = 8.691301982878566000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.40293170477949700E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.840066225933924000E-3 " "
absolute error = 8.840066225933924000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.53008930673799100E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.141254257252447000E-3 " "
absolute error = 9.141254257252447000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 2.053282360032254 " "
Order of pole = 8.29043500516490900000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.65724690869648600E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.447314714326247000E-3 " "
absolute error = 9.447314714326247000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.72082570967573300E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.602169492379418000E-3 " "
absolute error = 9.602169492379418000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.84798331163422700E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.915522933759866000E-3 " "
absolute error = 9.915522933759866000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.91156211261347400E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.007401951381543700E-2 " "
absolute error = 1.007401951381543700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.03871971457196800E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.0394647190043099E-2 " "
absolute error = 1.0394647190043099E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.9542278696046742 " "
Order of pole = 2.27728946811112100000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.10229851555121500E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.055677620739065800E-2 " "
absolute error = 1.055677620739065800E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.22945611750970900E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.088465940903075900E-2 " "
absolute error = 1.088465940903075900E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.35661371946820300E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.121736925316189600E-2 " "
absolute error = 1.121736925316189600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.4201925204474500E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.138553157637878500E-2 " "
absolute error = 1.138553157637878500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.54735012240594400E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.172546585196303200E-2 " "
absolute error = 1.172546585196303200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.61092892338519200E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.189723573726290700E-2 " "
absolute error = 1.189723573726290700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.73808652534368600E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.224437584067918600E-2 " "
absolute error = 1.224437584067918600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 9.29516181835589 " "
Order of pole = 4.7465142927194390000000000E-10 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.80166532632293300E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.241974399609911400E-2 " "
absolute error = 1.241974399609911400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.92882292828142700E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.277407136306547600E-2 " "
absolute error = 1.277407136306547600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 8.335433435648362 " "
Order of pole = 7.7785067276181510000000000E-10 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.05598053023992100E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.313317994491860800E-2 " "
absolute error = 1.313317994491860800E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.11955933121916800E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.331452462165549400E-2 " "
absolute error = 1.331452462165549400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.4550543139271082 " "
Order of pole = 3.25464100114913900000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.24671693317766200E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.368078961350955300E-2 " "
absolute error = 1.368078961350955300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.31029573415690900E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.386570787748661300E-2 " "
absolute error = 1.386570787748661300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.43745333611540300E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.42391108190671500E-2 " "
absolute error = 1.42391108190671500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.5010321370946500E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.442759344982715300E-2 " "
absolute error = 1.442759344982715300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.62818973905314500E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.480811591952960000E-2 " "
absolute error = 1.480811591952960000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.75534734101163900E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.519337452610340400E-2 " "
absolute error = 1.519337452610340400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.81892614199088600E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.538777733061518500E-2 " "
absolute error = 1.538777733061518500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.9460837439493800E-2 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.578012484808206700E-2 " "
absolute error = 1.578012484808206700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10009662544928627 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.597806752555412700E-2 " "
absolute error = 1.597806752555412700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10136820146887121 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.637748563455366800E-2 " "
absolute error = 1.637748563455366800E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10200398947866368 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.65789590348221600E-2 " "
absolute error = 1.65789590348221600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.2021823966066216 " "
Order of pole = 1.698374774150579500000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10327556549824862 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.69854294540104780E-2 " "
absolute error = 1.69854294540104780E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10454714151783356 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.73965912757166200E-2 " "
absolute error = 1.73965912757166200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10518292952762603 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.760392893175013500E-2 " "
absolute error = 1.760392893175013500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 7.893477591970908 " "
Order of pole = 6.835403354443770000000000E-10 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10645450554721098 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.802211267874365000E-2 " "
absolute error = 1.802211267874365000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10709029355700345 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.82329567496138100E-2 " "
absolute error = 1.82329567496138100E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10836186957658839 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.865814424107338500E-2 " "
absolute error = 1.865814424107338500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 7.62022512488552 " "
Order of pole = 3.0015989693765730000000000E-10 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10963344559617333 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.908799081351969000E-2 " "
absolute error = 1.908799081351969000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1102692336059658 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.930465873820907400E-2 " "
absolute error = 1.930465873820907400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11154080962555074 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.974147883673152700E-2 " "
absolute error = 1.974147883673152700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 3.1987687234338287 " "
Order of pole = 4.73896477615198800000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11217659763534321 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.996162900150763600E-2 " "
absolute error = 1.996162900150763600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11344817365492815 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.04054045445810380E-2 " "
absolute error = 2.04054045445810380E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.037550242301034 " "
Order of pole = 3.808509063674137000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11408396166472062 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.062902791792404800E-2 " "
absolute error = 2.062902791792404800E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11535553768430556 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.107974086094736600E-2 " "
absolute error = 2.107974086094736600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1166271137038905 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.15350687306501700E-2 " "
absolute error = 2.15350687306501700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11726290171368298 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.176446076488532400E-2 " "
absolute error = 2.176446076488532400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 3.068479347353561 " "
Order of pole = 7.75344233261421300000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11853447773326792 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.22266960417998100E-2 " "
absolute error = 2.22266960417998100E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11917026574306039 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.24595372903741820E-2 " "
absolute error = 2.24595372903741820E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12044184176264533 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.29286620275434400E-2 " "
absolute error = 2.29286620275434400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1210776297724378 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.316494352606802700E-2 " "
absolute error = 2.316494352606802700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12234920579202274 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.364093981284716700E-2 " "
absolute error = 2.364093981284716700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12362078181160768 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.412150720019867700E-2 " "
absolute error = 2.412150720019867700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12425656982140015 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.436350257693951000E-2 " "
absolute error = 2.436350257693951000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1255281458409851 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.485091174307331700E-2 " "
absolute error = 2.485091174307331700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12616393385077757 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.509632355306607400E-2 " "
absolute error = 2.509632355306607400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1274355098703625 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.559055668336829300E-2 " "
absolute error = 2.559055668336829300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12807129788015498 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.583937602824578600E-2 " "
absolute error = 2.583937602824578600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12934287389973992 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.634041534381680000E-2 " "
absolute error = 2.634041534381680000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13061444991932486 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.684598225663116000E-2 " "
absolute error = 2.684598225663116000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13125023792911733 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.71004611005226100E-2 " "
absolute error = 2.71004611005226100E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13252181394870227 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.761280464603575000E-2 " "
absolute error = 2.761280464603575000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13315760195849474 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.78706673827205300E-2 " "
absolute error = 2.78706673827205300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13442917797807968 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.838976987648859600E-2 " "
absolute error = 2.838976987648859600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13506496598787215 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.865100767253835300E-2 " "
absolute error = 2.865100767253835300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1363365420074571 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.917685146524802000E-2 " "
absolute error = 2.917685146524802000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13760811802704204 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.97071796693554200E-2 " "
absolute error = 2.97071796693554200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1382439060368345 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.99740229820720300E-2 " "
absolute error = 2.99740229820720300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13951548205641945 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.051106314724118000E-2 " "
absolute error = 3.051106314724118000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14015127006621192 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.07812580489843400E-2 " "
absolute error = 3.07812580489843400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14142284608579686 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.132499261881939000E-2 " "
absolute error = 3.132499261881939000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14205863409558933 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.159853034004194700E-2 " "
absolute error = 3.159853034004194700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14333021011517427 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.21489417927074860E-2 " "
absolute error = 3.21489417927074860E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1446017861347592 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.270379478323786600E-2 " "
absolute error = 3.270379478323786600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14523757414455168 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.29828844291720500E-2 " "
absolute error = 3.29828844291720500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14650915016413663 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.35443851758593600E-2 " "
absolute error = 3.35443851758593600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.4080401607274193 " "
Order of pole = 5.34683408659475400000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1471449381739291 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.38267943399003500E-2 " "
absolute error = 3.38267943399003500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14841651419351404 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.43949254123242950E-2 " "
absolute error = 3.43949254123242950E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1490523022033065 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.468064538777329600E-2 " "
absolute error = 3.468064538777329600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15032387822289145 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.52553893895172550E-2 " "
absolute error = 3.52553893895172550E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1515954542424764 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.58345323628562200E-2 " "
absolute error = 3.58345323628562200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15223124225226886 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.61257510551413250E-2 " "
absolute error = 3.61257510551413250E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1535028182718538 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.67114780389305500E-2 " "
absolute error = 3.67114780389305500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15413860628164627 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.7005984407494896E-2 " "
absolute error = 3.7005984407494896E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15541018230123121 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.7598278095265600E-2 " "
absolute error = 3.7598278095265600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 6.037368594855464 " "
Order of pole = 1.85572446298465370000000000E-10 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15604597031102369 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.78960634952499540E-2 " "
absolute error = 3.78960634952499540E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.1573146594041546 " "
Order of pole = 3.1814550993658486000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15731754633060863 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.849490661399327400E-2 " "
absolute error = 3.849490661399327400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15858912235019357 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.90981064403928900E-2 " "
absolute error = 3.90981064403928900E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15922491035998604 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.940133772725265500E-2 " "
absolute error = 3.940133772725265500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.3166904637823977 " "
Order of pole = 1.726796483580983500000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16049648637957098 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.00110582702357550E-2 " "
absolute error = 4.00110582702357550E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16113227438936345 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.031754561697203000E-2 " "
absolute error = 4.031754561697203000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1624038504089484 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.09337696920444600E-2 " "
absolute error = 4.09337696920444600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16303963841874086 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.12435045146523070E-2 " "
absolute error = 4.12435045146523070E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1643112144383258 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.186621497024871600E-2 " "
absolute error = 4.186621497024871600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5029395772786995 " "
Order of pole = 1.756994549850787700000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16558279045791074 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.24932401670768600E-2 " "
absolute error = 4.24932401670768600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16621857846770322 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.28083684184929700E-2 " "
absolute error = 4.28083684184929700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16749015448728816 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.34418514826907300E-2 " "
absolute error = 4.34418514826907300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16812594249708063 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.37602043994234900E-2 " "
absolute error = 4.37602043994234900E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16939751851666557 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.44001282665404400E-2 " "
absolute error = 4.44001282665404400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17003330652645804 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.47216973244768400E-2 " "
absolute error = 4.47216973244768400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17130488254604298 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.536804496247253700E-2 " "
absolute error = 4.536804496247253700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17257645856562792 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.60186656680845200E-2 " "
absolute error = 4.60186656680845200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1732122465754204 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.634557606277426300E-2 " "
absolute error = 4.634557606277426300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17448382259500533 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.70025922241749600E-2 " "
absolute error = 4.70025922241749600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1751196106047978 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.73326961079656100E-2 " "
absolute error = 4.73326961079656100E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17639118662438275 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.79960907788621900E-2 " "
absolute error = 4.79960907788621900E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17702697463417522 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.832937968659261600E-2 " "
absolute error = 4.832937968659261600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17829855065376016 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.899913595259547400E-2 " "
absolute error = 4.899913595259547400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.522712955872086 " "
Order of pole = 1.412203687323199000000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1795701266733451 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.96731239008124400E-2 " "
absolute error = 4.96731239008124400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5142712088309724 " "
Order of pole = 1.620037437533028400000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18020591468313757 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.0011702413508700E-2 " "
absolute error = 5.0011702413508700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.4385972203457934 " "
Order of pole = 2.93542967710891400000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1814774907027225 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.06920238367092700E-2 " "
absolute error = 5.06920238367092700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18211327871251498 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.10337648772171600E-2 " "
absolute error = 5.10337648772171600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18338485473209992 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.1720402945423700E-2 " "
absolute error = 5.1720402945423700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1840206427418924 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.20652981066157300E-2 " "
absolute error = 5.20652981066157300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18529221876147733 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.275823602125882000E-2 " "
absolute error = 5.275823602125882000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.2663738334263608 " "
Order of pole = 1.50350842886837200000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18656379478106228 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.34553645164376600E-2 " "
absolute error = 5.34553645164376600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18719958279085475 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.38054979054636300E-2 " "
absolute error = 5.38054979054636300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1884711588104397 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.45088983188983900E-2 " "
absolute error = 5.45088983188983900E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18910694682023216 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.486216348603468000E-2 " "
absolute error = 5.486216348603468000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 3.594480695790272 " "
Order of pole = 1.08574482737822110000000000E-10 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1903785228398171 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.55718191022631100E-2 " "
absolute error = 5.55718191022631100E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19101431084960957 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.59282076975188100E-2 " "
absolute error = 5.59282076975188100E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1922858868691945 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.664410183200328000E-2 " "
absolute error = 5.664410183200328000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19355746288877945 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.7364145724683400E-2 " "
absolute error = 5.7364145724683400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.3857475004927646 " "
Order of pole = 1.192290710605448100000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19419325089857192 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.77257215198147200E-2 " "
absolute error = 5.77257215198147200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19546482691815686 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.845197619155691000E-2 " "
absolute error = 5.845197619155691000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19610061492794933 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.88166532234238200E-2 " "
absolute error = 5.88166532234238200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19737219094753428 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.95491020715229600E-2 " "
absolute error = 5.95491020715229600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 7.332114231468750 " "
Order of pole = 2.62877719592324870000000000E-10 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19800797895732675 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.99168720463948100E-2 " "
absolute error = 5.99168720463948100E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1992795549769117 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.065549849859796000E-2 " "
absolute error = 6.065549849859796000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.098867992981662 " "
Order of pole = 2.24158469563917600000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20055113099649663 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.139823416171054000E-2 " "
absolute error = 6.139823416171054000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2011869190062891 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.17711406523177700E-2 " "
absolute error = 6.17711406523177700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20245849502587404 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.25200263664397800E-2 " "
absolute error = 6.25200263664397800E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2030942830356665 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.28960037575483100E-2 " "
absolute error = 6.28960037575483100E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20436585905525145 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.36510230310140600E-2 " "
absolute error = 6.36510230310140600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20500164706504392 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.40300630842973300E-2 " "
absolute error = 6.40300630842973300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20627322308462887 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.47911994554317600E-2 " "
absolute error = 6.47911994554317600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2075447991042138 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.55564047610575500E-2 " "
absolute error = 6.55564047610575500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20818058711400628 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.59405309845219500E-2 " "
absolute error = 6.59405309845219500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 2.0206043587122586 " "
Order of pole = 5.11466424768514100000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20945216313359122 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.67118260180004300E-2 " "
absolute error = 6.67118260180004300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.2518370663542261 " "
Order of pole = 1.7461587731304462000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2100879511433837 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.70989930077594800E-2 " "
absolute error = 6.70989930077594800E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21135952716296863 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.78763613867862100E-2 " "
absolute error = 6.78763613867862100E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 3.0370073144350282 " "
Order of pole = 2.975042434627539500000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21263110318255357 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.8657769576157300E-2 " "
absolute error = 6.8657769576157300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21326689119234604 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.90499863308911200E-2 " "
absolute error = 6.90499863308911200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21453846721193098 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.9837440627553390E-2 " "
absolute error = 6.9837440627553390E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 2.0441291426611246 " "
Order of pole = 3.657163460957235700000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21517425522172345 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.02326763579493800E-2 " "
absolute error = 7.02326763579493800E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.880700491026239 " "
Order of pole = 2.44035902596806400000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2164458312413084 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.10261604581017800E-2 " "
absolute error = 7.10261604581017800E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21708161925110087 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.14244070195722100E-2 " "
absolute error = 7.14244070195722100E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2183531952706858 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.22239046486318800E-2 " "
absolute error = 7.22239046486318800E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 3.0061258824730053 " "
Order of pole = 2.860645054170163300000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21962477129027075 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.30274022699028700E-2 " "
absolute error = 7.30274022699028700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22026055930006322 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.34306488236513600E-2 " "
absolute error = 7.34306488236513600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 5.946221713804997 " "
Order of pole = 3.61437102469608360000000000E-10 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22153213531964816 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.42401329141307600E-2 " "
absolute error = 7.42401329141307600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22216792332944063 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.46463686511683700E-2 " "
absolute error = 7.46463686511683700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22343949934902557 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.54618230136079200E-2 " "
absolute error = 7.54618230136079200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22407528735881804 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.58710398425148800E-2 " "
absolute error = 7.58710398425148800E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22534686337840298 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.66924483084512600E-2 " "
absolute error = 7.66924483084512600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7841949327930704 " "
Order of pole = 8.117950756059145000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22661843939798793 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.75178172084012700E-2 " "
absolute error = 7.75178172084012700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.9322342865433204 " "
Order of pole = 2.114752817305998200000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2272542274077804 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.79319845818094400E-2 " "
absolute error = 7.79319845818094400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22852580342736534 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.87632807014680100E-2 " "
absolute error = 7.87632807014680100E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2291615914371578 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.91804076596892700E-2 " "
absolute error = 7.91804076596892700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23043316745674275 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.0017614906785710E-2 " "
absolute error = 8.0017614906785710E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23106895546653522 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.04376934107830200E-2 " "
absolute error = 8.04376934107830200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23234053148612016 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.1280795721408200E-2 " "
absolute error = 8.1280795721408200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2336121075057051 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.21278191639461600E-2 " "
absolute error = 8.21278191639461600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23424789551549757 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.25527990847895400E-2 " "
absolute error = 8.25527990847895400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23551947153508251 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.34056908803915700E-2 " "
absolute error = 8.34056908803915700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23615525954487498 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.3833600978614200E-2 " "
absolute error = 8.3833600978614200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23742683556445993 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.46923451384479300E-2 " "
absolute error = 8.46923451384479300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2380626235742524 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.51231774266283600E-2 " "
absolute error = 8.51231774266283600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.617219833135012 " "
Order of pole = 2.6858515411731787000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23933419959383734 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.59877579898094200E-2 " "
absolute error = 8.59877579898094200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 7.68942982320332 " "
Order of pole = 6.0557958647677880000000000E-10 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24060577561342228 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.68562206351485300E-2 " "
absolute error = 8.68562206351485300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 3.4799723500484805 " "
Order of pole = 8.28475066327882800000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24124156362321475 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.7291905527953200E-2 " "
absolute error = 8.7291905527953200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2425131396427997 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.81661780369706800E-2 " "
absolute error = 8.81661780369706800E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.9846983190018055 " "
Order of pole = 5.238831590759219000000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24314892765259216 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.86047638879734900E-2 " "
absolute error = 8.86047638879734900E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2444205036721771 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.94848303737713200E-2 " "
absolute error = 8.94848303737713200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24505629168196957 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.99263092464167700E-2 " "
absolute error = 8.99263092464167700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24632786770155451 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.08121538496407500E-2 " "
absolute error = 9.08121538496407500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24759944372113946 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.17018417339491400E-2 " "
absolute error = 9.17018417339491400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24823523173093193 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.2148124709849100E-2 " "
absolute error = 9.2148124709849100E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24950680775051687 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.30435643402402600E-2 " "
absolute error = 9.30435643402402600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25014259576030934 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.34927192406842300E-2 " "
absolute error = 9.34927192406842300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2514141717798943 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.43938948307248400E-2 " "
absolute error = 9.43938948307248400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25204995978968675 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.48459137692907500E-2 " "
absolute error = 9.48459137692907500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2533215358092717 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.57528095596962500E-2 " "
absolute error = 9.57528095596962500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25459311182885663 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.66635100752123600E-2 " "
absolute error = 9.66635100752123600E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2552288998386491 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.71202849220383700E-2 " "
absolute error = 9.71202849220383700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25650047585823404 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.80366794324878400E-2 " "
absolute error = 9.80366794324878400E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 3.8417858956686928 " "
Order of pole = 1.19575460644227860000000000E-10 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2571362638680265 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.84962973530671700E-2 " "
absolute error = 9.84962973530671700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25840783988761146 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.94183701710451300E-2 " "
absolute error = 9.94183701710451300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2590436278974039 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.98808233283732800E-2 " "
absolute error = 9.98808233283732800E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 7.3466322217802835 " "
Order of pole = 2.66144439819981900000000000E-10 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.26031520391698887 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.10080855879323772 " "
absolute error = 0.10080855879323772 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2615867799365738 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.10174006066883902 " "
absolute error = 0.10174006066883902 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2622225679463663 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.10220722184143362 " "
absolute error = 0.10220722184143362 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2634941439659512 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.10314436032204288 " "
absolute error = 0.10314436032204288 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2641299319757437 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.10361433589786062 " "
absolute error = 0.10361433589786062 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.26540150799532863 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.10455709539369798 " "
absolute error = 0.10455709539369798 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2660372960051211 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.10502987758445241 " "
absolute error = 0.10502987758445241 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.26730887202470605 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.10597824253212369 " "
absolute error = 0.10597824253212369 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.268580448044291 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.10693033581433817 " "
absolute error = 0.10693033581433817 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.26921623605408346 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.10740777842509107 " "
absolute error = 0.10740777842509107 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2704878120736684 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.10836545127850883 " "
absolute error = 0.10836545127850883 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27112360008346087 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.10884567979967158 " "
absolute error = 0.10884567979967158 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.2601475501552546 " "
Order of pole = 2.081357308725273500000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2723951761030458 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.10980891673076626 " "
absolute error = 0.10980891673076626 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2730309641128383 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.11029192342208685 " "
absolute error = 0.11029192342208685 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.3344344651225585 " "
Order of pole = 3.4372504842394846000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2743025401324232 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1112607089633491 " "
absolute error = 0.1112607089633491 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27557411615200816 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.11223318499779869 " "
absolute error = 0.11223318499779869 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27620990416180063 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.11272080480739761 " "
absolute error = 0.11272080480739761 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2774814801813856 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.11369880373037934 " "
absolute error = 0.11369880373037934 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27811726819117805 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1141891811328059 " "
absolute error = 0.1141891811328059 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.279388844210763 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.11517268754570648 " "
absolute error = 0.11517268754570648 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28002463222055546 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.11566581484807499 " "
absolute error = 0.11566581484807499 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2812962082401404 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.11665481337793787 " "
absolute error = 0.11665481337793787 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28256778425972534 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.11764746479120375 " "
absolute error = 0.11764746479120375 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2832035722695178 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.11814515819959541 " "
absolute error = 0.11814515819959541 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28447514828910275 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1191432761649818 " "
absolute error = 0.1191432761649818 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2851109362988952 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.11964369902142061 " "
absolute error = 0.11964369902142061 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28638251231848016 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.12064726823391733 " "
absolute error = 0.12064726823391733 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28701830032827264 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.12115041289223097 " "
absolute error = 0.12115041289223097 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2882898763478576 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.12215941807213257 " "
absolute error = 0.12215941807213257 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2895614523674425 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.12317203875403214 " "
absolute error = 0.12317203875403214 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.290197240377235 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.12367970279158848 " "
absolute error = 0.12367970279158848 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29146881639681993 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.12469773403069309 " "
absolute error = 0.12469773403069309 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2921046044066124 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.12520809954194353 " "
absolute error = 0.12520809954194353 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29337618042619734 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.12623152612556593 " "
absolute error = 0.12623152612556593 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2940119684359898 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.12674458551041343 " "
absolute error = 0.12674458551041343 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6323637865361624 " "
Order of pole = 3.082334387727314600000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29528354445557475 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1277733922508269 " "
absolute error = 0.1277733922508269 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2965551204751597 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.12880577733709286 " "
absolute error = 0.12880577733709286 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29719090848495217 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1293233096559776 " "
absolute error = 0.1293233096559776 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2984624845045371 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.13036104964137396 " "
absolute error = 0.13036104964137396 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2990982725143296 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1308812556277068 " "
absolute error = 0.1308812556277068 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3003698485339145 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1319243353906179 " "
absolute error = 0.1319243353906179 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.301005636543707 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.13244720748975342 " "
absolute error = 0.13244720748975342 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30227721256329193 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.13349561193318793 " "
absolute error = 0.13349561193318793 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 5.656982910437292 " "
Order of pole = 1.58287605245277520000000000E-10 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30354878858287687 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.13454755778853986 " "
absolute error = 0.13454755778853986 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.645894557020275 " "
Order of pole = 4.99174035439864400000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30418457659266934 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1350748566542707 " "
absolute error = 0.1350748566542707 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3054561526122543 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.13613210208296922 " "
absolute error = 0.13613210208296922 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30609194062204675 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.13666204697574136 " "
absolute error = 0.13666204697574136 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 8.918828271718628 " "
Order of pole = 3.96910948552431360000000000E-10 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3073635166416317 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1377245769460196 " "
absolute error = 0.1377245769460196 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.7611016781478487 " "
Order of pole = 2.4282797994601424000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30863509266121664 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.13879062160503752 " "
absolute error = 0.13879062160503752 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3092708806710091 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1393249598604163 " "
absolute error = 0.1393249598604163 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31054245669059405 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.14039626406201564 " "
absolute error = 0.14039626406201564 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3111782447003865 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.14093322834521751 " "
absolute error = 0.14093322834521751 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31244982071997146 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.14200977712222365 " "
absolute error = 0.14200977712222365 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31308560872976393 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1425493599556827 " "
absolute error = 0.1425493599556827 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3143571847493489 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.14363113836498217 " "
absolute error = 0.14363113836498217 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3156287607689338 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1447163949059236 " "
absolute error = 0.1447163949059236 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 2.0108394943301513 " "
Order of pole = 3.383959779057477000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3162645487787263 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.14526032540559497 " "
absolute error = 0.14526032540559497 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3175361247983112 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.14635078672687438 " "
absolute error = 0.14635078672687438 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3181719128081037 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.14689731589521943 " "
absolute error = 0.14689731589521943 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31944348882768864 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.14799296711746338 " "
absolute error = 0.14799296711746338 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200792768374811 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1485420875207376 " "
absolute error = 0.1485420875207376 " "
relative error = -1. "%"
Correct digits = -1
h = 6.3578800979247700000E-4 " "
"NO POLE for equation 1"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = sin(x) / (0.2 * x + 0.3);"
Iterations = 502
"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 0 Hours 43 Minutes 40 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 43 Minutes 30 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 46 Minutes 30 Seconds
"Time to Timeout " Unknown
Percent Done = 6.439732817337170 "%"
(%o58) true
(%o58) diffeq.max