(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m,
n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new,
ratio, term], n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m
1, m - 2
array_y_higher
1, m
: m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1,
array_y_higher
1, m - 2
if omniabs(hdrc) > glob_small_float glob_small_float
glob_h
then (rcs : ------, ord_no :
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
-----------------------------------------------------,
hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found_sing : 1,
1, 2 1, 2
array_type_pole : 2, if glob_display_flag
1
then (if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1"))),
if (1 # found_sing) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > - 1.0 glob_smallish_float)
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found_sing : 1, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE for equation 1")),
if (1 # found_sing) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole > - 1.0
1, 1 1, 2
glob_smallish_float))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2,
1, 2 1, 2 1
found_sing : 1, if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))),
if 1 # found_sing then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m,
n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new,
ratio, term], n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m
1, m - 2
array_y_higher
1, m
: m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1,
array_y_higher
1, m - 2
if omniabs(hdrc) > glob_small_float glob_small_float
glob_h
then (rcs : ------, ord_no :
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
-----------------------------------------------------,
hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found_sing : 1,
1, 2 1, 2
array_type_pole : 2, if glob_display_flag
1
then (if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1"))),
if (1 # found_sing) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > - 1.0 glob_smallish_float)
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found_sing : 1, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE for equation 1")),
if (1 # found_sing) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole > - 1.0
1, 1 1, 2
glob_smallish_float))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2,
1, 2 1, 2 1
found_sing : 1, if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))),
if 1 # found_sing then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_y array_y ,
1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp2 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 : ats(2, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1 : ats(3, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1 : ats(4, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1 : ats(5, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 :
kkk
ats(kkk, array_y, array_y, 1), array_tmp2 : array_tmp1 , 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_tmp2 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_y array_y ,
1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp2 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 : ats(2, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1 : ats(3, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1 : ats(4, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1 : ats(5, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 :
kkk
ats(kkk, array_y, array_y, 1), array_tmp2 : array_tmp1 , 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_tmp2 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)
2.0
(%i56) exact_soln_y(x) := block(-----------)
1.0 - 2.0 x
2.0
(%o56) exact_soln_y(x) := block(-----------)
1.0 - 2.0 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/nonlinear2postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;"), 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:0.2,"),
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, "/* 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, " (2.0/(1.0 - 2.0*x)) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32,
max_terms : 30, glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_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_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 : 0.2, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
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 ) = y * y;"),
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,
"2013-01-28T18:58:47-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "nonlinear2"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;"),
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, "nonlinear2 diffeq.max"),
logitem_str(html_log_file,
"nonlinear2 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/nonlinear2postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;"), 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:0.2,"),
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, "/* 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, " (2.0/(1.0 - 2.0*x)) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32,
max_terms : 30, glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_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_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 : 0.2, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
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 ) = y * y;"),
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,
"2013-01-28T18:58:47-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "nonlinear2"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;"),
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, "nonlinear2 diffeq.max"),
logitem_str(html_log_file,
"nonlinear2 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/nonlinear2postode.ode#################"
"diff ( y , x , 1 ) = y * y;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.0,"
"x_end:0.2,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"/* 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("
" (2.0/(1.0 - 2.0*x)) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 0.2 ""
estimated_steps = 200. ""
step_error = 5.0000000000000E-13 ""
est_needed_step_err = 5.0000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 1.34352079945727950000000000000000000000000000000000000000000000000000000000000000000000E-70 ""
max_value3 = 1.34352079945727950000000000000000000000000000000000000000000000000000000000000000000000E-70 ""
value3 = 1.34352079945727950000000000000000000000000000000000000000000000000000000000000000000000E-70 ""
best_h = 1.000E-3 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.0 " "
y[1] (analytic) = 2. " "
y[1] (numeric) = 2. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.5000000000000152 " "
Order of pole = 651.00000000002 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.000E-3 " "
y[1] (analytic) = 2.004008016032064 " "
y[1] (numeric) = 2.004008016032064 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4990000000000116 " "
Order of pole = 651.0000000000153 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.000E-3 " "
y[1] (analytic) = 2.0080321285140563 " "
y[1] (numeric) = 2.008032128514056 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.211564265053311800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.49800000000000244 " "
Order of pole = 651.0000000000031 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.000E-3 " "
y[1] (analytic) = 2.0120724346076457 " "
y[1] (numeric) = 2.0120724346076457 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4970000000000139 " "
Order of pole = 651.0000000000186 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.000E-3 " "
y[1] (analytic) = 2.0161290322580645 " "
y[1] (numeric) = 2.0161290322580645 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.49599999999998506 " "
Order of pole = 650.9999999999799 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.000E-3 " "
y[1] (analytic) = 2.0202020202020203 " "
y[1] (numeric) = 2.0202020202020203 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4950000000000121 " "
Order of pole = 651.0000000000161 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.000E-3 " "
y[1] (analytic) = 2.0242914979757085 " "
y[1] (numeric) = 2.0242914979757085 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4939999999999987 " "
Order of pole = 650.9999999999984 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.000E-3 " "
y[1] (analytic) = 2.028397565922921 " "
y[1] (numeric) = 2.028397565922921 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.49299999999999666 " "
Order of pole = 650.9999999999953 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.000E-3 " "
y[1] (analytic) = 2.032520325203252 " "
y[1] (numeric) = 2.032520325203252 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4920000000000024 " "
Order of pole = 651.0000000000032 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.000000000000001000E-3 " "
y[1] (analytic) = 2.0366598778004072 " "
y[1] (numeric) = 2.0366598778004077 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.180478020363807400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4910000000000006 " "
Order of pole = 651.000000000001 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.000000000000000200E-2 " "
y[1] (analytic) = 2.0408163265306123 " "
y[1] (numeric) = 2.0408163265306127 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.176037128265306800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4900000000000058 " "
Order of pole = 651.0000000000078 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.100000000000000300E-2 " "
y[1] (analytic) = 2.044989775051125 " "
y[1] (numeric) = 2.0449897750511252 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.17159623616680620000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4890000000000117 " "
Order of pole = 651.0000000000159 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.200000000000000400E-2 " "
y[1] (analytic) = 2.0491803278688523 " "
y[1] (numeric) = 2.0491803278688527 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.167155344068305800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.48800000000001104 " "
Order of pole = 651.0000000000151 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.300000000000000600E-2 " "
y[1] (analytic) = 2.053388090349076 " "
y[1] (numeric) = 2.053388090349076 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.48699999999999116 " "
Order of pole = 650.9999999999877 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.400000000000000700E-2 " "
y[1] (analytic) = 2.05761316872428 " "
y[1] (numeric) = 2.0576131687242802 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.158273559871304300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4860000000000055 " "
Order of pole = 651.0000000000077 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.500000000000000800E-2 " "
y[1] (analytic) = 2.061855670103093 " "
y[1] (numeric) = 2.061855670103093 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4850000000000017 " "
Order of pole = 651.0000000000025 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.600000000000001000E-2 " "
y[1] (analytic) = 2.066115702479339 " "
y[1] (numeric) = 2.066115702479339 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.48400000000000326 " "
Order of pole = 651.0000000000043 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.700000000000001000E-2 " "
y[1] (analytic) = 2.070393374741201 " "
y[1] (numeric) = 2.070393374741201 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.48299999999999693 " "
Order of pole = 650.999999999996 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.80000000000000100E-2 " "
y[1] (analytic) = 2.074688796680498 " "
y[1] (numeric) = 2.074688796680498 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.48199999999999366 " "
Order of pole = 650.9999999999912 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.90000000000000100E-2 " "
y[1] (analytic) = 2.079002079002079 " "
y[1] (numeric) = 2.079002079002079 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.481 " "
Order of pole = 651. " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.00000000000000120E-2 " "
y[1] (analytic) = 2.0833333333333335 " "
y[1] (numeric) = 2.0833333333333335 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.47999999999999693 " "
Order of pole = 650.999999999996 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.10000000000000130E-2 " "
y[1] (analytic) = 2.0876826722338206 " "
y[1] (numeric) = 2.0876826722338206 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4790000000000054 " "
Order of pole = 651.0000000000074 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.200000000000001400E-2 " "
y[1] (analytic) = 2.092050209205021 " "
y[1] (numeric) = 2.0920502092050213 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.122746423083299600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4779999999999861 " "
Order of pole = 650.9999999999808 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.300000000000001500E-2 " "
y[1] (analytic) = 2.0964360587002098 " "
y[1] (numeric) = 2.09643605870021 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.118305530984798400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4770000000000138 " "
Order of pole = 651.0000000000194 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.400000000000001600E-2 " "
y[1] (analytic) = 2.100840336134454 " "
y[1] (numeric) = 2.1008403361344543 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.11386463888629800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4760000000000017 " "
Order of pole = 651.0000000000025 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.500000000000001700E-2 " "
y[1] (analytic) = 2.1052631578947367 " "
y[1] (numeric) = 2.105263157894737 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.109423746787797400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.47499999999999415 " "
Order of pole = 650.9999999999922 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.600000000000002000E-2 " "
y[1] (analytic) = 2.109704641350211 " "
y[1] (numeric) = 2.1097046413502114 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.104982854689296800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.47400000000000736 " "
Order of pole = 651.0000000000102 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.700000000000002000E-2 " "
y[1] (analytic) = 2.1141649048625792 " "
y[1] (numeric) = 2.1141649048625797 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.100541962590796500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.47300000000001796 " "
Order of pole = 651.0000000000256 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.800000000000002000E-2 " "
y[1] (analytic) = 2.1186440677966103 " "
y[1] (numeric) = 2.1186440677966107 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.096101070492295300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4719999999999997 " "
Order of pole = 650.9999999999999 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.90000000000000200E-2 " "
y[1] (analytic) = 2.1231422505307855 " "
y[1] (numeric) = 2.123142250530786 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.09166017839379500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.47099999999998626 " "
Order of pole = 650.9999999999808 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.00000000000000200E-2 " "
y[1] (analytic) = 2.127659574468085 " "
y[1] (numeric) = 2.1276595744680855 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.087219286295294300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4700000000000024 " "
Order of pole = 651.0000000000036 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.10000000000000200E-2 " "
y[1] (analytic) = 2.1321961620469083 " "
y[1] (numeric) = 2.1321961620469088 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.082778394196793700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.46899999999999736 " "
Order of pole = 650.9999999999962 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.20000000000000230E-2 " "
y[1] (analytic) = 2.1367521367521367 " "
y[1] (numeric) = 2.136752136752137 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.078337502098293300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4679999999999956 " "
Order of pole = 650.9999999999937 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.30000000000000240E-2 " "
y[1] (analytic) = 2.1413276231263385 " "
y[1] (numeric) = 2.141327623126339 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.073896609999792100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.466999999999998 " "
Order of pole = 650.9999999999973 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.40000000000000250E-2 " "
y[1] (analytic) = 2.145922746781116 " "
y[1] (numeric) = 2.1459227467811166 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.069455717901291500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4659999999999861 " "
Order of pole = 650.9999999999804 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.500000000000002600E-2 " "
y[1] (analytic) = 2.1505376344086025 " "
y[1] (numeric) = 2.150537634408603 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.06501482580279100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4649999999999923 " "
Order of pole = 650.9999999999893 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.600000000000002600E-2 " "
y[1] (analytic) = 2.1551724137931036 " "
y[1] (numeric) = 2.155172413793104 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.060573933704290500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4640000000000051 " "
Order of pole = 651.0000000000072 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.700000000000003000E-2 " "
y[1] (analytic) = 2.1598272138228944 " "
y[1] (numeric) = 2.159827213822895 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.056133041605790000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.46300000000000024 " "
Order of pole = 651.0000000000006 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.80000000000000300E-2 " "
y[1] (analytic) = 2.1645021645021645 " "
y[1] (numeric) = 2.1645021645021654 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.10338429901457860000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.46199999999999786 " "
Order of pole = 650.9999999999973 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.90000000000000300E-2 " "
y[1] (analytic) = 2.1691973969631237 " "
y[1] (numeric) = 2.1691973969631246 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.09450251481757700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4610000000000141 " "
Order of pole = 651.0000000000207 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.00000000000000300E-2 " "
y[1] (analytic) = 2.173913043478261 " "
y[1] (numeric) = 2.173913043478262 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.085620730620575500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4599999999999777 " "
Order of pole = 650.9999999999682 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.10000000000000300E-2 " "
y[1] (analytic) = 2.178649237472767 " "
y[1] (numeric) = 2.178649237472768 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.11510841963536200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.45900000000000407 " "
Order of pole = 651.0000000000061 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.20000000000000300E-2 " "
y[1] (analytic) = 2.183406113537118 " "
y[1] (numeric) = 2.183406113537119 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.06785716222657360000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4579999999999829 " "
Order of pole = 650.9999999999757 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.30000000000000300E-2 " "
y[1] (analytic) = 2.188183807439825 " "
y[1] (numeric) = 2.188183807439826 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.05897537802957200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4570000000000098 " "
Order of pole = 651.0000000000146 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.40000000000000340E-2 " "
y[1] (analytic) = 2.192982456140351 " "
y[1] (numeric) = 2.192982456140352 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.050093593832570500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.45599999999999424 " "
Order of pole = 650.9999999999922 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.50000000000000340E-2 " "
y[1] (analytic) = 2.197802197802198 " "
y[1] (numeric) = 2.197802197802199 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.04121180963556900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.45499999999999446 " "
Order of pole = 650.9999999999923 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.600000000000003500E-2 " "
y[1] (analytic) = 2.2026431718061676 " "
y[1] (numeric) = 2.2026431718061685 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.03233002543856800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.45400000000000507 " "
Order of pole = 651.0000000000075 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.700000000000003600E-2 " "
y[1] (analytic) = 2.207505518763797 " "
y[1] (numeric) = 2.207505518763798 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.02344824124156730000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4530000000000148 " "
Order of pole = 651.0000000000217 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.800000000000003700E-2 " "
y[1] (analytic) = 2.212389380530974 " "
y[1] (numeric) = 2.2123893805309747 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.014566457044565500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.45200000000000495 " "
Order of pole = 651.0000000000074 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.90000000000000400E-2 " "
y[1] (analytic) = 2.21729490022173 " "
y[1] (numeric) = 2.217294900221731 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.00568467284756400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4510000000000023 " "
Order of pole = 651.0000000000039 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.00000000000000300E-2 " "
y[1] (analytic) = 2.2222222222222223 " "
y[1] (numeric) = 2.2222222222222237 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.99520433297584500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4499999999999957 " "
Order of pole = 650.999999999994 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.10000000000000300E-2 " "
y[1] (analytic) = 2.2271714922049 " "
y[1] (numeric) = 2.227171492204901 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.987921104453562000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4489999999999856 " "
Order of pole = 650.999999999979 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.20000000000000400E-2 " "
y[1] (analytic) = 2.232142857142857 " "
y[1] (numeric) = 2.2321428571428585 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.96855898038484200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.448000000000003 " "
Order of pole = 651.0000000000048 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.30000000000000400E-2 " "
y[1] (analytic) = 2.237136465324385 " "
y[1] (numeric) = 2.237136465324386 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.9552363040893400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4470000000000057 " "
Order of pole = 651.0000000000089 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.40000000000000400E-2 " "
y[1] (analytic) = 2.2421524663677133 " "
y[1] (numeric) = 2.2421524663677146 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.94191362779383700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4460000000000056 " "
Order of pole = 651.0000000000089 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.50000000000000400E-2 " "
y[1] (analytic) = 2.247191011235955 " "
y[1] (numeric) = 2.2471910112359565 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.92859095149833600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.44500000000001566 " "
Order of pole = 651.0000000000241 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.60000000000000400E-2 " "
y[1] (analytic) = 2.2522522522522523 " "
y[1] (numeric) = 2.2522522522522537 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.91526827520283400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.44399999999999906 " "
Order of pole = 650.9999999999991 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.700000000000004000E-2 " "
y[1] (analytic) = 2.2573363431151243 " "
y[1] (numeric) = 2.2573363431151257 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.90194559890733100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4429999999999875 " "
Order of pole = 650.9999999999817 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.800000000000004000E-2 " "
y[1] (analytic) = 2.2624434389140275 " "
y[1] (numeric) = 2.2624434389140284 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.92574861507455300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.44200000000000295 " "
Order of pole = 651.0000000000048 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.900000000000004000E-2 " "
y[1] (analytic) = 2.267573696145125 " "
y[1] (numeric) = 2.267573696145126 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.91686683087755170000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.44100000000001255 " "
Order of pole = 651.0000000000192 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.000000000000004000E-2 " "
y[1] (analytic) = 2.272727272727273 " "
y[1] (numeric) = 2.2727272727272743 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.86197757002082700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4399999999999945 " "
Order of pole = 650.999999999992 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.10000000000000400E-2 " "
y[1] (analytic) = 2.2779043280182236 " "
y[1] (numeric) = 2.277904328018225 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.84865489372532500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4389999999999951 " "
Order of pole = 650.999999999993 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.20000000000000400E-2 " "
y[1] (analytic) = 2.2831050228310503 " "
y[1] (numeric) = 2.283105022831052 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.78044295657309700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4380000000000133 " "
Order of pole = 651.0000000000208 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.30000000000000400E-2 " "
y[1] (analytic) = 2.288329519450801 " "
y[1] (numeric) = 2.288329519450803 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.76267938817909300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4370000000000001 " "
Order of pole = 651.0000000000006 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.40000000000000500E-2 " "
y[1] (analytic) = 2.2935779816513766 " "
y[1] (numeric) = 2.293577981651378 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.80868686483881800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.43599999999999206 " "
Order of pole = 650.9999999999883 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.50000000000000500E-2 " "
y[1] (analytic) = 2.298850574712644 " "
y[1] (numeric) = 2.2988505747126453 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.79536418854331600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.43499999999999345 " "
Order of pole = 650.9999999999905 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.60000000000000500E-2 " "
y[1] (analytic) = 2.3041474654377883 " "
y[1] (numeric) = 2.3041474654377896 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.78204151224781500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.43399999999999667 " "
Order of pole = 650.9999999999952 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.70000000000000500E-2 " "
y[1] (analytic) = 2.309468822170901 " "
y[1] (numeric) = 2.3094688221709023 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.76871883595231200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4330000000000087 " "
Order of pole = 651.0000000000141 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.80000000000000500E-2 " "
y[1] (analytic) = 2.3148148148148153 " "
y[1] (numeric) = 2.3148148148148167 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.7553961596568100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4320000000000059 " "
Order of pole = 651.0000000000094 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.90000000000000500E-2 " "
y[1] (analytic) = 2.3201856148491884 " "
y[1] (numeric) = 2.3201856148491897 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.74207348336130900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4309999999999897 " "
Order of pole = 650.9999999999847 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.00000000000000500E-2 " "
y[1] (analytic) = 2.3255813953488373 " "
y[1] (numeric) = 2.325581395348839 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.63833440942107700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.43000000000000643 " "
Order of pole = 651.0000000000107 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.10000000000000500E-2 " "
y[1] (analytic) = 2.3310023310023316 " "
y[1] (numeric) = 2.331002331002333 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.71542813077030400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4290000000000043 " "
Order of pole = 651.0000000000074 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.20000000000000500E-2 " "
y[1] (analytic) = 2.3364485981308416 " "
y[1] (numeric) = 2.336448598130843 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.70210545447480300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.42799999999999744 " "
Order of pole = 650.9999999999966 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.30000000000000500E-2 " "
y[1] (analytic) = 2.3419203747072603 " "
y[1] (numeric) = 2.3419203747072617 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.688782778179301000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4270000000000046 " "
Order of pole = 651.0000000000076 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.40000000000000500E-2 " "
y[1] (analytic) = 2.3474178403755874 " "
y[1] (numeric) = 2.3474178403755888 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.67546010188379900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.42600000000000143 " "
Order of pole = 651.0000000000026 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.50000000000000600E-2 " "
y[1] (analytic) = 2.3529411764705888 " "
y[1] (numeric) = 2.35294117647059 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.66213742558829700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.42500000000000804 " "
Order of pole = 651.000000000013 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.60000000000000600E-2 " "
y[1] (analytic) = 2.3584905660377364 " "
y[1] (numeric) = 2.3584905660377378 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.648814749292795000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4240000000000126 " "
Order of pole = 651.0000000000203 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.70000000000000600E-2 " "
y[1] (analytic) = 2.364066193853428 " "
y[1] (numeric) = 2.36406619385343 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.51398943066306000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.42299999999999194 " "
Order of pole = 650.999999999988 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.80000000000000600E-2 " "
y[1] (analytic) = 2.369668246445498 " "
y[1] (numeric) = 2.3696682464455 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.49622586226905500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4220000000000105 " "
Order of pole = 651.000000000017 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.90000000000000600E-2 " "
y[1] (analytic) = 2.3752969121140146 " "
y[1] (numeric) = 2.3752969121140164 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.47846229387505300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.42100000000000354 " "
Order of pole = 651.0000000000063 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.00000000000000600E-2 " "
y[1] (analytic) = 2.3809523809523814 " "
y[1] (numeric) = 2.380952380952383 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.46069872548105100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4200000000000015 " "
Order of pole = 651.0000000000028 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.10000000000000600E-2 " "
y[1] (analytic) = 2.3866348448687353 " "
y[1] (numeric) = 2.386634844868737 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.44293515708705000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4189999999999962 " "
Order of pole = 650.9999999999947 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.20000000000000600E-2 " "
y[1] (analytic) = 2.392344497607656 " "
y[1] (numeric) = 2.3923444976076573 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.56887869151978400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.41800000000000026 " "
Order of pole = 651.0000000000008 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.30000000000000600E-2 " "
y[1] (analytic) = 2.398081534772183 " "
y[1] (numeric) = 2.398081534772184 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.55555601522428200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.41700000000000986 " "
Order of pole = 651.0000000000161 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.40000000000000600E-2 " "
y[1] (analytic) = 2.403846153846154 " "
y[1] (numeric) = 2.403846153846156 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.38964445190504100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4159999999999991 " "
Order of pole = 650.9999999999991 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.50000000000000600E-2 " "
y[1] (analytic) = 2.409638554216868 " "
y[1] (numeric) = 2.4096385542168695 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.52891066263327800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.41500000000001586 " "
Order of pole = 651.0000000000257 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.60000000000000700E-2 " "
y[1] (analytic) = 2.415458937198068 " "
y[1] (numeric) = 2.4154589371980695 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.515587986337777000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.41399999999999343 " "
Order of pole = 650.9999999999899 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.70000000000000700E-2 " "
y[1] (analytic) = 2.421307506053269 " "
y[1] (numeric) = 2.4213075060532705 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.50226531004227500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4130000000000028 " "
Order of pole = 651.000000000005 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.80000000000000700E-2 " "
y[1] (analytic) = 2.4271844660194177 " "
y[1] (numeric) = 2.427184466019419 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.48894263374677300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.41200000000000253 " "
Order of pole = 651.0000000000044 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.90000000000000700E-2 " "
y[1] (analytic) = 2.433090024330901 " "
y[1] (numeric) = 2.4330900243309017 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.650413304967513600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.41099999999999814 " "
Order of pole = 650.9999999999974 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.00000000000000700E-2 " "
y[1] (analytic) = 2.439024390243903 " "
y[1] (numeric) = 2.4390243902439037 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.64153152077051300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4100000000000043 " "
Order of pole = 651.0000000000073 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.10000000000000700E-2 " "
y[1] (analytic) = 2.4449877750611253 " "
y[1] (numeric) = 2.444987775061126 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.632649736573511600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4089999999999935 " "
Order of pole = 650.9999999999897 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.20000000000000700E-2 " "
y[1] (analytic) = 2.4509803921568634 " "
y[1] (numeric) = 2.4509803921568643 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.6237679523765100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4080000000000061 " "
Order of pole = 651.0000000000102 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.30000000000000700E-2 " "
y[1] (analytic) = 2.4570024570024573 " "
y[1] (numeric) = 2.4570024570024587 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.422329252269263000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.40699999999999664 " "
Order of pole = 650.9999999999948 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.40000000000000700E-2 " "
y[1] (analytic) = 2.4630541871921188 " "
y[1] (numeric) = 2.46305418719212 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.40900657597376200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.40600000000000736 " "
Order of pole = 651.0000000000126 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.50000000000000700E-2 " "
y[1] (analytic) = 2.469135802469136 " "
y[1] (numeric) = 2.469135802469138 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.19424519957101300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4049999999999918 " "
Order of pole = 650.9999999999873 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.60000000000000700E-2 " "
y[1] (analytic) = 2.4752475247524757 " "
y[1] (numeric) = 2.4752475247524774 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.1764816311770110000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4040000000000019 " "
Order of pole = 651.0000000000035 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.70000000000000800E-2 " "
y[1] (analytic) = 2.481389578163772 " "
y[1] (numeric) = 2.481389578163774 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.15871806278300900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.40300000000000974 " "
Order of pole = 651.0000000000166 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.80000000000000800E-2 " "
y[1] (analytic) = 2.487562189054727 " "
y[1] (numeric) = 2.4875621890547284 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.355715870791754000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4020000000000063 " "
Order of pole = 651.0000000000111 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.90000000000000800E-2 " "
y[1] (analytic) = 2.4937655860349133 " "
y[1] (numeric) = 2.4937655860349146 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.34239319449625200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4010000000000049 " "
Order of pole = 651.0000000000086 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10000000000000007 " "
y[1] (analytic) = 2.5000000000000004 " "
y[1] (numeric) = 2.5000000000000018 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.32907051820075000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.4000000000000174 " "
Order of pole = 651.0000000000293 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10100000000000008 " "
y[1] (analytic) = 2.5062656641604018 " "
y[1] (numeric) = 2.5062656641604026 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.54383189460349900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.39900000000000446 " "
Order of pole = 651.0000000000076 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10200000000000008 " "
y[1] (analytic) = 2.5125628140703524 " "
y[1] (numeric) = 2.5125628140703533 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.534950110406497300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3979999999999917 " "
Order of pole = 650.9999999999867 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10300000000000008 " "
y[1] (analytic) = 2.5188916876574314 " "
y[1] (numeric) = 2.5188916876574323 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.52606832620949600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.39699999999999414 " "
Order of pole = 650.9999999999905 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10400000000000008 " "
y[1] (analytic) = 2.525252525252526 " "
y[1] (numeric) = 2.525252525252527 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.51718654201249500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3959999999999909 " "
Order of pole = 650.9999999999852 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10500000000000008 " "
y[1] (analytic) = 2.5316455696202538 " "
y[1] (numeric) = 2.5316455696202547 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.50830475781549400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.39500000000001523 " "
Order of pole = 651.0000000000261 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10600000000000008 " "
y[1] (analytic) = 2.538071065989848 " "
y[1] (numeric) = 2.538071065989849 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.499422973618493000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.39399999999999236 " "
Order of pole = 650.9999999999873 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10700000000000008 " "
y[1] (analytic) = 2.5445292620865145 " "
y[1] (numeric) = 2.5445292620865154 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.49054118942149100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3929999999999879 " "
Order of pole = 650.99999999998 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10800000000000008 " "
y[1] (analytic) = 2.551020408163266 " "
y[1] (numeric) = 2.5510204081632666 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.74082970261224500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3920000000000124 " "
Order of pole = 651.0000000000215 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10900000000000008 " "
y[1] (analytic) = 2.5575447570332486 " "
y[1] (numeric) = 2.5575447570332495 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.47277762102748900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3909999999999975 " "
Order of pole = 650.9999999999962 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000008 " "
y[1] (analytic) = 2.5641025641025648 " "
y[1] (numeric) = 2.5641025641025657 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.46389583683048800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.39000000000000984 " "
Order of pole = 651.0000000000172 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11100000000000008 " "
y[1] (analytic) = 2.5706940874035995 " "
y[1] (numeric) = 2.5706940874036004 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.455014052633486600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3889999999999941 " "
Order of pole = 650.9999999999903 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11200000000000009 " "
y[1] (analytic) = 2.5773195876288666 " "
y[1] (numeric) = 2.5773195876288675 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.44613226843648500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.387999999999993 " "
Order of pole = 650.9999999999887 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11300000000000009 " "
y[1] (analytic) = 2.5839793281653756 " "
y[1] (numeric) = 2.583979328165376 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.718625242119741800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.387000000000009 " "
Order of pole = 651.0000000000159 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11400000000000009 " "
y[1] (analytic) = 2.5906735751295344 " "
y[1] (numeric) = 2.590673575129535 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.71418435002124110000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.386000000000009 " "
Order of pole = 651.0000000000158 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11500000000000009 " "
y[1] (analytic) = 2.5974025974025983 " "
y[1] (numeric) = 2.5974025974025987 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.709743457922740500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.38500000000001017 " "
Order of pole = 651.0000000000177 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11600000000000009 " "
y[1] (analytic) = 2.6041666666666674 " "
y[1] (numeric) = 2.604166666666668 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.7053025658242402000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.38400000000000545 " "
Order of pole = 651.0000000000098 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11700000000000009 " "
y[1] (analytic) = 2.610966057441254 " "
y[1] (numeric) = 2.6109660574412543 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.700861673725739300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3830000000000062 " "
Order of pole = 651.0000000000111 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11800000000000009 " "
y[1] (analytic) = 2.6178010471204196 " "
y[1] (numeric) = 2.61780104712042 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.696420781627238600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3820000000000118 " "
Order of pole = 651.0000000000208 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11900000000000009 " "
y[1] (analytic) = 2.624671916010499 " "
y[1] (numeric) = 2.6246719160105 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.383959779057476600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.38099999999999395 " "
Order of pole = 650.9999999999899 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000009 " "
y[1] (analytic) = 2.6315789473684217 " "
y[1] (numeric) = 2.6315789473684226 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.37507799486047530000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.38000000000001083 " "
Order of pole = 651.0000000000193 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1210000000000001 " "
y[1] (analytic) = 2.638522427440634 " "
y[1] (numeric) = 2.638522427440635 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.36619621066347400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3790000000000066 " "
Order of pole = 651.0000000000118 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1220000000000001 " "
y[1] (analytic) = 2.6455026455026465 " "
y[1] (numeric) = 2.6455026455026474 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.35731442646647170000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.37799999999999806 " "
Order of pole = 650.9999999999968 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1230000000000001 " "
y[1] (analytic) = 2.652519893899205 " "
y[1] (numeric) = 2.652519893899206 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.34843264226947100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.377000000000005 " "
Order of pole = 651.0000000000094 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1240000000000001 " "
y[1] (analytic) = 2.6595744680851072 " "
y[1] (numeric) = 2.659574468085108 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.3395508580724700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3759999999999877 " "
Order of pole = 650.9999999999786 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12500000000000008 " "
y[1] (analytic) = 2.6666666666666674 " "
y[1] (numeric) = 2.6666666666666683 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.33066907387546900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.37500000000000033 " "
Order of pole = 651.000000000001 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12600000000000008 " "
y[1] (analytic) = 2.673796791443851 " "
y[1] (numeric) = 2.673796791443852 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.32178728967846670000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3739999999999946 " "
Order of pole = 650.9999999999908 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12700000000000009 " "
y[1] (analytic) = 2.680965147453084 " "
y[1] (numeric) = 2.680965147453085 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.31290550548146600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3729999999999998 " "
Order of pole = 650.9999999999998 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12800000000000009 " "
y[1] (analytic) = 2.6881720430107534 " "
y[1] (numeric) = 2.6881720430107543 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.30402372128446500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.37199999999999267 " "
Order of pole = 650.9999999999874 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1290000000000001 " "
y[1] (analytic) = 2.695417789757413 " "
y[1] (numeric) = 2.695417789757414 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.295141937087463500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3709999999999897 " "
Order of pole = 650.9999999999819 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1300000000000001 " "
y[1] (analytic) = 2.7027027027027035 " "
y[1] (numeric) = 2.7027027027027044 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.28626015289046200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3700000000000057 " "
Order of pole = 651.0000000000102 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1310000000000001 " "
y[1] (analytic) = 2.7100271002710037 " "
y[1] (numeric) = 2.7100271002710046 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.27737836869346040000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.36900000000000177 " "
Order of pole = 651.0000000000036 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1320000000000001 " "
y[1] (analytic) = 2.717391304347827 " "
y[1] (numeric) = 2.717391304347828 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.2684965844964600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.368000000000004 " "
Order of pole = 651.0000000000076 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1330000000000001 " "
y[1] (analytic) = 2.724795640326976 " "
y[1] (numeric) = 2.7247956403269775 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.88942220044918800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3669999999999983 " "
Order of pole = 650.9999999999977 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1340000000000001 " "
y[1] (analytic) = 2.7322404371584708 " "
y[1] (numeric) = 2.732240437158472 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.87609952415368600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.36599999999999033 " "
Order of pole = 650.9999999999831 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1350000000000001 " "
y[1] (analytic) = 2.739726027397261 " "
y[1] (numeric) = 2.7397260273972623 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.862776847858184500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.36500000000000704 " "
Order of pole = 651.0000000000133 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1360000000000001 " "
y[1] (analytic) = 2.747252747252748 " "
y[1] (numeric) = 2.7472527472527495 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.84945417156268200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.36399999999998844 " "
Order of pole = 650.9999999999793 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1370000000000001 " "
y[1] (analytic) = 2.754820936639119 " "
y[1] (numeric) = 2.7548209366391205 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.83613149526718100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.36300000000000915 " "
Order of pole = 651.0000000000169 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1380000000000001 " "
y[1] (analytic) = 2.7624309392265203 " "
y[1] (numeric) = 2.7624309392265216 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.822808818971678300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.36200000000000637 " "
Order of pole = 651.0000000000124 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1390000000000001 " "
y[1] (analytic) = 2.770083102493076 " "
y[1] (numeric) = 2.770083102493077 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.80948614267617600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.36100000000000526 " "
Order of pole = 651.0000000000103 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1400000000000001 " "
y[1] (analytic) = 2.7777777777777786 " "
y[1] (numeric) = 2.7777777777777803 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.394884621840901000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3599999999999959 " "
Order of pole = 650.9999999999928 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1410000000000001 " "
y[1] (analytic) = 2.785515320334263 " "
y[1] (numeric) = 2.7855153203342646 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.37712105344689600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.35900000000000004 " "
Order of pole = 651.0000000000008 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1420000000000001 " "
y[1] (analytic) = 2.7932960893854757 " "
y[1] (numeric) = 2.7932960893854775 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.35935748505289400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.35800000000000215 " "
Order of pole = 651.0000000000047 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1430000000000001 " "
y[1] (analytic) = 2.801120448179273 " "
y[1] (numeric) = 2.801120448179274 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.756195437494168400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.35700000000000304 " "
Order of pole = 651.0000000000061 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1440000000000001 " "
y[1] (analytic) = 2.808988764044945 " "
y[1] (numeric) = 2.8089887640449462 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.74287276119866650000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3559999999999956 " "
Order of pole = 650.9999999999925 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1450000000000001 " "
y[1] (analytic) = 2.8169014084507054 " "
y[1] (numeric) = 2.8169014084507067 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.72955008490316500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.35500000000000925 " "
Order of pole = 651.000000000018 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1460000000000001 " "
y[1] (analytic) = 2.824858757062148 " "
y[1] (numeric) = 2.8248587570621493 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.71622740860766330000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.35400000000000503 " "
Order of pole = 651.0000000000098 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1470000000000001 " "
y[1] (analytic) = 2.832861189801701 " "
y[1] (numeric) = 2.832861189801702 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.702904732312161400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3530000000000007 " "
Order of pole = 651.0000000000016 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1480000000000001 " "
y[1] (analytic) = 2.840909090909092 " "
y[1] (numeric) = 2.8409090909090935 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.68958205601665900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3519999999999986 " "
Order of pole = 650.999999999998 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1490000000000001 " "
y[1] (analytic) = 2.8490028490028503 " "
y[1] (numeric) = 2.8490028490028516 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.676259379721157000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.350999999999999 " "
Order of pole = 650.9999999999983 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1500000000000001 " "
y[1] (analytic) = 2.857142857142858 " "
y[1] (numeric) = 2.85714285714286 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.21724893790087400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3500000000000009 " "
Order of pole = 651.000000000002 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1510000000000001 " "
y[1] (analytic) = 2.8653295128939837 " "
y[1] (numeric) = 2.8653295128939855 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.19948536950687300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.34899999999999903 " "
Order of pole = 650.9999999999987 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1520000000000001 " "
y[1] (analytic) = 2.8735632183908058 " "
y[1] (numeric) = 2.8735632183908075 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.18172180111286800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3480000000000004 " "
Order of pole = 651.0000000000015 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1530000000000001 " "
y[1] (analytic) = 2.8818443804034595 " "
y[1] (numeric) = 2.8818443804034612 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.16395823271886600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3469999999999989 " "
Order of pole = 650.9999999999984 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1540000000000001 " "
y[1] (analytic) = 2.8901734104046253 " "
y[1] (numeric) = 2.8901734104046275 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 7.68274333040608100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.34599999999999353 " "
Order of pole = 650.9999999999885 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1550000000000001 " "
y[1] (analytic) = 2.8985507246376825 " "
y[1] (numeric) = 2.8985507246376843 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.12843109593086200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3450000000000031 " "
Order of pole = 651.0000000000066 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1560000000000001 " "
y[1] (analytic) = 2.9069767441860477 " "
y[1] (numeric) = 2.9069767441860495 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.11066752753685800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.34400000000000924 " "
Order of pole = 651.0000000000183 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1570000000000001 " "
y[1] (analytic) = 2.915451895043733 " "
y[1] (numeric) = 2.9154518950437347 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.09290395914285700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.34299999999999825 " "
Order of pole = 650.9999999999974 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1580000000000001 " "
y[1] (analytic) = 2.923976608187136 " "
y[1] (numeric) = 2.9239766081871372 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.5563552930616400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.34200000000000164 " "
Order of pole = 651.0000000000038 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1590000000000001 " "
y[1] (analytic) = 2.9325513196480952 " "
y[1] (numeric) = 2.9325513196480966 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.543032616766138300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.34099999999999064 " "
Order of pole = 650.9999999999822 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000011 " "
y[1] (analytic) = 2.9411764705882364 " "
y[1] (numeric) = 2.941176470588238 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.03961325396084900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.339999999999998 " "
Order of pole = 650.9999999999967 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16100000000000012 " "
y[1] (analytic) = 2.9498525073746324 " "
y[1] (numeric) = 2.9498525073746342 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.02184968556684600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3390000000000048 " "
Order of pole = 651.00000000001 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16200000000000012 " "
y[1] (analytic) = 2.958579881656806 " "
y[1] (numeric) = 2.958579881656808 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.00408611717284300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3380000000000062 " "
Order of pole = 651.0000000000128 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16300000000000012 " "
y[1] (analytic) = 2.967359050445105 " "
y[1] (numeric) = 2.967359050445107 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.98632254877884200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.33699999999999625 " "
Order of pole = 650.9999999999932 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16400000000000012 " "
y[1] (analytic) = 2.9761904761904776 " "
y[1] (numeric) = 2.9761904761904794 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.96855898038483900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.33599999999998864 " "
Order of pole = 650.9999999999784 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16500000000000012 " "
y[1] (analytic) = 2.985074626865673 " "
y[1] (numeric) = 2.985074626865675 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.95079541199083700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3349999999999965 " "
Order of pole = 650.9999999999937 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16600000000000012 " "
y[1] (analytic) = 2.9940119760479056 " "
y[1] (numeric) = 2.9940119760479074 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.93303184359683300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.33400000000000357 " "
Order of pole = 651.0000000000076 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16700000000000012 " "
y[1] (analytic) = 3.003003003003004 " "
y[1] (numeric) = 3.0030030030030064 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 7.3940853440035400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3330000000000029 " "
Order of pole = 651.0000000000066 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16800000000000012 " "
y[1] (analytic) = 3.012048192771086 " "
y[1] (numeric) = 3.0120481927710876 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.89750470680882800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3319999999999867 " "
Order of pole = 650.9999999999742 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16900000000000012 " "
y[1] (analytic) = 3.021148036253778 " "
y[1] (numeric) = 3.0211480362537797 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.87974113841482700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.33099999999999974 " "
Order of pole = 651.0000000000001 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000012 " "
y[1] (analytic) = 3.0303030303030316 " "
y[1] (numeric) = 3.0303030303030334 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.86197757002082400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.32999999999999335 " "
Order of pole = 650.9999999999874 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17100000000000012 " "
y[1] (analytic) = 3.0395136778115517 " "
y[1] (numeric) = 3.0395136778115535 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.84421400162682100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.32899999999999396 " "
Order of pole = 650.9999999999882 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17200000000000013 " "
y[1] (analytic) = 3.0487804878048794 " "
y[1] (numeric) = 3.048780487804881 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.82645043323281800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3280000000000027 " "
Order of pole = 651.0000000000061 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17300000000000013 " "
y[1] (analytic) = 3.0581039755351695 " "
y[1] (numeric) = 3.0581039755351713 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.80868686483881700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3269999999999965 " "
Order of pole = 650.9999999999936 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17400000000000013 " "
y[1] (analytic) = 3.0674846625766885 " "
y[1] (numeric) = 3.0674846625766903 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.79092329644481400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.32599999999999746 " "
Order of pole = 650.9999999999957 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17500000000000013 " "
y[1] (analytic) = 3.0769230769230784 " "
y[1] (numeric) = 3.07692307692308 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.77315972805081200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3250000000000076 " "
Order of pole = 651.0000000000163 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17600000000000013 " "
y[1] (analytic) = 3.086419753086421 " "
y[1] (numeric) = 3.0864197530864232 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 7.19424519957101200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.324 " "
Order of pole = 651.0000000000008 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17700000000000013 " "
y[1] (analytic) = 3.095975232198144 " "
y[1] (numeric) = 3.0959752321981457 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.73763259126280600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.32300000000000495 " "
Order of pole = 651.0000000000109 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17800000000000013 " "
y[1] (analytic) = 3.1055900621118027 " "
y[1] (numeric) = 3.1055900621118044 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.71986902286880400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3220000000000037 " "
Order of pole = 651.0000000000084 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17900000000000013 " "
y[1] (analytic) = 3.11526479750779 " "
y[1] (numeric) = 3.115264797507791 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.27657909085610100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.32100000000001 " "
Order of pole = 651.0000000000214 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000013 " "
y[1] (analytic) = 3.1250000000000018 " "
y[1] (numeric) = 3.125000000000003 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.263256414560598300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.31999999999999545 " "
Order of pole = 650.9999999999914 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18100000000000013 " "
y[1] (analytic) = 3.134796238244516 " "
y[1] (numeric) = 3.134796238244517 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.24993373826509700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.31899999999999834 " "
Order of pole = 650.999999999997 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18200000000000013 " "
y[1] (analytic) = 3.144654088050316 " "
y[1] (numeric) = 3.1446540880503173 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.23661106196959500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.31799999999999584 " "
Order of pole = 650.9999999999923 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18300000000000013 " "
y[1] (analytic) = 3.1545741324921153 " "
y[1] (numeric) = 3.1545741324921166 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.223288385674093000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3170000000000048 " "
Order of pole = 651.0000000000103 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18400000000000014 " "
y[1] (analytic) = 3.164556962025318 " "
y[1] (numeric) = 3.1645569620253196 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.20996570937859100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3160000000000039 " "
Order of pole = 651.0000000000088 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18500000000000014 " "
y[1] (analytic) = 3.174603174603176 " "
y[1] (numeric) = 3.1746031746031775 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.1966430330830900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3150000000000053 " "
Order of pole = 651.0000000000116 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18600000000000014 " "
y[1] (analytic) = 3.18471337579618 " "
y[1] (numeric) = 3.184713375796181 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.18332035678758800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.31400000000000006 " "
Order of pole = 651.0000000000009 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18700000000000014 " "
y[1] (analytic) = 3.1948881789137396 " "
y[1] (numeric) = 3.194888178913741 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.16999768049208600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3130000000000041 " "
Order of pole = 651.0000000000092 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18800000000000014 " "
y[1] (analytic) = 3.205128205128207 " "
y[1] (numeric) = 3.205128205128208 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.77111666946438900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3120000000000011 " "
Order of pole = 651.0000000000027 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18900000000000014 " "
y[1] (analytic) = 3.215434083601288 " "
y[1] (numeric) = 3.215434083601289 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.14335232790108200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3109999999999977 " "
Order of pole = 650.9999999999957 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000014 " "
y[1] (analytic) = 3.225806451612905 " "
y[1] (numeric) = 3.225806451612906 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.130029651605580700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.31000000000000855 " "
Order of pole = 651.0000000000188 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19100000000000014 " "
y[1] (analytic) = 3.2362459546925586 " "
y[1] (numeric) = 3.2362459546925595 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.744471316873385300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3089999999999984 " "
Order of pole = 650.9999999999968 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19200000000000014 " "
y[1] (analytic) = 3.2467532467532485 " "
y[1] (numeric) = 3.24675324675325 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.10338429901457640000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3080000000000012 " "
Order of pole = 651.0000000000031 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19300000000000014 " "
y[1] (analytic) = 3.257328990228015 " "
y[1] (numeric) = 3.2573289902280163 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.090061622719074500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.30699999999999855 " "
Order of pole = 650.9999999999977 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19400000000000014 " "
y[1] (analytic) = 3.267973856209152 " "
y[1] (numeric) = 3.2679738562091534 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.07673894642357260000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.3060000000000024 " "
Order of pole = 651.0000000000056 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19500000000000015 " "
y[1] (analytic) = 3.278688524590166 " "
y[1] (numeric) = 3.278688524590167 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.063416270128070000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.30500000000001154 " "
Order of pole = 651.0000000000256 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19600000000000015 " "
y[1] (analytic) = 3.2894736842105283 " "
y[1] (numeric) = 3.2894736842105297 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.050093593832569000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.30400000000000804 " "
Order of pole = 651.0000000000182 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19700000000000015 " "
y[1] (analytic) = 3.300330033003302 " "
y[1] (numeric) = 3.300330033003304 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.38236122338275600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.30300000000000016 " "
Order of pole = 651.0000000000011 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19800000000000015 " "
y[1] (analytic) = 3.311258278145697 " "
y[1] (numeric) = 3.311258278145699 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.36459765498875400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.30199999999999594 " "
Order of pole = 650.9999999999918 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19900000000000015 " "
y[1] (analytic) = 3.3222591362126264 " "
y[1] (numeric) = 3.322259136212628 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.34683408659475100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.30100000000000054 " "
Order of pole = 651.0000000000017 " "
"Finished!"
"diff ( y , x , 1 ) = y * y;"
Iterations = 200
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 1 Minutes 13 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 1 Minutes 13 Seconds
"Time to Timeout "= 0 Years 0 Days 0 Hours 1 Minutes 46 Seconds
Percent Done = 100.50000000000007 "%"
(%o58) true
(%o58) diffeq.max