(%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 # 0.0 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 # 0.0 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
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
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
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 (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
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
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
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 (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_0D1 array_x ,
1 1 1
array_tmp2 : array_const_0D2 + array_tmp1 ,
1 1 1
array_tmp3 : arcsin(array_tmp2 ), array_tmp3_a1 : cos(array_tmp3 ),
1 1 1 1
array_tmp4 : array_tmp3 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1),
1
temporary
array_y : temporary, array_y_higher : temporary, temporary : ---------,
2 1, 2 glob_h
array_y_higher : temporary, 0)), kkk : 2,
2, 1
array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp2
2
array_tmp3 : --------------, array_tmp3_a1 : - array_tmp2 array_tmp3 ,
2 array_tmp3_a1 2 1 2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary
array_y_higher : temporary, temporary : ---------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
- att(2, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : --------------------------------------,
3 array_tmp3_a1
1
array_tmp3 array_tmp2 1
2 2
array_tmp3_a1 : - ------------------------- - array_tmp3 array_tmp2 ,
3 2 3 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
- att(3, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : --------------------------------------,
4 array_tmp3_a1
1
array_tmp3 array_tmp2 2
3 2
array_tmp3_a1 : - ------------------------- - array_tmp3 array_tmp2 ,
4 3 4 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
- att(4, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : --------------------------------------,
5 array_tmp3_a1
1
array_tmp3 array_tmp2 3
4 2
array_tmp3_a1 : - ------------------------- - array_tmp3 array_tmp2 ,
5 4 5 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp3 :
kkk
- att(kkk - 1, array_tmp3_a1, array_tmp3, 2)
--------------------------------------------,
array_tmp3_a1
1
array_tmp3 array_tmp2 (kkk - 2)
kkk - 1 2
array_tmp3_a1 : - ---------------------------------------
kkk kkk - 1
- array_tmp3 array_tmp2 , array_tmp4 : array_tmp3 , order_d : 1,
kkk 1 kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
array_tmp4 expt(glob_h, order_d)
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y : temporary, array_y_higher : temporary,
order_d + kkk 1, order_d + kkk
term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2,
while term >= 1 do (if adj3 <= 1 + order_d
temporary convfp(adj2)
then (if adj2 > 1 then temporary : ----------------------
glob_h
temporary
else temporary : ---------, array_y_higher : temporary),
glob_h adj3, term
term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_0D1 array_x ,
1 1 1
array_tmp2 : array_const_0D2 + array_tmp1 ,
1 1 1
array_tmp3 : arcsin(array_tmp2 ), array_tmp3_a1 : cos(array_tmp3 ),
1 1 1 1
array_tmp4 : array_tmp3 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1),
1
temporary
array_y : temporary, array_y_higher : temporary, temporary : ---------,
2 1, 2 glob_h
array_y_higher : temporary, 0)), kkk : 2,
2, 1
array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp2
2
array_tmp3 : --------------, array_tmp3_a1 : - array_tmp2 array_tmp3 ,
2 array_tmp3_a1 2 1 2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary
array_y_higher : temporary, temporary : ---------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
- att(2, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : --------------------------------------,
3 array_tmp3_a1
1
array_tmp3 array_tmp2 1
2 2
array_tmp3_a1 : - ------------------------- - array_tmp3 array_tmp2 ,
3 2 3 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
- att(3, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : --------------------------------------,
4 array_tmp3_a1
1
array_tmp3 array_tmp2 2
3 2
array_tmp3_a1 : - ------------------------- - array_tmp3 array_tmp2 ,
4 3 4 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
- att(4, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : --------------------------------------,
5 array_tmp3_a1
1
array_tmp3 array_tmp2 3
4 2
array_tmp3_a1 : - ------------------------- - array_tmp3 array_tmp2 ,
5 4 5 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp3 :
kkk
- att(kkk - 1, array_tmp3_a1, array_tmp3, 2)
--------------------------------------------,
array_tmp3_a1
1
array_tmp3 array_tmp2 (kkk - 2)
kkk - 1 2
array_tmp3_a1 : - ---------------------------------------
kkk kkk - 1
- array_tmp3 array_tmp2 , array_tmp4 : array_tmp3 , order_d : 1,
kkk 1 kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
array_tmp4 expt(glob_h, order_d)
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y : temporary, array_y_higher : temporary,
order_d + kkk 1, order_d + kkk
term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2,
while term >= 1 do (if adj3 <= 1 + order_d
temporary convfp(adj2)
then (if adj2 > 1 then temporary : ----------------------
glob_h
temporary
else temporary : ---------, array_y_higher : temporary),
glob_h adj3, term
term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error # 0.0
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error # 0.0
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i32) log_revs(file, revs) := printf(file, revs)
(%o32) log_revs(file, revs) := printf(file, revs)
(%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i35) logstart(file) := printf(file, "")
(%o35) logstart(file) := printf(file, "
")
(%i36) logend(file) := printf(file, "
~%")
(%o36) logend(file) := printf(file, "~%")
(%i37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i40) factorial_2(nnn) := nnn!
(%o40) factorial_2(nnn) := nnn!
(%i41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i46) arcsin(x) := asin(x)
(%o46) arcsin(x) := asin(x)
(%i47) arccos(x) := acos(x)
(%o47) arccos(x) := acos(x)
(%i48) arctan(x) := atan(x)
(%o48) arctan(x) := atan(x)
(%i49) omniabs(x) := abs(x)
(%o49) omniabs(x) := abs(x)
y
(%i50) expt(x, y) := x
y
(%o50) expt(x, y) := x
(%i51) 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)
(%o51) 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)
(%i52) exact_soln_y(x) := block(10.0 sqrt(1.0 - expt(0.2 + 0.1 x, 2))
+ 10.0 (0.2 + 0.1 x) arcsin(0.2 + 0.1 x))
(%o52) exact_soln_y(x) := block(10.0 sqrt(1.0 - expt(0.2 + 0.1 x, 2))
+ 10.0 (0.2 + 0.1 x) arcsin(0.2 + 0.1 x))
(%i53) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h], define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\
########temp/lin_arcsinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms:30,"),
omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-0.8,"), omniout_str(ALWAYS, "x_end:0.8,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.00001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (10.\
0 * (0.1 * x + 0.2) * arcsin(0.1 * x + 0.2 ) + 10.0 * sqrt(1.0 -"),
omniout_str(ALWAYS, "expt((0.1 * x + 0.2) , 2 ))) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, max_terms : 30, Digits : 32,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3_a1, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3_a1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term),
term
array_const_0D2 : 0.2, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 0.8, x_end : 0.8, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
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 : 1, 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
display_alot(current_iter)), 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 ) = arcsin (0.1 * x + 0.2) ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-12-14T22:58:28-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_arcsin"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 151 | "), logitem_str(html_log_file, "lin_arcsin diffeq.max"),
logitem_str(html_log_file,
"lin_arcsin maxima results"),
logitem_str(html_log_file, "Languages compared"), logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%o53) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h], define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\
########temp/lin_arcsinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms:30,"),
omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-0.8,"), omniout_str(ALWAYS, "x_end:0.8,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.00001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (10.\
0 * (0.1 * x + 0.2) * arcsin(0.1 * x + 0.2 ) + 10.0 * sqrt(1.0 -"),
omniout_str(ALWAYS, "expt((0.1 * x + 0.2) , 2 ))) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, max_terms : 30, Digits : 32,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3_a1, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3_a1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term),
term
array_const_0D2 : 0.2, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 0.8, x_end : 0.8, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
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 : 1, 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
display_alot(current_iter)), 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 ) = arcsin (0.1 * x + 0.2) ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-12-14T22:58:28-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_arcsin"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 151 | "), logitem_str(html_log_file, "lin_arcsin diffeq.max"),
logitem_str(html_log_file,
"lin_arcsin maxima results"),
logitem_str(html_log_file, "Languages compared"), logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i54) main()
"##############ECHO OF PROBLEM#################"
"##############temp/lin_arcsinpostode.ode#################"
"diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"max_terms:30,"
"Digits:32,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:-0.8,"
"x_end:0.8,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.00001,"
"glob_look_poles:true,"
"glob_max_iter:100,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (10.0 * (0.1 * x + 0.2) * arcsin(0.1 * x + 0.2 ) + 10.0 * sqrt(1.0 -"
"expt((0.1 * x + 0.2) , 2 ))) "
"));"
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1.6 ""
estimated_steps = 1600. ""
step_error = 6.2500000000000000E-14 ""
est_needed_step_err = 6.2500000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 1.927332782487510000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 ""
max_value3 = 1.927332782487510000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 ""
value3 = 1.927332782487510000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = -0.8 " "
y[1] (analytic) = 10.072086775666431 " "
y[1] (numeric) = 10.072086775666431 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 12.255215200502686 " "
Order of pole = 10.623650523505582 " "
x[1] = -0.799 " "
y[1] (analytic) = 10.072207115912965 " "
y[1] (numeric) = 10.072207115912965 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 12.229841430327255 " "
Order of pole = 10.552869778015953 " "
x[1] = -0.798 " "
y[1] (analytic) = 10.072327556888597 " "
y[1] (numeric) = 10.072327556888597 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 12.204684132210465 " "
Order of pole = 10.48271186315457 " "
x[1] = -0.797 " "
y[1] (analytic) = 10.072448098594556 " "
y[1] (numeric) = 10.072448098594554 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.763580037357662400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 12.17974074807891 " "
Order of pole = 10.41316944041452 " "
x[1] = -0.796 " "
y[1] (analytic) = 10.072568741032068 " "
y[1] (numeric) = 10.072568741032066 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.763558914384971000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 12.155008759371183 " "
Order of pole = 10.344235284597225 " "
x[1] = -0.795 " "
y[1] (analytic) = 10.072689484202364 " "
y[1] (numeric) = 10.072689484202364 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 12.130485686279824 " "
Order of pole = 10.275902281638857 " "
x[1] = -0.794 " "
y[1] (analytic) = 10.072810328106677 " "
y[1] (numeric) = 10.072810328106677 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 12.106169087009073 " "
Order of pole = 10.208163426481612 " "
x[1] = -0.793 " "
y[1] (analytic) = 10.072931272746237 " "
y[1] (numeric) = 10.072931272746237 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 12.082056557046553 " "
Order of pole = 10.141011820985021 " "
x[1] = -0.792 " "
y[1] (analytic) = 10.07305231812228 " "
y[1] (numeric) = 10.07305231812228 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 12.058145728452415 " "
Order of pole = 10.07444067188709 " "
x[1] = -0.791 " "
y[1] (analytic) = 10.073173464236037 " "
y[1] (numeric) = 10.073173464236037 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 12.034434269172031 " "
Order of pole = 10.008443288833796 " "
x[1] = -0.79 " "
y[1] (analytic) = 10.073294711088748 " "
y[1] (numeric) = 10.073294711088746 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.763431816846205700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 12.010919882350448 " "
Order of pole = 9.94301308241242 " "
x[1] = -0.789 " "
y[1] (analytic) = 10.073416058681646 " "
y[1] (numeric) = 10.073416058681643 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52682114796463660000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.98760030567517 " "
Order of pole = 9.87814356226717 " "
x[1] = -0.788 " "
y[1] (analytic) = 10.073537507015969 " "
y[1] (numeric) = 10.073537507015965 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.526778627990538300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.964473310728655 " "
Order of pole = 9.81382833524227 " "
x[1] = -0.787 " "
y[1] (analytic) = 10.073659056092955 " "
y[1] (numeric) = 10.073659056092952 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.526736073772197600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.94153670235269 " "
Order of pole = 9.750061103558828 " "
x[1] = -0.786 " "
y[1] (analytic) = 10.073780705913848 " "
y[1] (numeric) = 10.073780705913842 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.290040227967542000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.918788318030025 " "
Order of pole = 9.686835663041599 " "
x[1] = -0.785 " "
y[1] (analytic) = 10.073902456479882 " "
y[1] (numeric) = 10.073902456479878 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52665086261111540000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.896226027282506 " "
Order of pole = 9.624145901393156 " "
x[1] = -0.784 " "
y[1] (analytic) = 10.074024307792303 " "
y[1] (numeric) = 10.074024307792302 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.763304102836272300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.873847731075331 " "
Order of pole = 9.561985796485104 " "
x[1] = -0.783 " "
y[1] (analytic) = 10.074146259852357 " "
y[1] (numeric) = 10.074146259852354 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52656551449806730000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.851651361241318 " "
Order of pole = 9.500349414707067 " "
x[1] = -0.782 " "
y[1] (analytic) = 10.074268312661282 " "
y[1] (numeric) = 10.07426831266128 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.763261394544887700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.829634879913026 " "
Order of pole = 9.439230909338214 " "
x[1] = -0.781 " "
y[1] (analytic) = 10.074390466220326 " "
y[1] (numeric) = 10.074390466220324 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.763240014724878600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.807796278972214 " "
Order of pole = 9.378624518968408 " "
x[1] = -0.78 " "
y[1] (analytic) = 10.074512720530736 " "
y[1] (numeric) = 10.074512720530732 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.526437235580104400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.78613357950511 " "
Order of pole = 9.318524565935874 " "
x[1] = -0.779 " "
y[1] (analytic) = 10.074635075593758 " "
y[1] (numeric) = 10.074635075593752 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28959161122436800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.764644831276037 " "
Order of pole = 9.258925454817891 " "
x[1] = -0.778 " "
y[1] (analytic) = 10.074757531410636 " "
y[1] (numeric) = 10.074757531410633 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.526351545160274500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.743328112206433 " "
Order of pole = 9.199821670936402 " "
x[1] = -0.777 " "
y[1] (analytic) = 10.074880087982628 " "
y[1] (numeric) = 10.074880087982624 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52630864861428700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.722181527869843 " "
Order of pole = 9.14120777891003 " "
x[1] = -0.776 " "
y[1] (analytic) = 10.075002745310979 " "
y[1] (numeric) = 10.075002745310975 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52626571784704900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.701203210996132 " "
Order of pole = 9.083078421232202 " "
x[1] = -0.775 " "
y[1] (analytic) = 10.07512550339694 " "
y[1] (numeric) = 10.075125503396938 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.763111376430330500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.680391320986601 " "
Order of pole = 9.025428316880621 " "
x[1] = -0.774 " "
y[1] (analytic) = 10.075248362241767 " "
y[1] (numeric) = 10.075248362241766 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.763089876828611300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.659744043435387 " "
Order of pole = 8.968252259944435 " "
x[1] = -0.773 " "
y[1] (analytic) = 10.075371321846712 " "
y[1] (numeric) = 10.07537132184671 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.76306836011941900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.63925958967038 " "
Order of pole = 8.911545118308183 " "
x[1] = -0.772 " "
y[1] (analytic) = 10.07549438221303 " "
y[1] (numeric) = 10.075494382213027 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52609365260761100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.618936196293285 " "
Order of pole = 8.855301832332373 " "
x[1] = -0.771 " "
y[1] (analytic) = 10.075617543341975 " "
y[1] (numeric) = 10.075617543341972 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.526050550765649000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.598772124738593 " "
Order of pole = 8.799517413588987 " "
x[1] = -0.77 " "
y[1] (analytic) = 10.075740805234805 " "
y[1] (numeric) = 10.075740805234801 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.5260074147150594000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.578765660833488 " "
Order of pole = 8.744186943599125 " "
x[1] = -0.769 " "
y[1] (analytic) = 10.075864167892778 " "
y[1] (numeric) = 10.075864167892775 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52596424445795200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.558915114376045 " "
Order of pole = 8.689305572623695 " "
x[1] = -0.768 " "
y[1] (analytic) = 10.075987631317151 " "
y[1] (numeric) = 10.07598763131715 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.762960519998218500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.539218818709918 " "
Order of pole = 8.634868518443156 " "
x[1] = -0.767 " "
y[1] (analytic) = 10.07611119550919 " "
y[1] (numeric) = 10.076111195509187 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52587780133262700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.51967513032443 " "
Order of pole = 8.58087106521139 " "
x[1] = -0.766 " "
y[1] (analytic) = 10.07623486047015 " "
y[1] (numeric) = 10.076234860470146 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.525834528468636500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.50028242844767 " "
Order of pole = 8.527308562288262 " "
x[1] = -0.765 " "
y[1] (analytic) = 10.076358626201296 " "
y[1] (numeric) = 10.076358626201293 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.525791221406582000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.481039114656962 " "
Order of pole = 8.474176423122763 " "
x[1] = -0.764 " "
y[1] (analytic) = 10.07648249270389 " "
y[1] (numeric) = 10.076482492703887 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52574788014857900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.4619436124915 " "
Order of pole = 8.42147012414189 " "
x[1] = -0.763 " "
y[1] (analytic) = 10.076606459979196 " "
y[1] (numeric) = 10.076606459979194 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.762852252348374200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.442994367080876 " "
Order of pole = 8.369185203685696 " "
x[1] = -0.762 " "
y[1] (analytic) = 10.076730528028483 " "
y[1] (numeric) = 10.07673052802848 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.525661095053209700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.424189844773146 " "
Order of pole = 8.317317260940456 " "
x[1] = -0.761 " "
y[1] (analytic) = 10.076854696853013 " "
y[1] (numeric) = 10.07685469685301 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.525617651220085400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.40552853277404 " "
Order of pole = 8.265861954903968 " "
x[1] = -0.76 " "
y[1] (analytic) = 10.076978966454057 " "
y[1] (numeric) = 10.076978966454053 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.525574173199500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.387008938795091 " "
Order of pole = 8.214815003376607 " "
x[1] = -0.759 " "
y[1] (analytic) = 10.07710333683288 " "
y[1] (numeric) = 10.077103336832877 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52553066099357700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.368629590704948 " "
Order of pole = 8.16417218196127 " "
x[1] = -0.758 " "
y[1] (analytic) = 10.077227807990756 " "
y[1] (numeric) = 10.077227807990752 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52548711460444530000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.350389036191547 " "
Order of pole = 8.113929323094602 " "
x[1] = -0.757 " "
y[1] (analytic) = 10.077352379928952 " "
y[1] (numeric) = 10.077352379928948 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52544353403423270000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.332285842428726 " "
Order of pole = 8.064082315090907 " "
x[1] = -0.756 " "
y[1] (analytic) = 10.07747705264874 " "
y[1] (numeric) = 10.077477052648737 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52539991928506940000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.314318595750024 " "
Order of pole = 8.014627101206692 " "
x[1] = -0.755 " "
y[1] (analytic) = 10.077601826151396 " "
y[1] (numeric) = 10.077601826151392 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52535627035908700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.296485901330007 " "
Order of pole = 7.965559678726777 " "
x[1] = -0.754 " "
y[1] (analytic) = 10.077726700438193 " "
y[1] (numeric) = 10.077726700438188 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28796888088762700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.278786382871926 " "
Order of pole = 7.916876098068705 " "
x[1] = -0.753 " "
y[1] (analytic) = 10.077851675510404 " "
y[1] (numeric) = 10.077851675510399 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28790330497779900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.261218682297633 " "
Order of pole = 7.868572461893187 " "
x[1] = -0.752 " "
y[1] (analytic) = 10.077976751369308 " "
y[1] (numeric) = 10.0779767513693 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.0504502370831300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.243781459450675 " "
Order of pole = 7.820644924252967 " "
x[1] = -0.751 " "
y[1] (analytic) = 10.078101928016178 " "
y[1] (numeric) = 10.078101928016173 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28777199939448500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.226473391799109 " "
Order of pole = 7.773089689740367 " "
x[1] = -0.75 " "
y[1] (analytic) = 10.078227205452297 " "
y[1] (numeric) = 10.078227205452292 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28770626972741500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.209293174148794 " "
Order of pole = 7.725903012665313 " "
x[1] = -0.749 " "
y[1] (analytic) = 10.078352583678942 " "
y[1] (numeric) = 10.078352583678937 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.287640488814352000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.19223951835686 " "
Order of pole = 7.679081196233312 " "
x[1] = -0.748 " "
y[1] (analytic) = 10.078478062697393 " "
y[1] (numeric) = 10.078478062697387 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28757465665851200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.175311153056425 " "
Order of pole = 7.6326205917562575 " "
x[1] = -0.747 " "
y[1] (analytic) = 10.07860364250893 " "
y[1] (numeric) = 10.078603642508927 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52500584884207400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.158506823383174 " "
Order of pole = 7.586517597868216 " "
x[1] = -0.746 " "
y[1] (analytic) = 10.07872932311484 " "
y[1] (numeric) = 10.078729323114837 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.524961892420910300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.14182529070896 " "
Order of pole = 7.540768659761532 " "
x[1] = -0.745 " "
y[1] (analytic) = 10.078855104516405 " "
y[1] (numeric) = 10.078855104516402 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.524917901844333000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.125265332380508 " "
Order of pole = 7.495370268437554 " "
x[1] = -0.744 " "
y[1] (analytic) = 10.078980986714908 " "
y[1] (numeric) = 10.078980986714905 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.5248738771144900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.108825741459613 " "
Order of pole = 7.450318959961322 " "
x[1] = -0.743 " "
y[1] (analytic) = 10.079106969711637 " "
y[1] (numeric) = 10.079106969711633 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52482981823353300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.092505326475653 " "
Order of pole = 7.405611314752270 " "
x[1] = -0.742 " "
y[1] (analytic) = 10.079233053507878 " "
y[1] (numeric) = 10.079233053507872 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28717858780542200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.07630291117468 " "
Order of pole = 7.361243956864236 " "
x[1] = -0.741 " "
y[1] (analytic) = 10.079359238104916 " "
y[1] (numeric) = 10.079359238104912 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52474159802688900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.06021733428001 " "
Order of pole = 7.317213553299283 " "
x[1] = -0.74 " "
y[1] (analytic) = 10.079485523504044 " "
y[1] (numeric) = 10.07948552350404 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52469743670551060000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.044247449251575 " "
Order of pole = 7.273516813317265 " "
x[1] = -0.739 " "
y[1] (analytic) = 10.07961190970655 " "
y[1] (numeric) = 10.079611909706546 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52465324124163800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.028392124056621 " "
Order of pole = 7.23015048777863 " "
x[1] = -0.738 " "
y[1] (analytic) = 10.079738396713728 " "
y[1] (numeric) = 10.079738396713722 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28691351745614300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 11.012650240937084 " "
Order of pole = 7.18711136847687 " "
x[1] = -0.737 " "
y[1] (analytic) = 10.079864984526866 " "
y[1] (numeric) = 10.07986498452686 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28684712184256500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.99702069618751 " "
Order of pole = 7.1443962875020475 " "
x[1] = -0.736 " "
y[1] (analytic) = 10.07999167314726 " "
y[1] (numeric) = 10.079991673147255 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.286780675024967000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.981502399933678 " "
Order of pole = 7.102002116605690 " "
x[1] = -0.735 " "
y[1] (analytic) = 10.080118462576204 " "
y[1] (numeric) = 10.080118462576198 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.286714177006593000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.966094275918568 " "
Order of pole = 7.059925766587291 " "
x[1] = -0.734 " "
y[1] (analytic) = 10.080245352814993 " "
y[1] (numeric) = 10.080245352814988 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.2866476277906900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.950795261287265 " "
Order of pole = 7.018164186677119 " "
x[1] = -0.733 " "
y[1] (analytic) = 10.080372343864923 " "
y[1] (numeric) = 10.080372343864918 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28658102738051100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.935604306380434 " "
Order of pole = 6.976714363944204 " "
x[1] = -0.732 " "
y[1] (analytic) = 10.080499435727292 " "
y[1] (numeric) = 10.080499435727287 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28651437577930600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.920520374532298 " "
Order of pole = 6.9355733227171115 " "
x[1] = -0.731 " "
y[1] (analytic) = 10.080626628403401 " "
y[1] (numeric) = 10.080626628403394 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.0485968973204400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.905542441865204 " "
Order of pole = 6.894738123994400 " "
x[1] = -0.73 " "
y[1] (analytic) = 10.080753921894546 " "
y[1] (numeric) = 10.080753921894539 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04850789202245500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.890669497098218 " "
Order of pole = 6.854205864896215 " "
x[1] = -0.729 " "
y[1] (analytic) = 10.080881316202031 " "
y[1] (numeric) = 10.080881316202023 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.81052352310349500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.875900541349644 " "
Order of pole = 6.8139736780975895 " "
x[1] = -0.728 " "
y[1] (analytic) = 10.081008811327154 " "
y[1] (numeric) = 10.081008811327147 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04832967670581800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.861234587951929 " "
Order of pole = 6.7740387312980275 " "
x[1] = -0.727 " "
y[1] (analytic) = 10.081136407271222 " "
y[1] (numeric) = 10.081136407271215 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04824046669586800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.846670662259715 " "
Order of pole = 6.734398226670514 " "
x[1] = -0.726 " "
y[1] (analytic) = 10.081264104035537 " "
y[1] (numeric) = 10.08126410403553 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04815118845730300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.83220780147459 " "
Order of pole = 6.6950494003597 " "
x[1] = -0.725 " "
y[1] (analytic) = 10.081391901621405 " "
y[1] (numeric) = 10.081391901621398 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04806184199448200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.817845054458852 " "
Order of pole = 6.65598952194712 " "
x[1] = -0.724 " "
y[1] (analytic) = 10.08151980003013 " "
y[1] (numeric) = 10.081519800030124 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.285979320483828000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.803581481563988 " "
Order of pole = 6.617215893959823 " "
x[1] = -0.723 " "
y[1] (analytic) = 10.081647799263022 " "
y[1] (numeric) = 10.081647799263017 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28591220831014500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.789416154455369 " "
Order of pole = 6.578725851367388 " "
x[1] = -0.722 " "
y[1] (analytic) = 10.08177589932139 " "
y[1] (numeric) = 10.081775899321384 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28584504497809100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.77534815594284 " "
Order of pole = 6.540516761096178 " "
x[1] = -0.721 " "
y[1] (analytic) = 10.08190410020654 " "
y[1] (numeric) = 10.081904100206534 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28577783049094800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.761376579816343 " "
Order of pole = 6.502586021558152 " "
x[1] = -0.72 " "
y[1] (analytic) = 10.082032401919786 " "
y[1] (numeric) = 10.08203240191978 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04761408646932200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.747500530678025 " "
Order of pole = 6.464931062169036 " "
x[1] = -0.719 " "
y[1] (analytic) = 10.082160804462436 " "
y[1] (numeric) = 10.08216080446243 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04752433075267800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.733719123784473 " "
Order of pole = 6.427549342896214 " "
x[1] = -0.718 " "
y[1] (analytic) = 10.082289307835804 " "
y[1] (numeric) = 10.082289307835799 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28557588013178400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.720031484888938 " "
Order of pole = 6.390438353806282 " "
x[1] = -0.717 " "
y[1] (analytic) = 10.082417912041207 " "
y[1] (numeric) = 10.082417912041201 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.285508461057106000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.706436750084388 " "
Order of pole = 6.353595614614797 " "
x[1] = -0.716 " "
y[1] (analytic) = 10.082546617079954 " "
y[1] (numeric) = 10.08254661707995 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52362732722917600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.692934065651096 " "
Order of pole = 6.317018674249233 " "
x[1] = -0.715 " "
y[1] (analytic) = 10.082675422953365 " "
y[1] (numeric) = 10.082675422953361 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52358231299670100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.679522587909025 " "
Order of pole = 6.280705110425856 " "
x[1] = -0.714 " "
y[1] (analytic) = 10.082804329662757 " "
y[1] (numeric) = 10.082804329662753 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52353726467617530000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.666201483069703 " "
Order of pole = 6.244652529224865 " "
x[1] = -0.713 " "
y[1] (analytic) = 10.082933337209447 " "
y[1] (numeric) = 10.082933337209443 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52349218226979800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.65296992709079 " "
Order of pole = 6.2088585646733065 " "
x[1] = -0.712 " "
y[1] (analytic) = 10.083062445594752 " "
y[1] (numeric) = 10.083062445594749 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52344706577976900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.63982710553556 " "
Order of pole = 6.173320878342146 " "
x[1] = -0.711 " "
y[1] (analytic) = 10.083191654819997 " "
y[1] (numeric) = 10.083191654819991 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28510287281243300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.626772213431607 " "
Order of pole = 6.138037158940982 " "
x[1] = -0.71 " "
y[1] (analytic) = 10.083320964886498 " "
y[1] (numeric) = 10.083320964886493 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28503509583634200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.61380445513684 " "
Order of pole = 6.10300512193411 " "
x[1] = -0.709 " "
y[1] (analytic) = 10.08345037579558 " "
y[1] (numeric) = 10.083450375795575 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28496726774468800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.600923044202357 " "
Order of pole = 6.068222509146963 " "
x[1] = -0.708 " "
y[1] (analytic) = 10.083579887548568 " "
y[1] (numeric) = 10.083579887548563 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.284899388540778000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.588127203239742 " "
Order of pole = 6.033687088385620 " "
x[1] = -0.707 " "
y[1] (analytic) = 10.083709500146783 " "
y[1] (numeric) = 10.083709500146778 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28483145822792500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.575416163794277 " "
Order of pole = 5.999396653073510 " "
x[1] = -0.706 " "
y[1] (analytic) = 10.083839213591554 " "
y[1] (numeric) = 10.083839213591547 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04635130241259200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.56278916621227 " "
Order of pole = 5.965349021870452 " "
x[1] = -0.705 " "
y[1] (analytic) = 10.083969027884205 " "
y[1] (numeric) = 10.083969027884198 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04626059238486800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.550245459519449 " "
Order of pole = 5.931542038324444 " "
x[1] = -0.704 " "
y[1] (analytic) = 10.084098943026065 " "
y[1] (numeric) = 10.084098943026058 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04616981422515200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.53778430129691 " "
Order of pole = 5.897973570515731 " "
x[1] = -0.703 " "
y[1] (analytic) = 10.084228959018462 " "
y[1] (numeric) = 10.084228959018455 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04607896793787200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.525404957557397 " "
Order of pole = 5.864641510701930 " "
x[1] = -0.702 " "
y[1] (analytic) = 10.084359075862727 " "
y[1] (numeric) = 10.08435907586272 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04598805352746300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.51310670262823 " "
Order of pole = 5.831543774982425 " "
x[1] = -0.701 " "
y[1] (analytic) = 10.08448929356019 " "
y[1] (numeric) = 10.084489293560184 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04589707099835600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.50088881903464 " "
Order of pole = 5.798678302963985 " "
x[1] = -0.7 " "
y[1] (analytic) = 10.084619612112185 " "
y[1] (numeric) = 10.084619612112178 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04580602035498900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.488750597380461 " "
Order of pole = 5.766043057418141 " "
x[1] = -0.699 " "
y[1] (analytic) = 10.08475003152004 " "
y[1] (numeric) = 10.084750031520034 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28428617620135400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.476691336240503 " "
Order of pole = 5.733636023973215 " "
x[1] = -0.698 " "
y[1] (analytic) = 10.084880551785096 " "
y[1] (numeric) = 10.084880551785089 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04562371474324700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.46471034204509 " "
Order of pole = 5.701455210782804 " "
x[1] = -0.697 " "
y[1] (analytic) = 10.085011172908684 " "
y[1] (numeric) = 10.085011172908677 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04553245978375900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.452806928970478 " "
Order of pole = 5.669498648211473 " "
x[1] = -0.696 " "
y[1] (analytic) = 10.085141894892141 " "
y[1] (numeric) = 10.085141894892136 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28408085254584800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.440980418834238 " "
Order of pole = 5.637764388535164 " "
x[1] = -0.695 " "
y[1] (analytic) = 10.085272717736807 " "
y[1] (numeric) = 10.0852727177368 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04534974557981100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.429230140985535 " "
Order of pole = 5.606250505626193 " "
x[1] = -0.694 " "
y[1] (analytic) = 10.085403641444016 " "
y[1] (numeric) = 10.085403641444008 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.0452582863442600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.417555432204802 " "
Order of pole = 5.574955094665864 " "
x[1] = -0.693 " "
y[1] (analytic) = 10.08553466601511 " "
y[1] (numeric) = 10.085534666015104 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04516675902560100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.405955636596369 " "
Order of pole = 5.543876271836147 " "
x[1] = -0.692 " "
y[1] (analytic) = 10.085665791451431 " "
y[1] (numeric) = 10.085665791451424 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04507516362829800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.394430105493726 " "
Order of pole = 5.513012174048615 " "
x[1] = -0.691 " "
y[1] (analytic) = 10.085797017754318 " "
y[1] (numeric) = 10.085797017754311 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.04498350015681800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.382978197355706 " "
Order of pole = 5.482360958646279 " "
x[1] = -0.69 " "
y[1] (analytic) = 10.085928344925117 " "
y[1] (numeric) = 10.08592834492511 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.0448917686156300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.371599277670905 " "
Order of pole = 5.451920803129667 " "
x[1] = -0.689 " "
y[1] (analytic) = 10.086059772965168 " "
y[1] (numeric) = 10.086059772965163 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28359997675690500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.360292718860938 " "
Order of pole = 5.421689904879347 " "
x[1] = -0.688 " "
y[1] (analytic) = 10.08619130187582 " "
y[1] (numeric) = 10.086191301875814 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.283531076006517000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.349057900187496 " "
Order of pole = 5.391666480889533 " "
x[1] = -0.6869999999999999 " "
y[1] (analytic) = 10.086322931658415 " "
y[1] (numeric) = 10.086322931658412 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52230808280927840000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.337894207659359 " "
Order of pole = 5.36184876750146 " "
x[1] = -0.6859999999999999 " "
y[1] (analytic) = 10.086454662314306 " "
y[1] (numeric) = 10.086454662314301 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28339312138246700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.326801033939786 " "
Order of pole = 5.33223502013767 " "
x[1] = -0.6849999999999999 " "
y[1] (analytic) = 10.086586493844836 " "
y[1] (numeric) = 10.08658649384483 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.283324067515530000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.315777778257791 " "
Order of pole = 5.302823513047652 " "
x[1] = -0.6839999999999999 " "
y[1] (analytic) = 10.086718426251355 " "
y[1] (numeric) = 10.08671842625135 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28325496261647500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.304823846319751 " "
Order of pole = 5.27361253905444 " "
x[1] = -0.6829999999999999 " "
y[1] (analytic) = 10.086850459535215 " "
y[1] (numeric) = 10.08685045953521 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28318580668866700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.293938650222804 " "
Order of pole = 5.244600409306305 " "
x[1] = -0.6819999999999999 " "
y[1] (analytic) = 10.086982593697767 " "
y[1] (numeric) = 10.086982593697762 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28311659973547900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.283121608368647 " "
Order of pole = 5.21578545302944 " "
x[1] = -0.6809999999999999 " "
y[1] (analytic) = 10.087114828740363 " "
y[1] (numeric) = 10.087114828740358 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.283047341760283000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.272372145380059 " "
Order of pole = 5.187166017288739 " "
x[1] = -0.6799999999999999 " "
y[1] (analytic) = 10.087247164664358 " "
y[1] (numeric) = 10.087247164664353 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.28297803276645600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.261689692018379 " "
Order of pole = 5.158740466751183 " "
x[1] = -0.6789999999999999 " "
y[1] (analytic) = 10.087379601471104 " "
y[1] (numeric) = 10.0873796014711 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52193911517158230000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.251073685099774 " "
Order of pole = 5.130507183445399 " "
x[1] = -0.6779999999999999 " "
y[1] (analytic) = 10.08751213916196 " "
y[1] (numeric) = 10.087512139161957 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.521892841157611700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.240523567418942 " "
Order of pole = 5.1024645665434605 " "
x[1] = -0.6769999999999999 " "
y[1] (analytic) = 10.087644777738282 " "
y[1] (numeric) = 10.087644777738278 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52184653313797900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.230038787667073 " "
Order of pole = 5.074611032125170 " "
x[1] = -0.6759999999999999 " "
y[1] (analytic) = 10.087777517201427 " "
y[1] (numeric) = 10.087777517201424 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52180019111494270000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.219618800356063 " "
Order of pole = 5.046945012961007 " "
x[1] = -0.6749999999999999 " "
y[1] (analytic) = 10.087910357552754 " "
y[1] (numeric) = 10.087910357552751 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.521753815090760000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.209263065739835 " "
Order of pole = 5.019464958286253 " "
x[1] = -0.6739999999999999 " "
y[1] (analytic) = 10.088043298793623 " "
y[1] (numeric) = 10.088043298793622 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.76085370253384600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.198971049742916 " "
Order of pole = 4.992169333596635 " "
x[1] = -0.6729999999999999 " "
y[1] (analytic) = 10.088176340925399 " "
y[1] (numeric) = 10.088176340925395 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52166096104799700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.188742223883457 " "
Order of pole = 4.965056620427259 " "
x[1] = -0.6719999999999999 " "
y[1] (analytic) = 10.08830948394944 " "
y[1] (numeric) = 10.088309483949436 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52161448303394100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.178576065200449 " "
Order of pole = 4.9381253161438785 " "
x[1] = -0.6709999999999999 " "
y[1] (analytic) = 10.088442727867108 " "
y[1] (numeric) = 10.088442727867106 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.76078398551389400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.168472056182404 " "
Order of pole = 4.911373933738464 " "
x[1] = -0.6699999999999999 " "
y[1] (analytic) = 10.088576072679771 " "
y[1] (numeric) = 10.08857607267977 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.76076071251590100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.158429684698689 " "
Order of pole = 4.884801001632564 " "
x[1] = -0.6689999999999999 " "
y[1] (analytic) = 10.088709518388795 " "
y[1] (numeric) = 10.088709518388793 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.76073742252412600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.148448443926927 " "
Order of pole = 4.858405063468712 " "
x[1] = -0.6679999999999999 " "
y[1] (analytic) = 10.088843064995544 " "
y[1] (numeric) = 10.088843064995542 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.760714115539703800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.138527832287572 " "
Order of pole = 4.8321846779232445 " "
x[1] = -0.6669999999999999 " "
y[1] (analytic) = 10.088976712501388 " "
y[1] (numeric) = 10.088976712501385 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.521381583127538600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.128667353373242 " "
Order of pole = 4.806138418503252 " "
x[1] = -0.6659999999999999 " "
y[1] (analytic) = 10.089110460907692 " "
y[1] (numeric) = 10.08911046090769 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.760667450597459300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.118866515886005 " "
Order of pole = 4.780264873367152 " "
x[1] = -0.6649999999999999 " "
y[1] (analytic) = 10.08924431021583 " "
y[1] (numeric) = 10.089244310215829 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7606440926419100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.109124833568687 " "
Order of pole = 4.7545626451274074 " "
x[1] = -0.6639999999999999 " "
y[1] (analytic) = 10.089378260427173 " "
y[1] (numeric) = 10.089378260427171 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.760620717698259400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.099441825143252 " "
Order of pole = 4.729030350674062 " "
x[1] = -0.6629999999999999 " "
y[1] (analytic) = 10.089512311543091 " "
y[1] (numeric) = 10.08951231154309 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.760597325767645800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.089817014245913 " "
Order of pole = 4.703666620988553 " "
x[1] = -0.6619999999999999 " "
y[1] (analytic) = 10.089646463564957 " "
y[1] (numeric) = 10.089646463564955 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.760573916851208800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.080249929365108 " "
Order of pole = 4.678470100965917 " "
x[1] = -0.6609999999999999 " "
y[1] (analytic) = 10.089780716494145 " "
y[1] (numeric) = 10.089780716494145 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.070740103781551 " "
Order of pole = 4.653439449243027 " "
x[1] = -0.6599999999999999 " "
y[1] (analytic) = 10.089915070332035 " "
y[1] (numeric) = 10.089915070332033 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.760527048065425300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.061287075505081 " "
Order of pole = 4.628573338017212 " "
x[1] = -0.6589999999999999 " "
y[1] (analytic) = 10.090049525079996 " "
y[1] (numeric) = 10.090049525079994 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.760503588198361300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.051890387216392 " "
Order of pole = 4.603870452879338 " "
x[1] = -0.6579999999999999 " "
y[1] (analytic) = 10.090184080739409 " "
y[1] (numeric) = 10.090184080739409 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.042549586210498 " "
Order of pole = 4.579329492651980 " "
x[1] = -0.6569999999999999 " "
y[1] (analytic) = 10.090318737311653 " "
y[1] (numeric) = 10.090318737311653 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.033264224334266 " "
Order of pole = 4.554949169209700 " "
x[1] = -0.6559999999999999 " "
y[1] (analytic) = 10.090453494798108 " "
y[1] (numeric) = 10.090453494798108 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.024033857934755 " "
Order of pole = 4.530728207331588 " "
x[1] = -0.6549999999999999 " "
y[1] (analytic) = 10.090588353200154 " "
y[1] (numeric) = 10.090588353200154 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.01485804779945 " "
Order of pole = 4.506665344529427 " "
x[1] = -0.6539999999999999 " "
y[1] (analytic) = 10.090723312519174 " "
y[1] (numeric) = 10.090723312519172 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.76038603416703800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 10.00573635910203 " "
Order of pole = 4.482759330892307 " "
x[1] = -0.6529999999999999 " "
y[1] (analytic) = 10.090858372756546 " "
y[1] (numeric) = 10.090858372756546 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.996668361349307 " "
Order of pole = 4.459008928934697 " "
x[1] = -0.6519999999999999 " "
y[1] (analytic) = 10.090993533913661 " "
y[1] (numeric) = 10.09099353391366 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.760338893717746400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.98765362832584 " "
Order of pole = 4.435412913437332 " "
x[1] = -0.6509999999999999 " "
y[1] (analytic) = 10.091128795991898 " "
y[1] (numeric) = 10.091128795991898 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.978691738042377 " "
Order of pole = 4.411970071299624 " "
x[1] = -0.6499999999999999 " "
y[1] (analytic) = 10.091264158992647 " "
y[1] (numeric) = 10.091264158992647 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.96978227268325 " "
Order of pole = 4.388679201388658 " "
x[1] = -0.6489999999999999 " "
y[1] (analytic) = 10.091399622917294 " "
y[1] (numeric) = 10.091399622917294 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.960924818555142 " "
Order of pole = 4.3655391143924085 " "
x[1] = -0.6479999999999999 " "
y[1] (analytic) = 10.091535187767226 " "
y[1] (numeric) = 10.091535187767226 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.952118966037006 " "
Order of pole = 4.342548632676063 " "
x[1] = -0.6469999999999999 " "
y[1] (analytic) = 10.091670853543835 " "
y[1] (numeric) = 10.091670853543835 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.943364309530203 " "
Order of pole = 4.3197065901391625 " "
x[1] = -0.6459999999999999 " "
y[1] (analytic) = 10.09180662024851 " "
y[1] (numeric) = 10.09180662024851 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.934660447410062 " "
Order of pole = 4.29701183207672 " "
x[1] = -0.6449999999999999 " "
y[1] (analytic) = 10.091942487882644 " "
y[1] (numeric) = 10.091942487882642 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.76017336754853200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.926006981975855 " "
Order of pole = 4.274463215035550 " "
x[1] = -0.6439999999999999 " "
y[1] (analytic) = 10.092078456447627 " "
y[1] (numeric) = 10.092078456447625 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7601496530829800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.917403519404838 " "
Order of pole = 4.252059606682778 " "
x[1] = -0.6429999999999999 " "
y[1] (analytic) = 10.092214525944854 " "
y[1] (numeric) = 10.092214525944852 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.760125921653398800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.908849669706287 " "
Order of pole = 4.229799885674083 " "
x[1] = -0.6419999999999999 " "
y[1] (analytic) = 10.09235069637572 " "
y[1] (numeric) = 10.092350696375718 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.760102173260943700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.900345046671452 " "
Order of pole = 4.207682941509773 " "
x[1] = -0.6409999999999999 " "
y[1] (analytic) = 10.092486967741623 " "
y[1] (numeric) = 10.09248696774162 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.52015681581354100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.891889267832273 " "
Order of pole = 4.185707674416928 " "
x[1] = -0.6399999999999999 " "
y[1] (analytic) = 10.092623340043954 " "
y[1] (numeric) = 10.092623340043952 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.76005462559203600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.883481954414838 " "
Order of pole = 4.163872995215787 " "
x[1] = -0.6389999999999999 " "
y[1] (analytic) = 10.092759813284117 " "
y[1] (numeric) = 10.092759813284115 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.760030826317896800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.875122731293585 " "
Order of pole = 4.1421778251881705 " "
x[1] = -0.6379999999999999 " "
y[1] (analytic) = 10.092896387463508 " "
y[1] (numeric) = 10.092896387463506 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.76000701008551100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.866811226950851 " "
Order of pole = 4.120621095961958 " "
x[1] = -0.6369999999999999 " "
y[1] (analytic) = 10.09303306258353 " "
y[1] (numeric) = 10.093033062583528 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.759983176896037500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.8585470734314 " "
Order of pole = 4.099201749380384 " "
x[1] = -0.6359999999999999 " "
y[1] (analytic) = 10.09316983864558 " "
y[1] (numeric) = 10.09316983864558 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.850329906301399 " "
Order of pole = 4.077918737384586 " "
x[1] = -0.6349999999999999 " "
y[1] (analytic) = 10.093306715651064 " "
y[1] (numeric) = 10.093306715651064 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.84215936460583 " "
Order of pole = 4.056771021891343 " "
x[1] = -0.6339999999999999 " "
y[1] (analytic) = 10.093443693601387 " "
y[1] (numeric) = 10.093443693601385 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.759911575596691500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.834035090827866 " "
Order of pole = 4.0357575746767544 " "
x[1] = -0.6329999999999999 " "
y[1] (analytic) = 10.093580772497951 " "
y[1] (numeric) = 10.093580772497948 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.51977534918094100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.825956730847842 " "
Order of pole = 4.0148773772584825 " "
x[1] = -0.6319999999999999 " "
y[1] (analytic) = 10.093717952342159 " "
y[1] (numeric) = 10.093717952342157 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.759863756632968300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.817923933905274 " "
Order of pole = 3.9941294207871323 " "
x[1] = -0.6309999999999999 " "
y[1] (analytic) = 10.093855233135422 " "
y[1] (numeric) = 10.09385523313542 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.759839821725347500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 9.809936352555656 " "
Order of pole = 3.9735127059219373 " "
x[1] = -0.6299999999999999 " "
y[1] (analytic) = 10.093992614879147 " "
y[1] (numeric) = 10.093992614879145 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75981586986877200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ;"
Iterations = 170
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds
"Expected Time Remaining "= 0 Years 0 Days 0 Hours 25 Minutes 17 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 25 Minutes 0 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 28 Minutes 2 Seconds
"Time to Timeout " Unknown
Percent Done = 10.687500000000009 "%"
(%o54) true
(%o54) diffeq.max