(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
array_tmp3 : array_tmp2 - array_const_1 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
array_tmp2 : array_tmp1 , array_tmp3 : array_tmp2 ,
2 2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
array_tmp2 : array_tmp1 , array_tmp3 : array_tmp2 ,
3 3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
array_tmp2 : array_tmp1 , array_tmp3 : array_tmp2 ,
4 4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
array_tmp2 : array_tmp1 , array_tmp3 : array_tmp2 ,
5 5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
array_tmp1_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------, array_tmp2 : array_tmp1 ,
kkk kkk - 1 kkk kkk
array_tmp3 : array_tmp2 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp3 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), order_d : 1, if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp3 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
array_tmp3 : array_tmp2 - array_const_1 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
array_tmp2 : array_tmp1 , array_tmp3 : array_tmp2 ,
2 2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
array_tmp2 : array_tmp1 , array_tmp3 : array_tmp2 ,
3 3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
array_tmp2 : array_tmp1 , array_tmp3 : array_tmp2 ,
4 4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
array_tmp2 : array_tmp1 , array_tmp3 : array_tmp2 ,
5 5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
array_tmp1_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------, array_tmp2 : array_tmp1 ,
kkk kkk - 1 kkk kkk
array_tmp3 : array_tmp2 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp3 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), order_d : 1, if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp3 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i32) log_revs(file, revs) := printf(file, revs)
(%o32) log_revs(file, revs) := printf(file, revs)
(%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i35) logstart(file) := printf(file, "")
(%o35) logstart(file) := printf(file, "
")
(%i36) logend(file) := printf(file, "
~%")
(%o36) logend(file) := printf(file, "~%")
(%i37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i40) factorial_2(nnn) := nnn!
(%o40) factorial_2(nnn) := nnn!
(%i41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i46) Si(x) := 0.0
(%o46) Si(x) := 0.0
(%i47) Ci(x) := 0.0
(%o47) Ci(x) := 0.0
(%i48) ln(x) := log(x)
(%o48) ln(x) := log(x)
(%i49) arcsin(x) := asin(x)
(%o49) arcsin(x) := asin(x)
(%i50) arccos(x) := acos(x)
(%o50) arccos(x) := acos(x)
(%i51) arctan(x) := atan(x)
(%o51) arctan(x) := atan(x)
(%i52) omniabs(x) := abs(x)
(%o52) omniabs(x) := abs(x)
(%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i54) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%o54) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%i55) exact_soln_y(x) := block(- x - cos(x) + 2.0)
(%o55) exact_soln_y(x) := block(- x - cos(x) + 2.0)
(%i56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/sub_sin_cpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x) - 1,0;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS,
"glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (2.0 - cos(x) - x) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_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_0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0 : 0.0, term : 1 + term),
term
array_const_0 : 0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05,
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = sin(x) - 1,0;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-13T02:49:50-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sub_sin_c"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x) - 1,0;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 156 | "), logitem_str(html_log_file, "sub_sin_c diffeq.max"),
logitem_str(html_log_file,
"sub_sin_c maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%o56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/sub_sin_cpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x) - 1,0;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS,
"glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (2.0 - cos(x) - x) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_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_0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0 : 0.0, term : 1 + term),
term
array_const_0 : 0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05,
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = sin(x) - 1,0;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-13T02:49:50-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sub_sin_c"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x) - 1,0;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 156 | "), logitem_str(html_log_file, "sub_sin_c diffeq.max"),
logitem_str(html_log_file,
"sub_sin_c maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i57) main()
"##############ECHO OF PROBLEM#################"
"##############temp/sub_sin_cpostode.ode#################"
"diff ( y , x , 1 ) = sin(x) - 1,0;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.1,"
"x_end:5.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.05,"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (2.0 - cos(x) - x) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 4.9 ""
estimated_steps = 4900. ""
step_error = 2.040816326530612300000000000000E-14 ""
est_needed_step_err = 2.040816326530612300000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 2.467204025104944900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
max_value3 = 2.467204025104944900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
value3 = 2.467204025104944900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = 0.1 " "
y[1] (analytic) = 0.9049958347219743 " "
y[1] (numeric) = 0.9049958347219743 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (analytic) = 0.9049958347219743 " "
y[1] (numeric) = 0.9049958347219743 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.101 " "
y[1] (analytic) = 0.9040961656240234 " "
y[1] (numeric) = 0.9040961656240234 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10200000000000001 " "
y[1] (analytic) = 0.9031974914298239 " "
y[1] (numeric) = 0.903197491429824 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.22921402590212800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10300000000000001 " "
y[1] (analytic) = 0.9022998120380501 " "
y[1] (numeric) = 0.9022998120380502 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.230436945473217400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10400000000000001 " "
y[1] (analytic) = 0.9014031273463815 " "
y[1] (numeric) = 0.9014031273463815 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10500000000000001 " "
y[1] (analytic) = 0.9005074372515027 " "
y[1] (numeric) = 0.9005074372515026 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.232886013705495200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10600000000000001 " "
y[1] (analytic) = 0.8996127416491037 " "
y[1] (numeric) = 0.8996127416491035 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.234112160961590700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10700000000000001 " "
y[1] (analytic) = 0.8987190404338798 " "
y[1] (numeric) = 0.89871904043388 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.235339382694248500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10800000000000001 " "
y[1] (analytic) = 0.8978263334995332 " "
y[1] (numeric) = 0.8978263334995331 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.236567678180864700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10900000000000001 " "
y[1] (analytic) = 0.8969346207387701 " "
y[1] (numeric) = 0.89693462073877 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.237797046690771200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000001 " "
y[1] (analytic) = 0.8960439020433032 " "
y[1] (numeric) = 0.8960439020433032 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11100000000000002 " "
y[1] (analytic) = 0.8951541773038516 " "
y[1] (numeric) = 0.8951541773038516 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11200000000000002 " "
y[1] (analytic) = 0.8942654464101397 " "
y[1] (numeric) = 0.8942654464101398 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.241491582932045400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11300000000000002 " "
y[1] (analytic) = 0.8933777092508988 " "
y[1] (numeric) = 0.8933777092508989 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.242725236066258600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11400000000000002 " "
y[1] (analytic) = 0.8924909657138657 " "
y[1] (numeric) = 0.8924909657138659 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.48791991689716700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11500000000000002 " "
y[1] (analytic) = 0.8916052156857843 " "
y[1] (numeric) = 0.8916052156857843 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11600000000000002 " "
y[1] (analytic) = 0.8907204590524042 " "
y[1] (numeric) = 0.8907204590524043 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.246432607831048200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11700000000000002 " "
y[1] (analytic) = 0.8898366956984822 " "
y[1] (numeric) = 0.8898366956984824 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.495341066494635400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11800000000000002 " "
y[1] (analytic) = 0.888953925507782 " "
y[1] (numeric) = 0.8889539255077822 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.497819049487818600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11900000000000002 " "
y[1] (analytic) = 0.8880721483630734 " "
y[1] (numeric) = 0.8880721483630736 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.500299163016337400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000002 " "
y[1] (analytic) = 0.8871913641461339 " "
y[1] (numeric) = 0.8871913641461339 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12100000000000002 " "
y[1] (analytic) = 0.8863115727377471 " "
y[1] (numeric) = 0.8863115727377473 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.505265775094789000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12200000000000003 " "
y[1] (analytic) = 0.8854327740177051 " "
y[1] (numeric) = 0.8854327740177053 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.253876135155300400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12300000000000003 " "
y[1] (analytic) = 0.8845549678648064 " "
y[1] (numeric) = 0.8845549678648065 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.255120444696706300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12400000000000003 " "
y[1] (analytic) = 0.8836781541568571 " "
y[1] (numeric) = 0.8836781541568571 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12500000000000003 " "
y[1] (analytic) = 0.8828023327706709 " "
y[1] (numeric) = 0.882802332770671 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.25761224615336810000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12600000000000003 " "
y[1] (analytic) = 0.8819275035820694 " "
y[1] (numeric) = 0.8819275035820694 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12700000000000003 " "
y[1] (analytic) = 0.8810536664658815 " "
y[1] (numeric) = 0.8810536664658816 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.260108284979425400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12800000000000003 " "
y[1] (analytic) = 0.8801808212959444 " "
y[1] (numeric) = 0.8801808212959445 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.261357891200704500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12900000000000003 " "
y[1] (analytic) = 0.8793089679451036 " "
y[1] (numeric) = 0.8793089679451036 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13000000000000003 " "
y[1] (analytic) = 0.8784381062852119 " "
y[1] (numeric) = 0.878438106285212 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.263860272774515200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13100000000000003 " "
y[1] (analytic) = 0.8775682361871315 " "
y[1] (numeric) = 0.8775682361871315 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13200000000000003 " "
y[1] (analytic) = 0.8766993575207321 " "
y[1] (numeric) = 0.8766993575207322 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.266366873776227400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13300000000000003 " "
y[1] (analytic) = 0.8758314701548928 " "
y[1] (numeric) = 0.8758314701548928 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13400000000000004 " "
y[1] (analytic) = 0.8749645739575008 " "
y[1] (numeric) = 0.8749645739575007 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.268877686788588700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13500000000000004 " "
y[1] (analytic) = 0.8740986687954522 " "
y[1] (numeric) = 0.8740986687954521 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.27013467044297700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13600000000000004 " "
y[1] (analytic) = 0.8732337545346521 " "
y[1] (numeric) = 0.873233754534652 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.271392704255685200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13700000000000004 " "
y[1] (analytic) = 0.872369831040015 " "
y[1] (numeric) = 0.8723698310400149 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.272651787260432600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13800000000000004 " "
y[1] (analytic) = 0.8715068981754642 " "
y[1] (numeric) = 0.8715068981754641 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.273911918482176500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13900000000000004 " "
y[1] (analytic) = 0.8706449558039326 " "
y[1] (numeric) = 0.8706449558039326 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14000000000000004 " "
y[1] (analytic) = 0.8697840037873629 " "
y[1] (numeric) = 0.8697840037873629 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14100000000000004 " "
y[1] (analytic) = 0.8689240419867068 " "
y[1] (numeric) = 0.8689240419867068 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14200000000000004 " "
y[1] (analytic) = 0.868065070261926 " "
y[1] (numeric) = 0.8680650702619263 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.55792581146056900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14300000000000004 " "
y[1] (analytic) = 0.8672070884719927 " "
y[1] (numeric) = 0.8672070884719929 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.5604565262061096000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14400000000000004 " "
y[1] (analytic) = 0.8663500964748884 " "
y[1] (numeric) = 0.8663500964748886 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.56298932531448500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14500000000000005 " "
y[1] (analytic) = 0.8654940941276053 " "
y[1] (numeric) = 0.8654940941276054 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.28276210335580800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14600000000000005 " "
y[1] (analytic) = 0.8646390812861454 " "
y[1] (numeric) = 0.8646390812861455 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.284030584152761600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14700000000000005 " "
y[1] (analytic) = 0.863785057805522 " "
y[1] (numeric) = 0.863785057805522 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14800000000000005 " "
y[1] (analytic) = 0.8629320235397581 " "
y[1] (numeric) = 0.8629320235397582 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.286570661812975500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14900000000000005 " "
y[1] (analytic) = 0.8620799783418882 " "
y[1] (numeric) = 0.8620799783418884 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.57568451307857300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000005 " "
y[1] (analytic) = 0.8612289220639576 " "
y[1] (numeric) = 0.861228922063958 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.867344661270123400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15100000000000005 " "
y[1] (analytic) = 0.8603788545570226 " "
y[1] (numeric) = 0.860378854557023 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.161554209496557000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15200000000000005 " "
y[1] (analytic) = 0.8595297756711507 " "
y[1] (numeric) = 0.8595297756711511 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.87498975387416600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15300000000000005 " "
y[1] (analytic) = 0.8586816852554207 " "
y[1] (numeric) = 0.8586816852554211 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.17175593092992700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15400000000000005 " "
y[1] (analytic) = 0.8578345831579232 " "
y[1] (numeric) = 0.8578345831579235 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.882647236736910000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15500000000000005 " "
y[1] (analytic) = 0.8569884692257601 " "
y[1] (numeric) = 0.8569884692257604 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.886480616109733000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15600000000000006 " "
y[1] (analytic) = 0.8561433433050455 " "
y[1] (numeric) = 0.8561433433050458 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.89031708290552670000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15700000000000006 " "
y[1] (analytic) = 0.8552992052409052 " "
y[1] (numeric) = 0.8552992052409055 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.894156633686274300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15800000000000006 " "
y[1] (analytic) = 0.8544560548774774 " "
y[1] (numeric) = 0.8544560548774777 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.598666176657509000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15900000000000006 " "
y[1] (analytic) = 0.8536138920579124 " "
y[1] (numeric) = 0.8536138920579127 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.90184497331201400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000006 " "
y[1] (analytic) = 0.8527727166243732 " "
y[1] (numeric) = 0.8527727166243734 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.603795836761471600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16100000000000006 " "
y[1] (analytic) = 0.8519325284180348 " "
y[1] (numeric) = 0.8519325284180351 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.90954560692762200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16200000000000006 " "
y[1] (analytic) = 0.851093327279086 " "
y[1] (numeric) = 0.8510933272790863 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.608933683394037400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16300000000000006 " "
y[1] (analytic) = 0.8502551130467275 " "
y[1] (numeric) = 0.8502551130467279 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.91725850602726800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16400000000000006 " "
y[1] (analytic) = 0.8494178855591737 " "
y[1] (numeric) = 0.8494178855591742 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.228159394803863000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16500000000000006 " "
y[1] (analytic) = 0.8485816446536523 " "
y[1] (numeric) = 0.8485816446536527 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.23331152220853400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16600000000000006 " "
y[1] (analytic) = 0.8477463901664039 " "
y[1] (numeric) = 0.8477463901664044 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.54808464832997500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16700000000000007 " "
y[1] (analytic) = 0.8469121219326834 " "
y[1] (numeric) = 0.8469121219326837 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.932720984409533400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16800000000000007 " "
y[1] (analytic) = 0.8460788397867584 " "
y[1] (numeric) = 0.8460788397867589 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.56099037357423900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16900000000000007 " "
y[1] (analytic) = 0.8452465435619119 " "
y[1] (numeric) = 0.8452465435619122 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.940470504428046400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000007 " "
y[1] (analytic) = 0.8444152330904394 " "
y[1] (numeric) = 0.8444152330904398 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.94434982145655500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17100000000000007 " "
y[1] (analytic) = 0.8435849082036515 " "
y[1] (numeric) = 0.8435849082036521 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.58038695232996900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17200000000000007 " "
y[1] (analytic) = 0.8427555687318736 " "
y[1] (numeric) = 0.8427555687318741 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.269490067188765000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17300000000000007 " "
y[1] (analytic) = 0.8419272145044447 " "
y[1] (numeric) = 0.8419272145044452 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.27467460606380300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17400000000000007 " "
y[1] (analytic) = 0.8410998453497193 " "
y[1] (numeric) = 0.8410998453497197 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.279863173264710000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17500000000000007 " "
y[1] (analytic) = 0.8402734610950666 " "
y[1] (numeric) = 0.8402734610950668 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.642527881764311600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17600000000000007 " "
y[1] (analytic) = 0.8394480615668704 " "
y[1] (numeric) = 0.8394480615668708 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.29025237155409800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17700000000000007 " "
y[1] (analytic) = 0.838623646590531 " "
y[1] (numeric) = 0.8386236465905311 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.323863248000252700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17800000000000007 " "
y[1] (analytic) = 0.8378002159904626 " "
y[1] (numeric) = 0.8378002159904628 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.650328809745246500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17900000000000008 " "
y[1] (analytic) = 0.8369777695900964 " "
y[1] (numeric) = 0.8369777695900966 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.652933124302405000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000008 " "
y[1] (analytic) = 0.8361563072118786 " "
y[1] (numeric) = 0.8361563072118788 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.655539436943649000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18100000000000008 " "
y[1] (analytic) = 0.8353358286772714 " "
y[1] (numeric) = 0.8353358286772719 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.31629548984226200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18200000000000008 " "
y[1] (analytic) = 0.8345163338067539 " "
y[1] (numeric) = 0.8345163338067542 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.66075804546744100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18300000000000008 " "
y[1] (analytic) = 0.8336978224198204 " "
y[1] (numeric) = 0.8336978224198207 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.99505550369335600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18400000000000008 " "
y[1] (analytic) = 0.8328802943349826 " "
y[1] (numeric) = 0.8328802943349829 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.9989769196482900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18500000000000008 " "
y[1] (analytic) = 0.8320637493697685 " "
y[1] (numeric) = 0.8320637493697688 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.00290131182643670000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18600000000000008 " "
y[1] (analytic) = 0.8312481873407233 " "
y[1] (numeric) = 0.8312481873407235 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.67121911730577600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18700000000000008 " "
y[1] (analytic) = 0.8304336080634085 " "
y[1] (numeric) = 0.8304336080634089 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.347678676994896000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18800000000000008 " "
y[1] (analytic) = 0.829620011352404 " "
y[1] (numeric) = 0.8296200113524044 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.01469230286041870000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18900000000000008 " "
y[1] (analytic) = 0.8288073970213063 " "
y[1] (numeric) = 0.8288073970213066 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.679085704628709000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000009 " "
y[1] (analytic) = 0.8279957648827295 " "
y[1] (numeric) = 0.82799576488273 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.363423687474533000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1910000000000001 " "
y[1] (analytic) = 0.8271851147483062 " "
y[1] (numeric) = 0.8271851147483066 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.02650992443078100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1920000000000001 " "
y[1] (analytic) = 0.8263754464286864 " "
y[1] (numeric) = 0.8263754464286867 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.686970019313044000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1930000000000001 " "
y[1] (analytic) = 0.8255667597335381 " "
y[1] (numeric) = 0.8255667597335385 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.37920409965873500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1940000000000001 " "
y[1] (analytic) = 0.8247590544715487 " "
y[1] (numeric) = 0.8247590544715488 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.34611801908196600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1950000000000001 " "
y[1] (analytic) = 0.8239523304504226 " "
y[1] (numeric) = 0.8239523304504229 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.04230797193658400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1960000000000001 " "
y[1] (analytic) = 0.8231465874768845 " "
y[1] (numeric) = 0.8231465874768849 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.04626481424731800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1970000000000001 " "
y[1] (analytic) = 0.8223418253566774 " "
y[1] (numeric) = 0.8223418253566775 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.35007485985966400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1980000000000001 " "
y[1] (analytic) = 0.8215380438945629 " "
y[1] (numeric) = 0.8215380438945632 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.05418726330211370000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1990000000000001 " "
y[1] (analytic) = 0.8207352428943229 " "
y[1] (numeric) = 0.8207352428943232 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.058152860756734600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2000000000000001 " "
y[1] (analytic) = 0.8199334221587583 " "
y[1] (numeric) = 0.8199334221587586 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.06212136725239370000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2010000000000001 " "
y[1] (analytic) = 0.8191325814896899 " "
y[1] (numeric) = 0.8191325814896903 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.066092778068053400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2020000000000001 " "
y[1] (analytic) = 0.8183327206879584 " "
y[1] (numeric) = 0.8183327206879587 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.07006708845203300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2030000000000001 " "
y[1] (analytic) = 0.8175338395534244 " "
y[1] (numeric) = 0.8175338395534248 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.43205905816259700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2040000000000001 " "
y[1] (analytic) = 0.8167359378849693 " "
y[1] (numeric) = 0.8167359378849698 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.43736585168619100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2050000000000001 " "
y[1] (analytic) = 0.8159390154804949 " "
y[1] (numeric) = 0.8159390154804952 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.082007369036136000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2060000000000001 " "
y[1] (analytic) = 0.8151430721369234 " "
y[1] (numeric) = 0.8151430721369236 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.723995486374365400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2070000000000001 " "
y[1] (analytic) = 0.8143481076501979 " "
y[1] (numeric) = 0.8143481076501983 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.08998196543504940000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2080000000000001 " "
y[1] (analytic) = 0.8135541218152834 " "
y[1] (numeric) = 0.8135541218152837 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.093973571719785600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2090000000000001 " "
y[1] (analytic) = 0.8127611144261655 " "
y[1] (numeric) = 0.8127611144261658 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.097968043447828000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2100000000000001 " "
y[1] (analytic) = 0.8119690852758515 " "
y[1] (numeric) = 0.811969085275852 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.469287167493471000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2110000000000001 " "
y[1] (analytic) = 0.8111780341563712 " "
y[1] (numeric) = 0.8111780341563714 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.368655187735444000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2120000000000001 " "
y[1] (analytic) = 0.8103879608587748 " "
y[1] (numeric) = 0.8103879608587751 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.73997906742998500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2130000000000001 " "
y[1] (analytic) = 0.8095988651731363 " "
y[1] (numeric) = 0.8095988651731365 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.742649656228780500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2140000000000001 " "
y[1] (analytic) = 0.8088107468885511 " "
y[1] (numeric) = 0.8088107468885513 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.372661069225552800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2150000000000001 " "
y[1] (analytic) = 0.8080236057931376 " "
y[1] (numeric) = 0.8080236057931377 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.373998255329913200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2160000000000001 " "
y[1] (analytic) = 0.8072374416740368 " "
y[1] (numeric) = 0.807237441674037 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.750672769396803000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2170000000000001 " "
y[1] (analytic) = 0.8064522543174131 " "
y[1] (numeric) = 0.8064522543174132 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.376675455591425000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2180000000000001 " "
y[1] (analytic) = 0.8056680435084534 " "
y[1] (numeric) = 0.8056680435084537 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.75603093251769900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2190000000000001 " "
y[1] (analytic) = 0.8048848090313692 " "
y[1] (numeric) = 0.8048848090313693 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.37935641493997600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2200000000000001 " "
y[1] (analytic) = 0.8041025506693945 " "
y[1] (numeric) = 0.8041025506693945 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2210000000000001 " "
y[1] (analytic) = 0.8033212682047877 " "
y[1] (numeric) = 0.8033212682047878 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.382041119247612900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22200000000000011 " "
y[1] (analytic) = 0.8025409614188316 " "
y[1] (numeric) = 0.8025409614188316 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22300000000000011 " "
y[1] (analytic) = 0.8017616300918327 " "
y[1] (numeric) = 0.8017616300918327 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22400000000000012 " "
y[1] (analytic) = 0.8009832740031221 " "
y[1] (numeric) = 0.8009832740031223 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.772150332369684400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22500000000000012 " "
y[1] (analytic) = 0.8002058929310567 " "
y[1] (numeric) = 0.8002058929310567 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22600000000000012 " "
y[1] (analytic) = 0.7994294866530168 " "
y[1] (numeric) = 0.7994294866530169 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.388769169965626000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22700000000000012 " "
y[1] (analytic) = 0.7986540549454093 " "
y[1] (numeric) = 0.7986540549454093 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22800000000000012 " "
y[1] (analytic) = 0.7978795975836656 " "
y[1] (numeric) = 0.7978795975836656 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22900000000000012 " "
y[1] (analytic) = 0.7971061143422431 " "
y[1] (numeric) = 0.7971061143422431 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000012 " "
y[1] (analytic) = 0.7963336049946251 " "
y[1] (numeric) = 0.7963336049946251 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23100000000000012 " "
y[1] (analytic) = 0.795562069313321 " "
y[1] (numeric) = 0.795562069313321 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23200000000000012 " "
y[1] (analytic) = 0.7947915070698665 " "
y[1] (numeric) = 0.7947915070698665 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23300000000000012 " "
y[1] (analytic) = 0.7940219180348236 " "
y[1] (numeric) = 0.7940219180348237 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.398227176616131000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23400000000000012 " "
y[1] (analytic) = 0.7932533019777818 " "
y[1] (numeric) = 0.7932533019777819 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.399581976976444800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23500000000000013 " "
y[1] (analytic) = 0.792485658667357 " "
y[1] (numeric) = 0.792485658667357 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23600000000000013 " "
y[1] (analytic) = 0.7917189878711924 " "
y[1] (numeric) = 0.7917189878711924 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23700000000000013 " "
y[1] (analytic) = 0.7909532893559588 " "
y[1] (numeric) = 0.790953289355959 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.807303641228083300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23800000000000013 " "
y[1] (analytic) = 0.790188562887355 " "
y[1] (numeric) = 0.7901885628873552 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.810020485663304000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23900000000000013 " "
y[1] (analytic) = 0.7894248082301074 " "
y[1] (numeric) = 0.7894248082301074 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000013 " "
y[1] (analytic) = 0.7886620251479705 " "
y[1] (numeric) = 0.7886620251479705 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24100000000000013 " "
y[1] (analytic) = 0.7879002134037272 " "
y[1] (numeric) = 0.7879002134037274 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.81818180967103800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24200000000000013 " "
y[1] (analytic) = 0.7871393727591899 " "
y[1] (numeric) = 0.7871393727591901 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.820905834587969500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24300000000000013 " "
y[1] (analytic) = 0.786379502975199 " "
y[1] (numeric) = 0.7863795029751991 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.411815822290285500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24400000000000013 " "
y[1] (analytic) = 0.7856206038116241 " "
y[1] (numeric) = 0.7856206038116242 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.413179617793432500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24500000000000013 " "
y[1] (analytic) = 0.7848626750273646 " "
y[1] (numeric) = 0.7848626750273647 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.414544301761385400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24600000000000014 " "
y[1] (analytic) = 0.784105716380349 " "
y[1] (numeric) = 0.7841057163803493 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.24772961642311200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24700000000000014 " "
y[1] (analytic) = 0.7833497276275365 " "
y[1] (numeric) = 0.7833497276275367 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.834552653736391300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24800000000000014 " "
y[1] (analytic) = 0.7825947085249153 " "
y[1] (numeric) = 0.7825947085249156 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.25593099160270100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24900000000000014 " "
y[1] (analytic) = 0.7818406588275051 " "
y[1] (numeric) = 0.7818406588275053 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.840023762105473600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (analytic) = 0.7810875782893553 " "
y[1] (numeric) = 0.7810875782893554 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.42138097632615600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2510000000000001 " "
y[1] (analytic) = 0.7803354666635463 " "
y[1] (numeric) = 0.7803354666635464 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.422750947579121700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2520000000000001 " "
y[1] (analytic) = 0.7795843237021899 " "
y[1] (numeric) = 0.77958432370219 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.424121792691760700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2530000000000001 " "
y[1] (analytic) = 0.778834149156429 " "
y[1] (numeric) = 0.7788341491564292 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.85098701906602750000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2540000000000001 " "
y[1] (analytic) = 0.7780849427764384 " "
y[1] (numeric) = 0.7780849427764386 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.85373219192123400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2550000000000001 " "
y[1] (analytic) = 0.7773367043114243 " "
y[1] (numeric) = 0.7773367043114245 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.856479099642175000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2560000000000001 " "
y[1] (analytic) = 0.7765894335096254 " "
y[1] (numeric) = 0.7765894335096255 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.429613868949706500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2570000000000001 " "
y[1] (analytic) = 0.7758431301183122 " "
y[1] (numeric) = 0.7758431301183124 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.861978102341005700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2580000000000001 " "
y[1] (analytic) = 0.7750977938837885 " "
y[1] (numeric) = 0.7750977938837885 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2590000000000001 " "
y[1] (analytic) = 0.7743534245513901 " "
y[1] (numeric) = 0.7743534245513902 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.433741996128379500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (analytic) = 0.7736100218654866 " "
y[1] (numeric) = 0.7736100218654868 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.8702395089142200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2610000000000001 " "
y[1] (analytic) = 0.7728675855694809 " "
y[1] (numeric) = 0.772867585569481 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.43649836706128400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2620000000000001 " "
y[1] (analytic) = 0.7721261154058089 " "
y[1] (numeric) = 0.7721261154058091 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.875755663416857400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2630000000000001 " "
y[1] (analytic) = 0.7713856111159412 " "
y[1] (numeric) = 0.7713856111159413 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.439258146154721600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2640000000000001 " "
y[1] (analytic) = 0.770646072440382 " "
y[1] (numeric) = 0.770646072440382 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2650000000000001 " "
y[1] (analytic) = 0.7699074991186696 " "
y[1] (numeric) = 0.7699074991186697 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.442021315412635500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2660000000000001 " "
y[1] (analytic) = 0.7691698908893779 " "
y[1] (numeric) = 0.7691698908893779 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2670000000000001 " "
y[1] (analytic) = 0.7684332474901148 " "
y[1] (numeric) = 0.7684332474901149 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.44478785665691600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2680000000000001 " "
y[1] (analytic) = 0.7676975686575239 " "
y[1] (numeric) = 0.7676975686575239 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.26900000000000013 " "
y[1] (analytic) = 0.7669628541272839 " "
y[1] (numeric) = 0.7669628541272839 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (analytic) = 0.7662291036341092 " "
y[1] (numeric) = 0.7662291036341095 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.89788790156765400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27100000000000013 " "
y[1] (analytic) = 0.765496316911751 " "
y[1] (numeric) = 0.7654963169117511 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.450330981478970300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27200000000000013 " "
y[1] (analytic) = 0.7647644936929955 " "
y[1] (numeric) = 0.7647644936929956 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.45171884126571500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27300000000000013 " "
y[1] (analytic) = 0.764033633709666 " "
y[1] (numeric) = 0.764033633709666 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27400000000000013 " "
y[1] (analytic) = 0.7633037366926224 " "
y[1] (numeric) = 0.7633037366926225 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.454497038669989300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27500000000000013 " "
y[1] (analytic) = 0.762574802371762 " "
y[1] (numeric) = 0.7625748023717621 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.45588737153671800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27600000000000013 " "
y[1] (analytic) = 0.761846830476019 " "
y[1] (numeric) = 0.7618468304760191 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.45727852399341800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27700000000000014 " "
y[1] (analytic) = 0.7611198207333651 " "
y[1] (numeric) = 0.7611198207333655 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.376011480907507400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27800000000000014 " "
y[1] (analytic) = 0.7603937728708109 " "
y[1] (numeric) = 0.7603937728708109 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27900000000000014 " "
y[1] (analytic) = 0.7596686866144033 " "
y[1] (numeric) = 0.7596686866144033 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (analytic) = 0.7589445616892291 " "
y[1] (numeric) = 0.7589445616892291 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28100000000000014 " "
y[1] (analytic) = 0.7582213978194128 " "
y[1] (numeric) = 0.758221397819413 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.92849299114499700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28200000000000014 " "
y[1] (analytic) = 0.757499194728119 " "
y[1] (numeric) = 0.7574991947281191 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.465642514674404300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28300000000000014 " "
y[1] (analytic) = 0.7567779521375504 " "
y[1] (numeric) = 0.7567779521375504 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28400000000000014 " "
y[1] (analytic) = 0.7560576697689495 " "
y[1] (numeric) = 0.7560576697689495 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28500000000000014 " "
y[1] (analytic) = 0.7553383473425987 " "
y[1] (numeric) = 0.7553383473425989 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.469835377127480800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28600000000000014 " "
y[1] (analytic) = 0.7546199845778209 " "
y[1] (numeric) = 0.7546199845778209 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28700000000000014 " "
y[1] (analytic) = 0.7539025811929785 " "
y[1] (numeric) = 0.7539025811929784 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.472634598051561500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28800000000000014 " "
y[1] (analytic) = 0.7531861369054748 " "
y[1] (numeric) = 0.7531861369054748 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28900000000000015 " "
y[1] (analytic) = 0.7524706514317545 " "
y[1] (numeric) = 0.7524706514317544 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.47543697885451500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (analytic) = 0.7517561244873029 " "
y[1] (numeric) = 0.7517561244873027 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.95367869568692300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29100000000000015 " "
y[1] (analytic) = 0.7510425557866467 " "
y[1] (numeric) = 0.7510425557866466 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.478242499138150400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29200000000000015 " "
y[1] (analytic) = 0.750329945043355 " "
y[1] (numeric) = 0.7503299450433549 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.479646430159476700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29300000000000015 " "
y[1] (analytic) = 0.7496182919700385 " "
y[1] (numeric) = 0.7496182919700384 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.481051138316581000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29400000000000015 " "
y[1] (analytic) = 0.7489075962783501 " "
y[1] (numeric) = 0.7489075962783501 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29500000000000015 " "
y[1] (analytic) = 0.7481978576789861 " "
y[1] (numeric) = 0.7481978576789858 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.967725751231694600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29600000000000015 " "
y[1] (analytic) = 0.7474890758816845 " "
y[1] (numeric) = 0.7474890758816841 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.45580969855225160000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29700000000000015 " "
y[1] (analytic) = 0.7467812505952272 " "
y[1] (numeric) = 0.7467812505952268 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.4600330702206800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29800000000000015 " "
y[1] (analytic) = 0.7460743815274394 " "
y[1] (numeric) = 0.7460743815274392 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.97617248926895200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29900000000000015 " "
y[1] (analytic) = 0.7453684683851907 " "
y[1] (numeric) = 0.7453684683851904 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.978991121077091000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (analytic) = 0.7446635108743939 " "
y[1] (numeric) = 0.7446635108743936 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.981811270224636000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30100000000000016 " "
y[1] (analytic) = 0.7439595087000066 " "
y[1] (numeric) = 0.7439595087000064 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.98463293134100300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30200000000000016 " "
y[1] (analytic) = 0.7432564615660312 " "
y[1] (numeric) = 0.7432564615660309 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.481184148547859000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30300000000000016 " "
y[1] (analytic) = 0.7425543691755143 " "
y[1] (numeric) = 0.7425543691755142 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.49514038393966820000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30400000000000016 " "
y[1] (analytic) = 0.7418532312305489 " "
y[1] (numeric) = 0.7418532312305488 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.496553466220770500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30500000000000016 " "
y[1] (analytic) = 0.741153047432273 " "
y[1] (numeric) = 0.7411530474322726 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.49390188087950670000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30600000000000016 " "
y[1] (analytic) = 0.7404538174808698 " "
y[1] (numeric) = 0.7404538174808696 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.99876372682443500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30700000000000016 " "
y[1] (analytic) = 0.7397555410755696 " "
y[1] (numeric) = 0.7397555410755696 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30800000000000016 " "
y[1] (analytic) = 0.7390582179146491 " "
y[1] (numeric) = 0.7390582179146491 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30900000000000016 " "
y[1] (analytic) = 0.7383618476954315 " "
y[1] (numeric) = 0.7383618476954312 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.00725999884846400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (analytic) = 0.7376664301142865 " "
y[1] (numeric) = 0.7376664301142863 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.505047511045270200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31100000000000017 " "
y[1] (analytic) = 0.7369719648666322 " "
y[1] (numeric) = 0.736971964866632 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.01293150228874900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31200000000000017 " "
y[1] (analytic) = 0.7362784516469335 " "
y[1] (numeric) = 0.7362784516469334 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.507884716905364700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31300000000000017 " "
y[1] (analytic) = 0.735585890148704 " "
y[1] (numeric) = 0.7355858901487038 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.018608811000213500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31400000000000017 " "
y[1] (analytic) = 0.734894280064505 " "
y[1] (numeric) = 0.7348942800645049 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.510724814088507000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31500000000000017 " "
y[1] (analytic) = 0.7342036210859466 " "
y[1] (numeric) = 0.7342036210859465 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.512145939818502500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = sin(x) - 1,0;"
Iterations = 216
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds
"Expected Time Remaining "= 0 Years 0 Days 1 Hours 5 Minutes 0 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 1 Hours 4 Minutes 22 Seconds
"Expected Total Time "= 0 Years 0 Days 1 Hours 7 Minutes 23 Seconds
"Time to Timeout " Unknown
Percent Done = 4.4285714285714315 "%"
(%o57) true
(%o57) diffeq.max