(%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 , array_tmp3 : cos(array_x ),
1 1 1 1 1
array_tmp3_g : sin(array_x ), array_tmp4 : array_tmp2 - array_tmp3 ,
1 1 1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
- array_tmp3_g array_x
1 2
array_tmp2 : array_tmp1 , array_tmp3 : ------------------------,
2 2 2 1
array_tmp3 array_x
1 2
array_tmp3_g : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
2 1 2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
- array_tmp3_g array_x
2 2
array_tmp2 : array_tmp1 , array_tmp3 : ------------------------,
3 3 3 2
array_tmp3 array_x
2 2
array_tmp3_g : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
3 2 3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
- array_tmp3_g array_x
3 2
array_tmp2 : array_tmp1 , array_tmp3 : ------------------------,
4 4 4 3
array_tmp3 array_x
3 2
array_tmp3_g : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
4 3 4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
- array_tmp3_g array_x
4 2
array_tmp2 : array_tmp1 , array_tmp3 : ------------------------,
5 5 5 4
array_tmp3 array_x
4 2
array_tmp3_g : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
5 4 5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
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_g array_x
kkk - 1 2
array_tmp3 : ------------------------------,
kkk kkk - 1
array_tmp3 array_x
kkk - 1 2
array_tmp3_g : --------------------------,
kkk kkk - 1
array_tmp4 : array_tmp2 - array_tmp3 , order_d : 1,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp4 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 , array_tmp3 : cos(array_x ),
1 1 1 1 1
array_tmp3_g : sin(array_x ), array_tmp4 : array_tmp2 - array_tmp3 ,
1 1 1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
- array_tmp3_g array_x
1 2
array_tmp2 : array_tmp1 , array_tmp3 : ------------------------,
2 2 2 1
array_tmp3 array_x
1 2
array_tmp3_g : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
2 1 2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
- array_tmp3_g array_x
2 2
array_tmp2 : array_tmp1 , array_tmp3 : ------------------------,
3 3 3 2
array_tmp3 array_x
2 2
array_tmp3_g : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
3 2 3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
- array_tmp3_g array_x
3 2
array_tmp2 : array_tmp1 , array_tmp3 : ------------------------,
4 4 4 3
array_tmp3 array_x
3 2
array_tmp3_g : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
4 3 4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
- array_tmp3_g array_x
4 2
array_tmp2 : array_tmp1 , array_tmp3 : ------------------------,
5 5 5 4
array_tmp3 array_x
4 2
array_tmp3_g : --------------------, array_tmp4 : array_tmp2 - array_tmp3 ,
5 4 5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
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_g array_x
kkk - 1 2
array_tmp3 : ------------------------------,
kkk kkk - 1
array_tmp3 array_x
kkk - 1 2
array_tmp3_g : --------------------------,
kkk kkk - 1
array_tmp4 : array_tmp2 - array_tmp3 , order_d : 1,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp4 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "| ~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i32) log_revs(file, revs) := printf(file, revs)
(%o32) log_revs(file, revs) := printf(file, revs)
(%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i35) logstart(file) := printf(file, "")
(%o35) logstart(file) := printf(file, "
")
(%i36) logend(file) := printf(file, "
~%")
(%o36) logend(file) := printf(file, "~%")
(%i37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i40) factorial_2(nnn) := nnn!
(%o40) factorial_2(nnn) := nnn!
(%i41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i46) Si(x) := 0.0
(%o46) Si(x) := 0.0
(%i47) Ci(x) := 0.0
(%o47) Ci(x) := 0.0
(%i48) ln(x) := log(x)
(%o48) ln(x) := log(x)
(%i49) arcsin(x) := asin(x)
(%o49) arcsin(x) := asin(x)
(%i50) arccos(x) := acos(x)
(%o50) arccos(x) := acos(x)
(%i51) arctan(x) := atan(x)
(%o51) arctan(x) := atan(x)
(%i52) omniabs(x) := abs(x)
(%o52) omniabs(x) := abs(x)
(%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i54) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%o54) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%i55) exact_soln_y(x) := block(- sin(x) - cos(x) + 2.0)
(%o55) exact_soln_y(x) := block(- sin(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/subpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) - cos ( x );"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.0,"), omniout_str(ALWAYS, "x_end:10.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.00001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "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) - sin(x)) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, 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_g, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1_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_g : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + 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_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_g : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.0,
iiif, jjjf
x_end : 10.0, array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5,
1 + 0
glob_look_poles : true, glob_max_iter : 100, glob_desired_digits_correct : 10,
glob_display_interval : 0.001, glob_look_poles : true,
glob_max_iter : 10000000, glob_max_minutes : 3, glob_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 ) - cos ( x );"),
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,
"2013-01-13T02:45:34-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sub"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) - cos ( x );"),
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 diffeq.max"),
logitem_str(html_log_file,
"sub 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/subpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) - cos ( x );"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.0,"), omniout_str(ALWAYS, "x_end:10.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.00001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "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) - sin(x)) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, 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_g, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1_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_g : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + 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_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_g : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.0,
iiif, jjjf
x_end : 10.0, array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5,
1 + 0
glob_look_poles : true, glob_max_iter : 100, glob_desired_digits_correct : 10,
glob_display_interval : 0.001, glob_look_poles : true,
glob_max_iter : 10000000, glob_max_minutes : 3, glob_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 ) - cos ( x );"),
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,
"2013-01-13T02:45:34-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sub"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) - cos ( x );"),
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 diffeq.max"),
logitem_str(html_log_file,
"sub 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/subpostode.ode#################"
"diff ( y , x , 1 ) = sin ( x ) - cos ( x );"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.0,"
"x_end:10.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.00001,"
"glob_look_poles:true,"
"glob_max_iter:100,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (2.0 - cos(x) - sin(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 = 10. ""
estimated_steps = 10000. ""
step_error = 1.00000000000000E-14 ""
est_needed_step_err = 1.00000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 2.4796421808541458000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
max_value3 = 2.4796421808541458000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
value3 = 2.4796421808541458000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = 0.0 " "
y[1] (analytic) = 1. " "
y[1] (numeric) = 1. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.0 " "
y[1] (analytic) = 1. " "
y[1] (numeric) = 1. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.000E-3 " "
y[1] (analytic) = 0.999000500166625 " "
y[1] (numeric) = 0.999000500166625 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.000E-3 " "
y[1] (analytic) = 0.9980020013326664 " "
y[1] (numeric) = 0.9980020013326664 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.000E-3 " "
y[1] (analytic) = 0.997004504496623 " "
y[1] (numeric) = 0.9970045044966229 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.113558684657795200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.000E-3 " "
y[1] (analytic) = 0.9960080106559913 " "
y[1] (numeric) = 0.9960080106559914 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.114672786510964900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.000E-3 " "
y[1] (analytic) = 0.9950125208072657 " "
y[1] (numeric) = 0.9950125208072657 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.000E-3 " "
y[1] (analytic) = 0.9940180359459352 " "
y[1] (numeric) = 0.9940180359459353 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.116904306035692300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.000E-3 " "
y[1] (analytic) = 0.9930245570664852 " "
y[1] (numeric) = 0.9930245570664852 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.000E-3 " "
y[1] (analytic) = 0.9920320851623939 " "
y[1] (numeric) = 0.992032085162394 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.119140238738765100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.000000000000001000E-3 " "
y[1] (analytic) = 0.9910406212261336 " "
y[1] (numeric) = 0.9910406212261338 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.2405197140185198000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.000000000000000200E-2 " "
y[1] (analytic) = 0.9900501662491681 " "
y[1] (numeric) = 0.9900501662491682 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.121380574916992900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.100000000000000300E-2 " "
y[1] (analytic) = 0.9890607212219521 " "
y[1] (numeric) = 0.9890607212219522 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.122502391211646100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.200000000000000400E-2 " "
y[1] (analytic) = 0.9880722871339307 " "
y[1] (numeric) = 0.9880722871339307 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.300000000000000600E-2 " "
y[1] (analytic) = 0.9870848649735376 " "
y[1] (numeric) = 0.9870848649735378 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.124749313884900900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.400000000000000700E-2 " "
y[1] (analytic) = 0.9860984557281953 " "
y[1] (numeric) = 0.9860984557281954 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.125874417687126300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.500000000000000800E-2 " "
y[1] (analytic) = 0.9851130603843127 " "
y[1] (numeric) = 0.9851130603843129 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.25400122944677200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.600000000000001000E-2 " "
y[1] (analytic) = 0.9841286799272853 " "
y[1] (numeric) = 0.9841286799272854 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.128127903667219700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.700000000000001000E-2 " "
y[1] (analytic) = 0.9831453153414932 " "
y[1] (numeric) = 0.9831453153414933 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.129256283176737900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.80000000000000100E-2 " "
y[1] (analytic) = 0.982162967610301 " "
y[1] (numeric) = 0.9821629676103011 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.13038575189455400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.90000000000000100E-2 " "
y[1] (analytic) = 0.9811816377160564 " "
y[1] (numeric) = 0.9811816377160565 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.131516308447716200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.00000000000000120E-2 " "
y[1] (analytic) = 0.9802013266400892 " "
y[1] (numeric) = 0.9802013266400893 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.132647951447640600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.10000000000000130E-2 " "
y[1] (analytic) = 0.9792220353627102 " "
y[1] (numeric) = 0.9792220353627105 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.26756135898008600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.200000000000001400E-2 " "
y[1] (analytic) = 0.978243764863211 " "
y[1] (numeric) = 0.9782437648632112 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.269828982309742300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.300000000000001500E-2 " "
y[1] (analytic) = 0.9772665161198617 " "
y[1] (numeric) = 0.9772665161198619 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.272098770012473700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.400000000000001600E-2 " "
y[1] (analytic) = 0.9762902901099112 " "
y[1] (numeric) = 0.9762902901099113 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.137185359592347300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.500000000000001700E-2 " "
y[1] (analytic) = 0.975315087809585 " "
y[1] (numeric) = 0.9753150878095853 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.414967240336315700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.600000000000002000E-2 " "
y[1] (analytic) = 0.9743409101940858 " "
y[1] (numeric) = 0.9743409101940861 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.41838163524511200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.700000000000002000E-2 " "
y[1] (analytic) = 0.9733677582375908 " "
y[1] (numeric) = 0.9733677582375911 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.42179925900368830000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.800000000000002000E-2 " "
y[1] (analytic) = 0.972395632913252 " "
y[1] (numeric) = 0.9723956329132525 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.566960142751690400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.90000000000000200E-2 " "
y[1] (analytic) = 0.9714245351931949 " "
y[1] (numeric) = 0.9714245351931953 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.42864417482833400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.00000000000000200E-2 " "
y[1] (analytic) = 0.9704544660485168 " "
y[1] (numeric) = 0.9704544660485172 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.432071457651426000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.10000000000000200E-2 " "
y[1] (analytic) = 0.9694854264492869 " "
y[1] (numeric) = 0.9694854264492871 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.290334633891954700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.20000000000000230E-2 " "
y[1] (analytic) = 0.9685174173645446 " "
y[1] (numeric) = 0.9685174173645448 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.292623766428920600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.30000000000000240E-2 " "
y[1] (analytic) = 0.9675504397622988 " "
y[1] (numeric) = 0.9675504397622992 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.44237254927373670000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.40000000000000250E-2 " "
y[1] (analytic) = 0.9665844946095273 " "
y[1] (numeric) = 0.9665844946095277 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.4458126448851900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.500000000000002600E-2 " "
y[1] (analytic) = 0.9656195828721751 " "
y[1] (numeric) = 0.9656195828721755 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.599007908778600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.600000000000002600E-2 " "
y[1] (analytic) = 0.9646557055151539 " "
y[1] (numeric) = 0.9646557055151543 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.603603205901386500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.700000000000003000E-2 " "
y[1] (analytic) = 0.963692863502341 " "
y[1] (numeric) = 0.9636928635023413 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.45615205841708400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.80000000000000300E-2 " "
y[1] (analytic) = 0.962731057796578 " "
y[1] (numeric) = 0.9627310577965784 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.61280651801613800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.90000000000000300E-2 " "
y[1] (analytic) = 0.9617702893596707 " "
y[1] (numeric) = 0.9617702893596712 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.7717681493588400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.00000000000000300E-2 " "
y[1] (analytic) = 0.9608105591523879 " "
y[1] (numeric) = 0.9608105591523882 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.466520056579867600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.10000000000000300E-2 " "
y[1] (analytic) = 0.9598518681344591 " "
y[1] (numeric) = 0.9598518681344594 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.46998238420774600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.20000000000000300E-2 " "
y[1] (analytic) = 0.9588942172645757 " "
y[1] (numeric) = 0.9588942172645759 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.315631911499632400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.30000000000000300E-2 " "
y[1] (analytic) = 0.9579376075003878 " "
y[1] (numeric) = 0.9579376075003883 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.63588866720511200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.40000000000000340E-2 " "
y[1] (analytic) = 0.9569820397985059 " "
y[1] (numeric) = 0.9569820397985063 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.48038827831789500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.50000000000000340E-2 " "
y[1] (analytic) = 0.9560275151144972 " "
y[1] (numeric) = 0.9560275151144976 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.483863195586558400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.600000000000003500E-2 " "
y[1] (analytic) = 0.9550740344028864 " "
y[1] (numeric) = 0.9550740344028869 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.649788329003288000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.700000000000003600E-2 " "
y[1] (analytic) = 0.9541215986171543 " "
y[1] (numeric) = 0.9541215986171546 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.49082242630576500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.800000000000003700E-2 " "
y[1] (analytic) = 0.9531702087097362 " "
y[1] (numeric) = 0.9531702087097366 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.49430672868390140000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.90000000000000400E-2 " "
y[1] (analytic) = 0.9522198656320224 " "
y[1] (numeric) = 0.9522198656320225 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.165931382757134400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.00000000000000300E-2 " "
y[1] (analytic) = 0.9512705703343554 " "
y[1] (numeric) = 0.9512705703343556 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.3341897862664500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.10000000000000300E-2 " "
y[1] (analytic) = 0.9503223237660307 " "
y[1] (numeric) = 0.950322323766031 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.504778316346781600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.20000000000000400E-2 " "
y[1] (analytic) = 0.9493751268752948 " "
y[1] (numeric) = 0.9493751268752951 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.50827505333723600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.30000000000000400E-2 " "
y[1] (analytic) = 0.9484289806093446 " "
y[1] (numeric) = 0.9484289806093448 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.34118325636119420000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.40000000000000400E-2 " "
y[1] (analytic) = 0.947483885914326 " "
y[1] (numeric) = 0.9474838859143262 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.343518536051484600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.50000000000000400E-2 " "
y[1] (analytic) = 0.9465398437353338 " "
y[1] (numeric) = 0.9465398437353341 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.34585587067075600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.60000000000000400E-2 " "
y[1] (analytic) = 0.94559685501641 " "
y[1] (numeric) = 0.9455968550164103 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.52229288433670700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.700000000000004000E-2 " "
y[1] (analytic) = 0.9446549207005437 " "
y[1] (numeric) = 0.9446549207005438 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.175268344340841100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.800000000000004000E-2 " "
y[1] (analytic) = 0.9437140417296683 " "
y[1] (numeric) = 0.9437140417296686 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.352880163974895300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.900000000000004000E-2 " "
y[1] (analytic) = 0.9427742190446634 " "
y[1] (numeric) = 0.9427742190446635 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.177612838999960300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.000000000000004000E-2 " "
y[1] (analytic) = 0.941835453585351 " "
y[1] (numeric) = 0.9418354535853514 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.53635983992360700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.10000000000000400E-2 " "
y[1] (analytic) = 0.9408977462904972 " "
y[1] (numeric) = 0.9408977462904975 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.5398842084665205000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.20000000000000400E-2 " "
y[1] (analytic) = 0.9399610980978088 " "
y[1] (numeric) = 0.939961098097809 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.362274410870631400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.30000000000000400E-2 " "
y[1] (analytic) = 0.9390255099439339 " "
y[1] (numeric) = 0.9390255099439342 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.5469420570633200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.40000000000000500E-2 " "
y[1] (analytic) = 0.9380909827644608 " "
y[1] (numeric) = 0.9380909827644609 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.183491841434654600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.50000000000000500E-2 " "
y[1] (analytic) = 0.9371575174939163 " "
y[1] (numeric) = 0.9371575174939164 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.18467067051229600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.60000000000000500E-2 " "
y[1] (analytic) = 0.9362251150657659 " "
y[1] (numeric) = 0.9362251150657659 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.70000000000000500E-2 " "
y[1] (analytic) = 0.9352937764124114 " "
y[1] (numeric) = 0.9352937764124116 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.37406267982181280000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.80000000000000500E-2 " "
y[1] (analytic) = 0.934363502465192 " "
y[1] (numeric) = 0.9343635024651922 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.37642635162007700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.90000000000000500E-2 " "
y[1] (analytic) = 0.9334342941543812 " "
y[1] (numeric) = 0.9334342941543815 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.568188028588339400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.00000000000000500E-2 " "
y[1] (analytic) = 0.9325061524091875 " "
y[1] (numeric) = 0.9325061524091878 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.38115967762105700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.10000000000000500E-2 " "
y[1] (analytic) = 0.9315790781577526 " "
y[1] (numeric) = 0.9315790781577526 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.20000000000000500E-2 " "
y[1] (analytic) = 0.9306530723271502 " "
y[1] (numeric) = 0.9306530723271503 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.192950474927226700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.30000000000000500E-2 " "
y[1] (analytic) = 0.9297281358433866 " "
y[1] (numeric) = 0.9297281358433866 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.40000000000000500E-2 " "
y[1] (analytic) = 0.9288042696313976 " "
y[1] (numeric) = 0.928804269631398 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.58597519711797650000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.50000000000000600E-2 " "
y[1] (analytic) = 0.9278814746150503 " "
y[1] (numeric) = 0.9278814746150503 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.60000000000000600E-2 " "
y[1] (analytic) = 0.9269597517171385 " "
y[1] (numeric) = 0.9269597517171387 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.39540718476402800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.70000000000000600E-2 " "
y[1] (analytic) = 0.9260391018593859 " "
y[1] (numeric) = 0.926039101859386 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.198894325731979800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.80000000000000600E-2 " "
y[1] (analytic) = 0.9251195259624418 " "
y[1] (numeric) = 0.9251195259624418 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.90000000000000600E-2 " "
y[1] (analytic) = 0.9242010249458821 " "
y[1] (numeric) = 0.9242010249458822 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.201278720384634100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.00000000000000600E-2 " "
y[1] (analytic) = 0.923283599728208 " "
y[1] (numeric) = 0.923283599728208 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.10000000000000600E-2 " "
y[1] (analytic) = 0.9223672512268444 " "
y[1] (numeric) = 0.9223672512268443 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.203667002648288500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.20000000000000600E-2 " "
y[1] (analytic) = 0.9214519803581394 " "
y[1] (numeric) = 0.9214519803581396 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.40972519087461920000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.30000000000000600E-2 " "
y[1] (analytic) = 0.9205377880373645 " "
y[1] (numeric) = 0.9205377880373646 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.206059152652723700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.40000000000000600E-2 " "
y[1] (analytic) = 0.9196246751787116 " "
y[1] (numeric) = 0.9196246751787117 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.207256671760580800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.50000000000000600E-2 " "
y[1] (analytic) = 0.9187126426952935 " "
y[1] (numeric) = 0.9187126426952935 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.60000000000000700E-2 " "
y[1] (analytic) = 0.9178016914991424 " "
y[1] (numeric) = 0.9178016914991426 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.41930917083343380000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.70000000000000700E-2 " "
y[1] (analytic) = 0.9168918225012097 " "
y[1] (numeric) = 0.9168918225012099 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.421709949591554500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.80000000000000700E-2 " "
y[1] (analytic) = 0.9159830366113645 " "
y[1] (numeric) = 0.9159830366113645 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.90000000000000700E-2 " "
y[1] (analytic) = 0.9150753347383922 " "
y[1] (numeric) = 0.9150753347383922 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.00000000000000700E-2 " "
y[1] (analytic) = 0.9141687177899948 " "
y[1] (numeric) = 0.9141687177899948 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.10000000000000700E-2 " "
y[1] (analytic) = 0.913263186672789 " "
y[1] (numeric) = 0.9132631866727889 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.215666021390760100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.20000000000000700E-2 " "
y[1] (analytic) = 0.9123587422923058 " "
y[1] (numeric) = 0.912358742292306 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.21687114197614400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.30000000000000700E-2 " "
y[1] (analytic) = 0.91145538555299 " "
y[1] (numeric) = 0.91145538555299 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.40000000000000700E-2 " "
y[1] (analytic) = 0.9105531173581978 " "
y[1] (numeric) = 0.9105531173581978 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.50000000000000700E-2 " "
y[1] (analytic) = 0.9096519386101973 " "
y[1] (numeric) = 0.9096519386101974 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.220492121768464300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.60000000000000700E-2 " "
y[1] (analytic) = 0.9087518502101677 " "
y[1] (numeric) = 0.9087518502101676 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.221700978510684200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.70000000000000800E-2 " "
y[1] (analytic) = 0.9078528530581967 " "
y[1] (numeric) = 0.9078528530581966 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.222910762339133300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.80000000000000800E-2 " "
y[1] (analytic) = 0.9069549480532816 " "
y[1] (numeric) = 0.9069549480532816 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.90000000000000800E-2 " "
y[1] (analytic) = 0.9060581360933274 " "
y[1] (numeric) = 0.9060581360933274 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10000000000000007 " "
y[1] (analytic) = 0.9051624180751461 " "
y[1] (numeric) = 0.905162418075146 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.226545648002131700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10100000000000008 " "
y[1] (analytic) = 0.9042677948944553 " "
y[1] (numeric) = 0.9042677948944552 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.227759111729440800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10200000000000008 " "
y[1] (analytic) = 0.9033742674458782 " "
y[1] (numeric) = 0.9033742674458782 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10300000000000008 " "
y[1] (analytic) = 0.9024818366229425 " "
y[1] (numeric) = 0.9024818366229425 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10400000000000008 " "
y[1] (analytic) = 0.9015905033180787 " "
y[1] (numeric) = 0.9015905033180786 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.231404967709018700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10500000000000008 " "
y[1] (analytic) = 0.9007002684226202 " "
y[1] (numeric) = 0.9007002684226199 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.69786619438718400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10600000000000008 " "
y[1] (analytic) = 0.8998111328268014 " "
y[1] (numeric) = 0.8998111328268011 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.46768012557776600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10700000000000008 " "
y[1] (analytic) = 0.8989230974197578 " "
y[1] (numeric) = 0.8989230974197578 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10800000000000008 " "
y[1] (analytic) = 0.8980361630895257 " "
y[1] (numeric) = 0.8980361630895254 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.708836248216246000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10900000000000008 " "
y[1] (analytic) = 0.8971503307230384 " "
y[1] (numeric) = 0.8971503307230381 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.71249829578861200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000008 " "
y[1] (analytic) = 0.8962656012061283 " "
y[1] (numeric) = 0.8962656012061281 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.477442006322902700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11100000000000008 " "
y[1] (analytic) = 0.8953819754235252 " "
y[1] (numeric) = 0.8953819754235249 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.479886919993021500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11200000000000009 " "
y[1] (analytic) = 0.8944994542588545 " "
y[1] (numeric) = 0.8944994542588544 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.241166799307934400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11300000000000009 " "
y[1] (analytic) = 0.8936180385946375 " "
y[1] (numeric) = 0.8936180385946373 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.484782035893470500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11400000000000009 " "
y[1] (analytic) = 0.8927377293122896 " "
y[1] (numeric) = 0.8927377293122895 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.243616112741649500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11500000000000009 " "
y[1] (analytic) = 0.8918585272921205 " "
y[1] (numeric) = 0.89185852729212 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.97936832199626500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11600000000000009 " "
y[1] (analytic) = 0.8909804334133312 " "
y[1] (numeric) = 0.890980433413331 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.492137836005916800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11700000000000009 " "
y[1] (analytic) = 0.8901034485540162 " "
y[1] (numeric) = 0.8901034485540161 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.247296622014808600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11800000000000009 " "
y[1] (analytic) = 0.8892275735911604 " "
y[1] (numeric) = 0.8892275735911602 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.49705037854708500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11900000000000009 " "
y[1] (analytic) = 0.8883528094006383 " "
y[1] (numeric) = 0.8883528094006382 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.249754616495456900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000009 " "
y[1] (analytic) = 0.8874791568572145 " "
y[1] (numeric) = 0.8874791568572141 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.75295470112244800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1210000000000001 " "
y[1] (analytic) = 0.8866066168345406 " "
y[1] (numeric) = 0.8866066168345405 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.252216037580450000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1220000000000001 " "
y[1] (analytic) = 0.8857351902051573 " "
y[1] (numeric) = 0.8857351902051571 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.506896049524695000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1230000000000001 " "
y[1] (analytic) = 0.884864877840491 " "
y[1] (numeric) = 0.8848648778404907 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.509361717089848000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1240000000000001 " "
y[1] (analytic) = 0.8839956806108539 " "
y[1] (numeric) = 0.8839956806108537 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.51182907106056500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12500000000000008 " "
y[1] (analytic) = 0.883127599385443 " "
y[1] (numeric) = 0.8831275993854429 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.25714905229747800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12600000000000008 " "
y[1] (analytic) = 0.8822606350323401 " "
y[1] (numeric) = 0.8822606350323398 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.77515321620734100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12700000000000009 " "
y[1] (analytic) = 0.8813947884185086 " "
y[1] (numeric) = 0.8813947884185084 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.51924118275588100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12800000000000009 " "
y[1] (analytic) = 0.8805300604097956 " "
y[1] (numeric) = 0.8805300604097954 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.521715213466903500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1290000000000001 " "
y[1] (analytic) = 0.8796664518709291 " "
y[1] (numeric) = 0.8796664518709287 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.786286343865446500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1300000000000001 " "
y[1] (analytic) = 0.8788039636655172 " "
y[1] (numeric) = 0.8788039636655168 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.79000233451741700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1310000000000001 " "
y[1] (analytic) = 0.877942596656048 " "
y[1] (numeric) = 0.8779425966560478 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.529147187649466000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1320000000000001 " "
y[1] (analytic) = 0.8770823517038887 " "
y[1] (numeric) = 0.8770823517038886 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.265813891327707800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1330000000000001 " "
y[1] (analytic) = 0.8762232296692843 " "
y[1] (numeric) = 0.8762232296692841 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.53411000081381400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1340000000000001 " "
y[1] (analytic) = 0.8753652314113567 " "
y[1] (numeric) = 0.8753652314113564 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.804890752292517000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1350000000000001 " "
y[1] (analytic) = 0.8745083577881038 " "
y[1] (numeric) = 0.8745083577881034 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.808618916232818000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1360000000000001 " "
y[1] (analytic) = 0.8736526096563992 " "
y[1] (numeric) = 0.8736526096563989 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.812349482004518400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1370000000000001 " "
y[1] (analytic) = 0.8727979878719913 " "
y[1] (numeric) = 0.8727979878719909 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.81608243849888600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1380000000000001 " "
y[1] (analytic) = 0.8719444932895015 " "
y[1] (numeric) = 0.8719444932895011 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.093090366047153000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1390000000000001 " "
y[1] (analytic) = 0.8710921267624242 " "
y[1] (numeric) = 0.871092126762424 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.549036985907579500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1400000000000001 " "
y[1] (analytic) = 0.8702408891431264 " "
y[1] (numeric) = 0.870240889143126 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.82729554015208200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1410000000000001 " "
y[1] (analytic) = 0.8693907812828451 " "
y[1] (numeric) = 0.8693907812828447 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.83103794701025200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1420000000000001 " "
y[1] (analytic) = 0.8685418040316881 " "
y[1] (numeric) = 0.868541804031688 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.278260895988664300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1430000000000001 " "
y[1] (analytic) = 0.8676939582386332 " "
y[1] (numeric) = 0.8676939582386329 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.559019834317719500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1440000000000001 " "
y[1] (analytic) = 0.8668472447515254 " "
y[1] (numeric) = 0.8668472447515253 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.280759708642083500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1450000000000001 " "
y[1] (analytic) = 0.8660016644170787 " "
y[1] (numeric) = 0.8660016644170785 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.564020533084004300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1460000000000001 " "
y[1] (analytic) = 0.865157218080873 " "
y[1] (numeric) = 0.8651572180808728 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.566523173875607000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1470000000000001 " "
y[1] (analytic) = 0.8643139065873547 " "
y[1] (numeric) = 0.8643139065873544 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.8535409976523904000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1480000000000001 " "
y[1] (analytic) = 0.863471730779835 " "
y[1] (numeric) = 0.8634717307798347 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.571532998822025000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1490000000000001 " "
y[1] (analytic) = 0.8626306915004898 " "
y[1] (numeric) = 0.8626306915004897 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.287020083523803300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1500000000000001 " "
y[1] (analytic) = 0.8617907895903583 " "
y[1] (numeric) = 0.8617907895903583 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1510000000000001 " "
y[1] (analytic) = 0.8609520258893424 " "
y[1] (numeric) = 0.8609520258893424 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1520000000000001 " "
y[1] (analytic) = 0.8601144012362059 " "
y[1] (numeric) = 0.8601144012362058 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.290785299059613600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1530000000000001 " "
y[1] (analytic) = 0.8592779164685729 " "
y[1] (numeric) = 0.8592779164685729 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1540000000000001 " "
y[1] (analytic) = 0.8584425724229285 " "
y[1] (numeric) = 0.8584425724229284 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.293299121328041000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1550000000000001 " "
y[1] (analytic) = 0.8576083699346166 " "
y[1] (numeric) = 0.8576083699346164 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.589114247356981700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1560000000000001 " "
y[1] (analytic) = 0.8567753098378396 " "
y[1] (numeric) = 0.8567753098378393 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.591631695911701000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1570000000000001 " "
y[1] (analytic) = 0.8559433929656574 " "
y[1] (numeric) = 0.8559433929656571 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.594150579931403500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1580000000000001 " "
y[1] (analytic) = 0.8551126201499869 " "
y[1] (numeric) = 0.8551126201499867 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.596670890976730500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1590000000000001 " "
y[1] (analytic) = 0.8542829922216008 " "
y[1] (numeric) = 0.8542829922216006 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.299596310278836600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000011 " "
y[1] (analytic) = 0.8534545100101271 " "
y[1] (numeric) = 0.8534545100101268 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.601715760133443400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16100000000000012 " "
y[1] (analytic) = 0.8526271743440477 " "
y[1] (numeric) = 0.8526271743440476 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.30212015055617390000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16200000000000012 " "
y[1] (analytic) = 0.8518009860506985 " "
y[1] (numeric) = 0.8518009860506983 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.606766234851663000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16300000000000012 " "
y[1] (analytic) = 0.8509759459562675 " "
y[1] (numeric) = 0.8509759459562674 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.304646776328754200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16400000000000012 " "
y[1] (analytic) = 0.8501520548857946 " "
y[1] (numeric) = 0.8501520548857946 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16500000000000012 " "
y[1] (analytic) = 0.8493293136631712 " "
y[1] (numeric) = 0.8493293136631712 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16600000000000012 " "
y[1] (analytic) = 0.8485077231111382 " "
y[1] (numeric) = 0.8485077231111382 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16700000000000012 " "
y[1] (analytic) = 0.8476872840512863 " "
y[1] (numeric) = 0.8476872840512861 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.619416488871116300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16800000000000012 " "
y[1] (analytic) = 0.8468679973040539 " "
y[1] (numeric) = 0.846867997304054 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.310975297401100500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16900000000000012 " "
y[1] (analytic) = 0.8460498636887287 " "
y[1] (numeric) = 0.8460498636887285 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.624486031555275400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000012 " "
y[1] (analytic) = 0.8452328840234433 " "
y[1] (numeric) = 0.8452328840234431 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.627022790074891600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17100000000000012 " "
y[1] (analytic) = 0.8444170591251774 " "
y[1] (numeric) = 0.8444170591251775 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.314780430626728800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17200000000000013 " "
y[1] (analytic) = 0.8436023898097565 " "
y[1] (numeric) = 0.8436023898097564 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.316050117965558000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17300000000000013 " "
y[1] (analytic) = 0.8427888768918492 " "
y[1] (numeric) = 0.8427888768918492 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17400000000000013 " "
y[1] (analytic) = 0.8419765211849686 " "
y[1] (numeric) = 0.8419765211849687 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.318591429441128800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17500000000000013 " "
y[1] (analytic) = 0.8411653235014706 " "
y[1] (numeric) = 0.8411653235014704 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.319863044286817300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17600000000000013 " "
y[1] (analytic) = 0.840355284652552 " "
y[1] (numeric) = 0.8403552846525522 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.321135292299830400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17700000000000013 " "
y[1] (analytic) = 0.8395464054482527 " "
y[1] (numeric) = 0.8395464054482525 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.32240816876868600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17800000000000013 " "
y[1] (analytic) = 0.8387386866974508 " "
y[1] (numeric) = 0.8387386866974508 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17900000000000013 " "
y[1] (analytic) = 0.8379321292078656 " "
y[1] (numeric) = 0.8379321292078655 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.324955788095510000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000013 " "
y[1] (analytic) = 0.8371267337860544 " "
y[1] (numeric) = 0.8371267337860543 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.326230521397848100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18100000000000013 " "
y[1] (analytic) = 0.8363225012374123 " "
y[1] (numeric) = 0.8363225012374124 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.327505864044653300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18200000000000013 " "
y[1] (analytic) = 0.8355194323661723 " "
y[1] (numeric) = 0.8355194323661722 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.328781811191428200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18300000000000013 " "
y[1] (analytic) = 0.8347175279754026 " "
y[1] (numeric) = 0.8347175279754027 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.330058357966903400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18400000000000014 " "
y[1] (analytic) = 0.8339167888670079 " "
y[1] (numeric) = 0.833916788867008 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.33133549947297400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18500000000000014 " "
y[1] (analytic) = 0.8331172158417272 " "
y[1] (numeric) = 0.8331172158417274 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.665226461569300000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18600000000000014 " "
y[1] (analytic) = 0.8323188096991335 " "
y[1] (numeric) = 0.8323188096991336 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.33389154694999600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18700000000000014 " "
y[1] (analytic) = 0.8315215712376326 " "
y[1] (numeric) = 0.8315215712376328 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.670340885980158000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18800000000000014 " "
y[1] (analytic) = 0.8307255012544632 " "
y[1] (numeric) = 0.8307255012544634 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.672899827797820500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18900000000000014 " "
y[1] (analytic) = 0.8299306005456952 " "
y[1] (numeric) = 0.8299306005456953 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.337729954643392700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000014 " "
y[1] (analytic) = 0.8291368699062289 " "
y[1] (numeric) = 0.8291368699062291 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.67802112032653200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19100000000000014 " "
y[1] (analytic) = 0.8283443101297954 " "
y[1] (numeric) = 0.8283443101297955 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.340291725371051000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19200000000000014 " "
y[1] (analytic) = 0.827552922008954 " "
y[1] (numeric) = 0.8275529220089541 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.341573445151999800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19300000000000014 " "
y[1] (analytic) = 0.8267627063350929 " "
y[1] (numeric) = 0.8267627063350931 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.68571142872807600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19400000000000014 " "
y[1] (analytic) = 0.8259736638984277 " "
y[1] (numeric) = 0.8259736638984279 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.344138527837715200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19500000000000015 " "
y[1] (analytic) = 0.8251857954880006 " "
y[1] (numeric) = 0.8251857954880009 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.690843760752304000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19600000000000015 " "
y[1] (analytic) = 0.8243991018916803 " "
y[1] (numeric) = 0.8243991018916805 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.693411533509970600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19700000000000015 " "
y[1] (analytic) = 0.8236135838961604 " "
y[1] (numeric) = 0.8236135838961604 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19800000000000015 " "
y[1] (analytic) = 0.8228292422869581 " "
y[1] (numeric) = 0.8228292422869582 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.349275119998677700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19900000000000015 " "
y[1] (analytic) = 0.8220460778484155 " "
y[1] (numeric) = 0.8220460778484157 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.350560576276942600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20000000000000015 " "
y[1] (analytic) = 0.821264091363697 " "
y[1] (numeric) = 0.8212640913636972 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.351846545222313800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20100000000000015 " "
y[1] (analytic) = 0.820483283614789 " "
y[1] (numeric) = 0.8204832836147891 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.353133021472255000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20200000000000015 " "
y[1] (analytic) = 0.8197036553824989 " "
y[1] (numeric) = 0.819703655382499 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.354419999636444800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20300000000000015 " "
y[1] (analytic) = 0.818925207446455 " "
y[1] (numeric) = 0.8189252074464552 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.711414948593453600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20400000000000015 " "
y[1] (analytic) = 0.8181479405851054 " "
y[1] (numeric) = 0.8181479405851056 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.713990880014123000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20500000000000015 " "
y[1] (analytic) = 0.8173718555757168 " "
y[1] (numeric) = 0.8173718555757169 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.358283891293479400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20600000000000016 " "
y[1] (analytic) = 0.8165969531943741 " "
y[1] (numeric) = 0.8165969531943741 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20700000000000016 " "
y[1] (analytic) = 0.8158232342159794 " "
y[1] (numeric) = 0.8158232342159795 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.3608622285587400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20800000000000016 " "
y[1] (analytic) = 0.8150506994142518 " "
y[1] (numeric) = 0.8150506994142519 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.36215210344955800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20900000000000016 " "
y[1] (analytic) = 0.8142793495617261 " "
y[1] (numeric) = 0.8142793495617262 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.363442441740316500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21000000000000016 " "
y[1] (analytic) = 0.8135091854297521 " "
y[1] (numeric) = 0.8135091854297521 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21100000000000016 " "
y[1] (analytic) = 0.8127402077884938 " "
y[1] (numeric) = 0.8127402077884938 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21200000000000016 " "
y[1] (analytic) = 0.8119724174069286 " "
y[1] (numeric) = 0.8119724174069287 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.367316180727795000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21300000000000016 " "
y[1] (analytic) = 0.8112058150528471 " "
y[1] (numeric) = 0.8112058150528472 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.368608316192641600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21400000000000016 " "
y[1] (analytic) = 0.8104404014928515 " "
y[1] (numeric) = 0.8104404014928516 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.369900886703202300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21500000000000016 " "
y[1] (analytic) = 0.8096761774923552 " "
y[1] (numeric) = 0.8096761774923553 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.371193886503643800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21600000000000016 " "
y[1] (analytic) = 0.8089131438155822 " "
y[1] (numeric) = 0.8089131438155824 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.744974619619403000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21700000000000016 " "
y[1] (analytic) = 0.8081513012255663 " "
y[1] (numeric) = 0.8081513012255664 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.373781150808637800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21800000000000017 " "
y[1] (analytic) = 0.8073906504841496 " "
y[1] (numeric) = 0.8073906504841499 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.12522621097760170000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21900000000000017 " "
y[1] (analytic) = 0.8066311923519832 " "
y[1] (numeric) = 0.8066311923519836 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.12911018747473900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22000000000000017 " "
y[1] (analytic) = 0.8058729275885251 " "
y[1] (numeric) = 0.8058729275885254 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.75533024281473600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22100000000000017 " "
y[1] (analytic) = 0.8051158569520397 " "
y[1] (numeric) = 0.80511585695204 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.13688172343856300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22200000000000017 " "
y[1] (analytic) = 0.804359981199598 " "
y[1] (numeric) = 0.8043599811995982 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.7605128315046300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22300000000000017 " "
y[1] (analytic) = 0.8036053010870753 " "
y[1] (numeric) = 0.8036053010870755 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.763105278482620000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22400000000000017 " "
y[1] (analytic) = 0.8028518173691516 " "
y[1] (numeric) = 0.802851817369152 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.531396955733242000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22500000000000017 " "
y[1] (analytic) = 0.8020995307993112 " "
y[1] (numeric) = 0.8020995307993114 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.768292417572650000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22600000000000017 " "
y[1] (analytic) = 0.8013484421298398 " "
y[1] (numeric) = 0.8013484421298401 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.15633062818859600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22700000000000017 " "
y[1] (analytic) = 0.8005985521118266 " "
y[1] (numeric) = 0.8005985521118268 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.773482469326480000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22800000000000017 " "
y[1] (analytic) = 0.7998498614951614 " "
y[1] (numeric) = 0.7998498614951616 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.77607855691770400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22900000000000018 " "
y[1] (analytic) = 0.7991023710285345 " "
y[1] (numeric) = 0.7991023710285348 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.778675335917662000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000018 " "
y[1] (analytic) = 0.7983560814594366 " "
y[1] (numeric) = 0.7983560814594368 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.78127279395332200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23100000000000018 " "
y[1] (analytic) = 0.7976109935341571 " "
y[1] (numeric) = 0.7976109935341573 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.783870918593631700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23200000000000018 " "
y[1] (analytic) = 0.7968671079977839 " "
y[1] (numeric) = 0.796867107997784 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.393234848674722900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23300000000000018 " "
y[1] (analytic) = 0.7961244255942023 " "
y[1] (numeric) = 0.7961244255942025 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.789069117673461700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23400000000000018 " "
y[1] (analytic) = 0.7953829470660949 " "
y[1] (numeric) = 0.795382947066095 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.395834583480074200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23500000000000018 " "
y[1] (analytic) = 0.7946426731549401 " "
y[1] (numeric) = 0.7946426731549402 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.397134916272844400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23600000000000018 " "
y[1] (analytic) = 0.7939036046010117 " "
y[1] (numeric) = 0.7939036046010117 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23700000000000018 " "
y[1] (analytic) = 0.793165742143378 " "
y[1] (numeric) = 0.7931657421433781 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.399736480833113400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23800000000000018 " "
y[1] (analytic) = 0.7924290865199017 " "
y[1] (numeric) = 0.7924290865199018 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.401037699790785600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23900000000000018 " "
y[1] (analytic) = 0.7916936384672384 " "
y[1] (numeric) = 0.7916936384672384 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000019 " "
y[1] (analytic) = 0.7909593987208358 " "
y[1] (numeric) = 0.7909593987208358 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2410000000000002 " "
y[1] (analytic) = 0.7902263680149335 " "
y[1] (numeric) = 0.7902263680149337 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.80988605180073100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2420000000000002 " "
y[1] (analytic) = 0.7894945470825626 " "
y[1] (numeric) = 0.7894945470825628 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.81249067198193900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2430000000000002 " "
y[1] (analytic) = 0.7887639366555438 " "
y[1] (numeric) = 0.788763936655544 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.815095805045648700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2440000000000002 " "
y[1] (analytic) = 0.7880345374644874 " "
y[1] (numeric) = 0.7880345374644876 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.81770143780072200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2450000000000002 " "
y[1] (analytic) = 0.7873063502387925 " "
y[1] (numeric) = 0.7873063502387927 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.82030755699715200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2460000000000002 " "
y[1] (analytic) = 0.786579375706646 " "
y[1] (numeric) = 0.7865793757066465 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.64582829865202600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2470000000000002 " "
y[1] (analytic) = 0.7858536145950232 " "
y[1] (numeric) = 0.7858536145950235 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.82552120141940600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2480000000000002 " "
y[1] (analytic) = 0.7851290676296842 " "
y[1] (numeric) = 0.7851290676296846 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.65625739970084500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2490000000000002 " "
y[1] (analytic) = 0.7844057355351767 " "
y[1] (numeric) = 0.7844057355351769 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.830736631133081700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25000000000000017 " "
y[1] (analytic) = 0.7836836190348323 " "
y[1] (numeric) = 0.7836836190348324 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.416672490861150300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25100000000000017 " "
y[1] (analytic) = 0.7829627188507673 " "
y[1] (numeric) = 0.7829627188507675 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.835953738013840500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25200000000000017 " "
y[1] (analytic) = 0.7822430357038821 " "
y[1] (numeric) = 0.7822430357038823 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.838562886344267000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25300000000000017 " "
y[1] (analytic) = 0.7815245703138597 " "
y[1] (numeric) = 0.7815245703138599 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.841172412990910500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25400000000000017 " "
y[1] (analytic) = 0.7808073233991655 " "
y[1] (numeric) = 0.7808073233991657 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.84378230417182350000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25500000000000017 " "
y[1] (analytic) = 0.7800912956770463 " "
y[1] (numeric) = 0.7800912956770465 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.846392546045747000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25600000000000017 " "
y[1] (analytic) = 0.7793764878635296 " "
y[1] (numeric) = 0.77937648786353 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.27350468706810200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2570000000000002 " "
y[1] (analytic) = 0.7786629006734235 " "
y[1] (numeric) = 0.7786629006734238 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.27742103931618430000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2580000000000002 " "
y[1] (analytic) = 0.7779505348203151 " "
y[1] (numeric) = 0.7779505348203152 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.427112618261246200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2590000000000002 " "
y[1] (analytic) = 0.7772393910165698 " "
y[1] (numeric) = 0.7772393910165699 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.428418370784153800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000002 " "
y[1] (analytic) = 0.7765294699733314 " "
y[1] (numeric) = 0.7765294699733317 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.289172790814823600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2610000000000002 " "
y[1] (analytic) = 0.7758207724005215 " "
y[1] (numeric) = 0.7758207724005216 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.43103028962467380000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2620000000000002 " "
y[1] (analytic) = 0.7751132990068368 " "
y[1] (numeric) = 0.7751132990068371 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.29700932514395100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2630000000000002 " "
y[1] (analytic) = 0.7744070504997513 " "
y[1] (numeric) = 0.7744070504997516 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.86728542543276600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2640000000000002 " "
y[1] (analytic) = 0.7737020275855132 " "
y[1] (numeric) = 0.7737020275855133 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.434949095441590300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2650000000000002 " "
y[1] (analytic) = 0.7729982309691452 " "
y[1] (numeric) = 0.7729982309691453 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.436255582672183200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2660000000000002 " "
y[1] (analytic) = 0.772295661354444 " "
y[1] (numeric) = 0.7722956613544442 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.437562167160254500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2670000000000002 " "
y[1] (analytic) = 0.771594319443979 " "
y[1] (numeric) = 0.7715943194439793 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.877737683256138500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2680000000000002 " "
y[1] (analytic) = 0.7708942059390924 " "
y[1] (numeric) = 0.7708942059390926 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.8803511975361096000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2690000000000002 " "
y[1] (analytic) = 0.7701953215398973 " "
y[1] (numeric) = 0.7701953215398976 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.88296486248558800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2700000000000002 " "
y[1] (analytic) = 0.7694976669452782 " "
y[1] (numeric) = 0.7694976669452784 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.885578663370030300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2710000000000002 " "
y[1] (analytic) = 0.7688012428528896 " "
y[1] (numeric) = 0.7688012428528899 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.888192585395177300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2720000000000002 " "
y[1] (analytic) = 0.7681060499591557 " "
y[1] (numeric) = 0.7681060499591559 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.890806613707034300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2730000000000002 " "
y[1] (analytic) = 0.7674120889592692 " "
y[1] (numeric) = 0.7674120889592693 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.446710366695933600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2740000000000002 " "
y[1] (analytic) = 0.7667193605471907 " "
y[1] (numeric) = 0.7667193605471909 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.8960349294761900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2750000000000002 " "
y[1] (analytic) = 0.7660278654156492 " "
y[1] (numeric) = 0.7660278654156493 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.4493245934633803000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2760000000000002 " "
y[1] (analytic) = 0.7653376042561392 " "
y[1] (numeric) = 0.7653376042561394 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.901263490650572400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2770000000000002 " "
y[1] (analytic) = 0.7646485777589223 " "
y[1] (numeric) = 0.7646485777589224 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.451938912747427800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2780000000000002 " "
y[1] (analytic) = 0.7639607866130245 " "
y[1] (numeric) = 0.7639607866130247 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.9064921762470700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2790000000000002 " "
y[1] (analytic) = 0.7632742315062372 " "
y[1] (numeric) = 0.7632742315062373 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.454553263817454400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2800000000000002 " "
y[1] (analytic) = 0.7625889131251153 " "
y[1] (numeric) = 0.7625889131251153 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2810000000000002 " "
y[1] (analytic) = 0.7619048321549768 " "
y[1] (numeric) = 0.7619048321549772 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.371502756394105600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2820000000000002 " "
y[1] (analytic) = 0.7612219892799035 " "
y[1] (numeric) = 0.7612219892799037 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.91694943199262800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2830000000000002 " "
y[1] (analytic) = 0.7605403851827377 " "
y[1] (numeric) = 0.7605403851827377 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2840000000000002 " "
y[1] (analytic) = 0.7598600205450832 " "
y[1] (numeric) = 0.7598600205450833 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.4610888776971598000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2850000000000002 " "
y[1] (analytic) = 0.7591808960473047 " "
y[1] (numeric) = 0.7591808960473049 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.92479178653088300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2860000000000002 " "
y[1] (analytic) = 0.7585030123685269 " "
y[1] (numeric) = 0.758503012368527 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.463702854861890500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2870000000000002 " "
y[1] (analytic) = 0.7578263701866335 " "
y[1] (numeric) = 0.7578263701866333 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.46500975461138500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2880000000000002 " "
y[1] (analytic) = 0.7571509701782662 " "
y[1] (numeric) = 0.757150970178266 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.46631658460896100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2890000000000002 " "
y[1] (analytic) = 0.756476813018825 " "
y[1] (numeric) = 0.756476813018825 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2900000000000002 " "
y[1] (analytic) = 0.7558038993824674 " "
y[1] (numeric) = 0.7558038993824673 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.468930003579326200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2910000000000002 " "
y[1] (analytic) = 0.7551322299421064 " "
y[1] (numeric) = 0.7551322299421065 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.470236576593047500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2920000000000002 " "
y[1] (analytic) = 0.7544618053694119 " "
y[1] (numeric) = 0.754461805369412 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.471543047936735800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2930000000000002 " "
y[1] (analytic) = 0.7537926263348085 " "
y[1] (numeric) = 0.7537926263348084 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.472849409556355000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2940000000000002 " "
y[1] (analytic) = 0.7531246935074742 " "
y[1] (numeric) = 0.7531246935074746 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.422466960104284000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2950000000000002 " "
y[1] (analytic) = 0.7524580075553433 " "
y[1] (numeric) = 0.7524580075553433 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2960000000000002 " "
y[1] (analytic) = 0.7517925691451006 " "
y[1] (numeric) = 0.7517925691451005 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.47676775508388480000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2970000000000002 " "
y[1] (analytic) = 0.7511283789421848 " "
y[1] (numeric) = 0.7511283789421845 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.95614719334312800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2980000000000002 " "
y[1] (analytic) = 0.7504654376107855 " "
y[1] (numeric) = 0.7504654376107857 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.479379287818651500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2990000000000002 " "
y[1] (analytic) = 0.7498037458138449 " "
y[1] (numeric) = 0.749803745813845 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.48068482029268700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3000000000000002 " "
y[1] (analytic) = 0.7491433042130542 " "
y[1] (numeric) = 0.7491433042130543 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.48199018583153800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3010000000000002 " "
y[1] (analytic) = 0.7484841134688551 " "
y[1] (numeric) = 0.7484841134688552 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.48329537614341600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3020000000000002 " "
y[1] (analytic) = 0.7478261742404384 " "
y[1] (numeric) = 0.7478261742404384 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3030000000000002 " "
y[1] (analytic) = 0.7471694871857429 " "
y[1] (numeric) = 0.7471694871857429 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3040000000000002 " "
y[1] (analytic) = 0.7465140529614557 " "
y[1] (numeric) = 0.7465140529614559 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.97441962470994470000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3050000000000002 " "
y[1] (analytic) = 0.7458598722230114 " "
y[1] (numeric) = 0.7458598722230114 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3060000000000002 " "
y[1] (analytic) = 0.74520694562459 " "
y[1] (numeric) = 0.7452069456245902 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.979636814025212000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3070000000000002 " "
y[1] (analytic) = 0.7445552738191186 " "
y[1] (numeric) = 0.7445552738191188 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.982244740354556600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3080000000000002 " "
y[1] (analytic) = 0.743904857458269 " "
y[1] (numeric) = 0.743904857458269 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3090000000000002 " "
y[1] (analytic) = 0.7432556971924569 " "
y[1] (numeric) = 0.743255697192457 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.49372958568480100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3100000000000002 " "
y[1] (analytic) = 0.7426077936708428 " "
y[1] (numeric) = 0.7426077936708431 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.99006564188378900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3110000000000002 " "
y[1] (analytic) = 0.7419611475413307 " "
y[1] (numeric) = 0.7419611475413307 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3120000000000002 " "
y[1] (analytic) = 0.7413157594505659 " "
y[1] (numeric) = 0.7413157594505659 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3130000000000002 " "
y[1] (analytic) = 0.7406716300439369 " "
y[1] (numeric) = 0.7406716300439369 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3140000000000002 " "
y[1] (analytic) = 0.7400287599655728 " "
y[1] (numeric) = 0.7400287599655728 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3150000000000002 " "
y[1] (analytic) = 0.7393871498583438 " "
y[1] (numeric) = 0.7393871498583439 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.501544927901248500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3160000000000002 " "
y[1] (analytic) = 0.73874680036386 " "
y[1] (numeric) = 0.73874680036386 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3170000000000002 " "
y[1] (analytic) = 0.7381077121224704 " "
y[1] (numeric) = 0.7381077121224706 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.00829541919470700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3180000000000002 " "
y[1] (analytic) = 0.7374698857732638 " "
y[1] (numeric) = 0.7374698857732639 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.505448623791665300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31900000000000023 " "
y[1] (analytic) = 0.7368333219540661 " "
y[1] (numeric) = 0.7368333219540663 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.506749208465313300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.32000000000000023 " "
y[1] (analytic) = 0.7361980213014411 " "
y[1] (numeric) = 0.7361980213014414 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.524148364304969600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.32100000000000023 " "
y[1] (analytic) = 0.7355639844506896 " "
y[1] (numeric) = 0.7355639844506899 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.528048061465072500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.32200000000000023 " "
y[1] (analytic) = 0.7349312120358484 " "
y[1] (numeric) = 0.7349312120358487 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.02129779343485560000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.32300000000000023 " "
y[1] (analytic) = 0.7342997046896897 " "
y[1] (numeric) = 0.7342997046896899 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.51194807451860480000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.32400000000000023 " "
y[1] (analytic) = 0.7336694630437206 " "
y[1] (numeric) = 0.7336694630437209 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.53974063477818400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = sin ( x ) - cos ( x );"
Iterations = 325
"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 29 Minutes 14 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 1 Hours 28 Minutes 56 Seconds
"Expected Total Time "= 0 Years 0 Days 1 Hours 31 Minutes 56 Seconds
"Time to Timeout " Unknown
Percent Done = 3.2600000000000025 "%"
(%o57) true
(%o57) diffeq.max