(%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 : array_const_0D1 array_x ,
1 1 1
array_tmp2 : array_const_1D0 + array_tmp1 ,
1 1 1
array_tmp3 : array_tmp2 + array_const_0D0 , array_tmp4 : sin(array_x ),
1 1 1 1 1
array_tmp4_g : cos(array_x ), array_tmp5 : array_tmp3 - array_tmp4 ,
1 1 1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp4_g array_x
1 2
array_tmp3 : array_tmp2 , array_tmp4 : ----------------------,
2 2 2 1
- array_tmp4 array_x
1 2
array_tmp4_g : ----------------------,
2 1
array_tmp5 : array_tmp3 - array_tmp4 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp5 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_tmp4_g array_x - array_tmp4 array_x
2 2 2 2
array_tmp4 : ----------------------, array_tmp4_g : ----------------------,
3 2 3 2
array_tmp5 : - array_tmp4 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
array_tmp4_g array_x - array_tmp4 array_x
3 2 3 2
array_tmp4 : ----------------------, array_tmp4_g : ----------------------,
4 3 4 3
array_tmp5 : - array_tmp4 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
array_tmp4_g array_x - array_tmp4 array_x
4 2 4 2
array_tmp4 : ----------------------, array_tmp4_g : ----------------------,
5 4 5 4
array_tmp5 : - array_tmp4 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
array_tmp4_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp4 : ----------------------------,
kkk kkk - 1
- array_tmp4 array_x
kkk - 1 2
array_tmp4_g : ----------------------------,
kkk kkk - 1
array_tmp5 : - array_tmp4 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp5 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_0D1 array_x ,
1 1 1
array_tmp2 : array_const_1D0 + array_tmp1 ,
1 1 1
array_tmp3 : array_tmp2 + array_const_0D0 , array_tmp4 : sin(array_x ),
1 1 1 1 1
array_tmp4_g : cos(array_x ), array_tmp5 : array_tmp3 - array_tmp4 ,
1 1 1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp4_g array_x
1 2
array_tmp3 : array_tmp2 , array_tmp4 : ----------------------,
2 2 2 1
- array_tmp4 array_x
1 2
array_tmp4_g : ----------------------,
2 1
array_tmp5 : array_tmp3 - array_tmp4 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp5 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_tmp4_g array_x - array_tmp4 array_x
2 2 2 2
array_tmp4 : ----------------------, array_tmp4_g : ----------------------,
3 2 3 2
array_tmp5 : - array_tmp4 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
array_tmp4_g array_x - array_tmp4 array_x
3 2 3 2
array_tmp4 : ----------------------, array_tmp4_g : ----------------------,
4 3 4 3
array_tmp5 : - array_tmp4 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
array_tmp4_g array_x - array_tmp4 array_x
4 2 4 2
array_tmp4 : ----------------------, array_tmp4_g : ----------------------,
5 4 5 4
array_tmp5 : - array_tmp4 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
array_tmp4_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp4 : ----------------------------,
kkk kkk - 1
- array_tmp4 array_x
kkk - 1 2
array_tmp4_g : ----------------------------,
kkk kkk - 1
array_tmp5 : - array_tmp4 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp5 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i32) log_revs(file, revs) := printf(file, revs)
(%o32) log_revs(file, revs) := printf(file, revs)
(%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i35) logstart(file) := printf(file, "")
(%o35) logstart(file) := printf(file, "
")
(%i36) logend(file) := printf(file, "
~%")
(%o36) logend(file) := printf(file, "~%")
(%i37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i40) factorial_2(nnn) := nnn!
(%o40) factorial_2(nnn) := nnn!
(%i41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i46) Si(x) := 0.0
(%o46) Si(x) := 0.0
(%i47) Ci(x) := 0.0
(%o47) Ci(x) := 0.0
(%i48) ln(x) := log(x)
(%o48) ln(x) := log(x)
(%i49) arcsin(x) := asin(x)
(%o49) arcsin(x) := asin(x)
(%i50) arccos(x) := acos(x)
(%o50) arccos(x) := acos(x)
(%i51) arctan(x) := atan(x)
(%o51) arctan(x) := atan(x)
(%i52) omniabs(x) := abs(x)
(%o52) omniabs(x) := abs(x)
(%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i54) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%o54) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%i55) exact_soln_y(x) := block(x + 0.05 x x + cos(x))
(%o55) exact_soln_y(x) := block(x + 0.05 x x + cos(x))
(%i56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\
########temp/sub_lin_sinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.1 * x + 1.0) - sin(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:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS,
"glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (cos(x) + (0.05 * x * x) + x) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4_g, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_g : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05,
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = (0.1 * x + 1.0) - sin(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,
"2013-01-13T02:41:06-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sub_lin_sin"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.1 * x + 1.0) - sin(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_lin_sin diffeq.max"),
logitem_str(html_log_file,
"sub_lin_sin maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%o56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\
########temp/sub_lin_sinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.1 * x + 1.0) - sin(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:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS,
"glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (cos(x) + (0.05 * x * x) + x) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4_g, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_g : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05,
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = (0.1 * x + 1.0) - sin(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,
"2013-01-13T02:41:06-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sub_lin_sin"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.1 * x + 1.0) - sin(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_lin_sin diffeq.max"),
logitem_str(html_log_file,
"sub_lin_sin maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i57) main()
"##############ECHO OF PROBLEM#################"
"##############temp/sub_lin_sinpostode.ode#################"
"diff ( y , x , 1 ) = (0.1 * x + 1.0) - sin(x);"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.1,"
"x_end:5.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.05,"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (cos(x) + (0.05 * x * x) + x) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 4.9 ""
estimated_steps = 4900. ""
step_error = 2.040816326530612300000000000000E-14 ""
est_needed_step_err = 2.040816326530612300000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 2.467204025104944900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
max_value3 = 2.467204025104944900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
value3 = 2.467204025104944900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = 0.1 " "
y[1] (analytic) = 1.0955041652780257 " "
y[1] (numeric) = 1.0955041652780257 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (analytic) = 1.0955041652780257 " "
y[1] (numeric) = 1.0955041652780257 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.101 " "
y[1] (analytic) = 1.0964138843759768 " "
y[1] (numeric) = 1.0964138843759765 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.025189648628062000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10200000000000001 " "
y[1] (analytic) = 1.097322708570176 " "
y[1] (numeric) = 1.097322708570176 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10300000000000001 " "
y[1] (analytic) = 1.0982306379619498 " "
y[1] (numeric) = 1.0982306379619498 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10400000000000001 " "
y[1] (analytic) = 1.0991376726536186 " "
y[1] (numeric) = 1.0991376726536184 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.020170998133063400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10500000000000001 " "
y[1] (analytic) = 1.1000438127484975 " "
y[1] (numeric) = 1.1000438127484973 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.018506920831136800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10600000000000001 " "
y[1] (analytic) = 1.1009490583508965 " "
y[1] (numeric) = 1.1009490583508963 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.016847221411227400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10700000000000001 " "
y[1] (analytic) = 1.10185340956612 " "
y[1] (numeric) = 1.1018534095661199 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.015191884848516000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10800000000000001 " "
y[1] (analytic) = 1.102756866500467 " "
y[1] (numeric) = 1.1027568665004668 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.013540896187539200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10900000000000001 " "
y[1] (analytic) = 1.10365942926123 " "
y[1] (numeric) = 1.10365942926123 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000001 " "
y[1] (analytic) = 1.1045610979566969 " "
y[1] (numeric) = 1.1045610979566969 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11100000000000002 " "
y[1] (analytic) = 1.1054618726961485 " "
y[1] (numeric) = 1.1054618726961485 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11200000000000002 " "
y[1] (analytic) = 1.1063617535898604 " "
y[1] (numeric) = 1.1063617535898602 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.006980123856898200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11300000000000002 " "
y[1] (analytic) = 1.1072607407491013 " "
y[1] (numeric) = 1.1072607407491013 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11400000000000002 " "
y[1] (analytic) = 1.1081588342861344 " "
y[1] (numeric) = 1.1081588342861344 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11500000000000002 " "
y[1] (analytic) = 1.1090560343142157 " "
y[1] (numeric) = 1.109056034314216 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.002104474931534800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11600000000000002 " "
y[1] (analytic) = 1.109952340947596 " "
y[1] (numeric) = 1.109952340947596 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11700000000000002 " "
y[1] (analytic) = 1.1108477543015176 " "
y[1] (numeric) = 1.1108477543015178 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.998875219985921700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11800000000000002 " "
y[1] (analytic) = 1.111742274492218 " "
y[1] (numeric) = 1.111742274492218 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11900000000000002 " "
y[1] (analytic) = 1.1126359016369265 " "
y[1] (numeric) = 1.1126359016369267 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.99566277340463300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000002 " "
y[1] (analytic) = 1.1135286358538663 " "
y[1] (numeric) = 1.1135286358538663 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12100000000000002 " "
y[1] (analytic) = 1.1144204772622528 " "
y[1] (numeric) = 1.1144204772622528 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12200000000000003 " "
y[1] (analytic) = 1.115311425982295 " "
y[1] (numeric) = 1.1153114259822947 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.990875371239639600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12300000000000003 " "
y[1] (analytic) = 1.1162014821351935 " "
y[1] (numeric) = 1.1162014821351935 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12400000000000003 " "
y[1] (analytic) = 1.1170906458431429 " "
y[1] (numeric) = 1.1170906458431429 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12500000000000003 " "
y[1] (analytic) = 1.117978917229329 " "
y[1] (numeric) = 1.117978917229329 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12600000000000003 " "
y[1] (analytic) = 1.1188662964179308 " "
y[1] (numeric) = 1.1188662964179308 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12700000000000003 " "
y[1] (analytic) = 1.1197527835341186 " "
y[1] (numeric) = 1.1197527835341186 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12800000000000003 " "
y[1] (analytic) = 1.1206383787040557 " "
y[1] (numeric) = 1.1206383787040555 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.98141174838051900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12900000000000003 " "
y[1] (analytic) = 1.1215230820548965 " "
y[1] (numeric) = 1.1215230820548965 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13000000000000003 " "
y[1] (analytic) = 1.1224068937147882 " "
y[1] (numeric) = 1.122406893714788 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.978289746511967300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13100000000000003 " "
y[1] (analytic) = 1.1232898138128686 " "
y[1] (numeric) = 1.1232898138128684 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.97673478557887300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13200000000000003 " "
y[1] (analytic) = 1.1241718424792677 " "
y[1] (numeric) = 1.1241718424792677 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13300000000000003 " "
y[1] (analytic) = 1.1250529798451072 " "
y[1] (numeric) = 1.125052979845107 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.973636876688256200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13400000000000004 " "
y[1] (analytic) = 1.1259332260424992 " "
y[1] (numeric) = 1.1259332260424992 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13500000000000004 " "
y[1] (analytic) = 1.126812581204548 " "
y[1] (numeric) = 1.126812581204548 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13600000000000004 " "
y[1] (analytic) = 1.127691045465348 " "
y[1] (numeric) = 1.127691045465348 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13700000000000004 " "
y[1] (analytic) = 1.1285686189599853 " "
y[1] (numeric) = 1.128568618959985 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.967488739228395700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13800000000000004 " "
y[1] (analytic) = 1.1294453018245358 " "
y[1] (numeric) = 1.1294453018245358 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13900000000000004 " "
y[1] (analytic) = 1.1303210941960675 " "
y[1] (numeric) = 1.1303210941960673 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.964438300454428600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14000000000000004 " "
y[1] (analytic) = 1.1311959962126372 " "
y[1] (numeric) = 1.131195996212637 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.962918943034274400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14100000000000004 " "
y[1] (analytic) = 1.1320700080132933 " "
y[1] (numeric) = 1.132070008013293 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.961403476404296200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14200000000000004 " "
y[1] (analytic) = 1.1329431297380739 " "
y[1] (numeric) = 1.1329431297380737 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.959891887745203700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14300000000000004 " "
y[1] (analytic) = 1.1338153615280073 " "
y[1] (numeric) = 1.133815361528007 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.958384164294517700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14400000000000004 " "
y[1] (analytic) = 1.1346867035251116 " "
y[1] (numeric) = 1.1346867035251114 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.95688029334625290000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14500000000000005 " "
y[1] (analytic) = 1.1355571558723947 " "
y[1] (numeric) = 1.1355571558723947 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14600000000000005 " "
y[1] (analytic) = 1.1364267187138546 " "
y[1] (numeric) = 1.1364267187138546 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14700000000000005 " "
y[1] (analytic) = 1.1372953921944782 " "
y[1] (numeric) = 1.1372953921944782 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14800000000000005 " "
y[1] (analytic) = 1.138163176460242 " "
y[1] (numeric) = 1.138163176460242 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14900000000000005 " "
y[1] (analytic) = 1.1390300716581119 " "
y[1] (numeric) = 1.1390300716581119 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000005 " "
y[1] (analytic) = 1.1398960779360423 " "
y[1] (numeric) = 1.1398960779360423 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15100000000000005 " "
y[1] (analytic) = 1.1407611954429773 " "
y[1] (numeric) = 1.1407611954429773 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15200000000000005 " "
y[1] (analytic) = 1.1416254243288493 " "
y[1] (numeric) = 1.1416254243288493 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15300000000000005 " "
y[1] (analytic) = 1.1424887647445794 " "
y[1] (numeric) = 1.1424887647445792 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.943516748496627300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15400000000000005 " "
y[1] (analytic) = 1.1433512168420767 " "
y[1] (numeric) = 1.1433512168420767 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15500000000000005 " "
y[1] (analytic) = 1.14421278077424 " "
y[1] (numeric) = 1.14421278077424 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15600000000000006 " "
y[1] (analytic) = 1.1450734566949545 " "
y[1] (numeric) = 1.1450734566949545 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15700000000000006 " "
y[1] (analytic) = 1.1459332447590949 " "
y[1] (numeric) = 1.1459332447590949 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15800000000000006 " "
y[1] (analytic) = 1.1467921451225227 " "
y[1] (numeric) = 1.1467921451225227 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15900000000000006 " "
y[1] (analytic) = 1.1476501579420877 " "
y[1] (numeric) = 1.1476501579420877 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000006 " "
y[1] (analytic) = 1.148507283375627 " "
y[1] (numeric) = 1.1485072833756271 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.933332144593898600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16100000000000006 " "
y[1] (analytic) = 1.1493635215819653 " "
y[1] (numeric) = 1.1493635215819653 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16200000000000006 " "
y[1] (analytic) = 1.1502188727209142 " "
y[1] (numeric) = 1.1502188727209142 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16300000000000006 " "
y[1] (analytic) = 1.1510733369532726 " "
y[1] (numeric) = 1.1510733369532726 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16400000000000006 " "
y[1] (analytic) = 1.1519269144408264 " "
y[1] (numeric) = 1.1519269144408264 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16500000000000006 " "
y[1] (analytic) = 1.1527796053463477 " "
y[1] (numeric) = 1.152779605346348 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.926167013150089000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16600000000000006 " "
y[1] (analytic) = 1.153631409833596 " "
y[1] (numeric) = 1.1536314098335962 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.924744793114291400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16700000000000007 " "
y[1] (analytic) = 1.1544823280673169 " "
y[1] (numeric) = 1.1544823280673169 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16800000000000007 " "
y[1] (analytic) = 1.1553323602132415 " "
y[1] (numeric) = 1.1553323602132417 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.92191106708071600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16900000000000007 " "
y[1] (analytic) = 1.1561815064380883 " "
y[1] (numeric) = 1.1561815064380885 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.920499538252400400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000007 " "
y[1] (analytic) = 1.1570297669095608 " "
y[1] (numeric) = 1.1570297669095608 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17100000000000007 " "
y[1] (analytic) = 1.1578771417963485 " "
y[1] (numeric) = 1.1578771417963485 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17200000000000007 " "
y[1] (analytic) = 1.1587236312681264 " "
y[1] (numeric) = 1.1587236312681264 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17300000000000007 " "
y[1] (analytic) = 1.1595692354955554 " "
y[1] (numeric) = 1.1595692354955551 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.91488872012146800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17400000000000007 " "
y[1] (analytic) = 1.1604139546502807 " "
y[1] (numeric) = 1.1604139546502805 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.91349478378127500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17500000000000007 " "
y[1] (analytic) = 1.1612577889049336 " "
y[1] (numeric) = 1.1612577889049334 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.912104332444731800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17600000000000007 " "
y[1] (analytic) = 1.1621007384331297 " "
y[1] (numeric) = 1.1621007384331294 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.91071735505835700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17700000000000007 " "
y[1] (analytic) = 1.162942803409469 " "
y[1] (numeric) = 1.162942803409469 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17800000000000007 " "
y[1] (analytic) = 1.1637839840095374 " "
y[1] (numeric) = 1.1637839840095374 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17900000000000008 " "
y[1] (analytic) = 1.1646242804099036 " "
y[1] (numeric) = 1.1646242804099036 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000008 " "
y[1] (analytic) = 1.1654636927881215 " "
y[1] (numeric) = 1.1654636927881215 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18100000000000008 " "
y[1] (analytic) = 1.1663022213227285 " "
y[1] (numeric) = 1.1663022213227285 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18200000000000008 " "
y[1] (analytic) = 1.1671398661932462 " "
y[1] (numeric) = 1.1671398661932462 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18300000000000008 " "
y[1] (analytic) = 1.1679766275801797 " "
y[1] (numeric) = 1.1679766275801797 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18400000000000008 " "
y[1] (analytic) = 1.1688125056650176 " "
y[1] (numeric) = 1.1688125056650176 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18500000000000008 " "
y[1] (analytic) = 1.1696475006302316 " "
y[1] (numeric) = 1.1696475006302316 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18600000000000008 " "
y[1] (analytic) = 1.170481612659277 " "
y[1] (numeric) = 1.170481612659277 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18700000000000008 " "
y[1] (analytic) = 1.1713148419365915 " "
y[1] (numeric) = 1.1713148419365915 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18800000000000008 " "
y[1] (analytic) = 1.172147188647596 " "
y[1] (numeric) = 1.172147188647596 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18900000000000008 " "
y[1] (analytic) = 1.1729786529786939 " "
y[1] (numeric) = 1.1729786529786939 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000009 " "
y[1] (analytic) = 1.1738092351172704 " "
y[1] (numeric) = 1.1738092351172704 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1910000000000001 " "
y[1] (analytic) = 1.1746389352516937 " "
y[1] (numeric) = 1.1746389352516937 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1920000000000001 " "
y[1] (analytic) = 1.1754677535713136 " "
y[1] (numeric) = 1.1754677535713136 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1930000000000001 " "
y[1] (analytic) = 1.1762956902664619 " "
y[1] (numeric) = 1.1762956902664619 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1940000000000001 " "
y[1] (analytic) = 1.1771227455284514 " "
y[1] (numeric) = 1.1771227455284514 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1950000000000001 " "
y[1] (analytic) = 1.1779489195495774 " "
y[1] (numeric) = 1.1779489195495774 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1960000000000001 " "
y[1] (analytic) = 1.1787742125231155 " "
y[1] (numeric) = 1.1787742125231155 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1970000000000001 " "
y[1] (analytic) = 1.1795986246433228 " "
y[1] (numeric) = 1.1795986246433228 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1980000000000001 " "
y[1] (analytic) = 1.180422156105437 " "
y[1] (numeric) = 1.180422156105437 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1990000000000001 " "
y[1] (analytic) = 1.1812448071056771 " "
y[1] (numeric) = 1.1812448071056771 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2000000000000001 " "
y[1] (analytic) = 1.1820665778412418 " "
y[1] (numeric) = 1.1820665778412418 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2010000000000001 " "
y[1] (analytic) = 1.1828874685103101 " "
y[1] (numeric) = 1.1828874685103101 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2020000000000001 " "
y[1] (analytic) = 1.1837074793120417 " "
y[1] (numeric) = 1.1837074793120417 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2030000000000001 " "
y[1] (analytic) = 1.1845266104465755 " "
y[1] (numeric) = 1.1845266104465755 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2040000000000001 " "
y[1] (analytic) = 1.1853448621150307 " "
y[1] (numeric) = 1.1853448621150304 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.8732489760729500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2050000000000001 " "
y[1] (analytic) = 1.1861622345195053 " "
y[1] (numeric) = 1.1861622345195049 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.74391627828174640000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2060000000000001 " "
y[1] (analytic) = 1.1869787278630768 " "
y[1] (numeric) = 1.1869787278630766 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.870670465382132400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2070000000000001 " "
y[1] (analytic) = 1.187794342349802 " "
y[1] (numeric) = 1.1877943423498019 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.869385945093513500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2080000000000001 " "
y[1] (analytic) = 1.1886090781847167 " "
y[1] (numeric) = 1.1886090781847163 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.736209137223572300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2090000000000001 " "
y[1] (analytic) = 1.1894229355738346 " "
y[1] (numeric) = 1.1894229355738342 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.733652652626987500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2100000000000001 " "
y[1] (analytic) = 1.1902359147241484 " "
y[1] (numeric) = 1.190235914724148 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.731102417229492700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2110000000000001 " "
y[1] (analytic) = 1.191048015843629 " "
y[1] (numeric) = 1.1910480158436285 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.72855841194202950000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2120000000000001 " "
y[1] (analytic) = 1.1918592391412253 " "
y[1] (numeric) = 1.1918592391412248 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.726020617753853500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2130000000000001 " "
y[1] (analytic) = 1.1926695848268638 " "
y[1] (numeric) = 1.1926695848268634 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.72348901573212930000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2140000000000001 " "
y[1] (analytic) = 1.193479053111449 " "
y[1] (numeric) = 1.1934790531114485 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.72096358702152200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2150000000000001 " "
y[1] (analytic) = 1.1942876442068624 " "
y[1] (numeric) = 1.194287644206862 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.71844431284379940000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2160000000000001 " "
y[1] (analytic) = 1.1950953583259631 " "
y[1] (numeric) = 1.1950953583259627 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.71593117449743270000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2170000000000001 " "
y[1] (analytic) = 1.195902195682587 " "
y[1] (numeric) = 1.1959021956825866 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.71342415335719900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2180000000000001 " "
y[1] (analytic) = 1.1967081564915465 " "
y[1] (numeric) = 1.196708156491546 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.71092323087378940000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2190000000000001 " "
y[1] (analytic) = 1.1975132409686309 " "
y[1] (numeric) = 1.1975132409686304 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.70842838857341400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2200000000000001 " "
y[1] (analytic) = 1.1983174493306057 " "
y[1] (numeric) = 1.1983174493306052 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.70593960805741500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2210000000000001 " "
y[1] (analytic) = 1.1991207817952123 " "
y[1] (numeric) = 1.1991207817952119 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.70345687100188060000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22200000000000011 " "
y[1] (analytic) = 1.1999232385811687 " "
y[1] (numeric) = 1.199923238581168 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.55147023873588700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22300000000000011 " "
y[1] (analytic) = 1.2007248199081675 " "
y[1] (numeric) = 1.200724819908167 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.69850945434797400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22400000000000012 " "
y[1] (analytic) = 1.2015255259968778 " "
y[1] (numeric) = 1.2015255259968773 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.69604473847205300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22500000000000012 " "
y[1] (analytic) = 1.2023253570689434 " "
y[1] (numeric) = 1.202325357068943 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.69358599350074100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22600000000000012 " "
y[1] (analytic) = 1.203124313346983 " "
y[1] (numeric) = 1.2031243133469827 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.691133201478129500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22700000000000012 " "
y[1] (analytic) = 1.2039223950545908 " "
y[1] (numeric) = 1.2039223950545903 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.68868634452078400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22800000000000012 " "
y[1] (analytic) = 1.2047196024163345 " "
y[1] (numeric) = 1.204719602416334 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.686245404817374000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22900000000000012 " "
y[1] (analytic) = 1.205515935657757 " "
y[1] (numeric) = 1.2055159356577565 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.683810364628298000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000012 " "
y[1] (analytic) = 1.206311395005375 " "
y[1] (numeric) = 1.2063113950053745 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.6813812062853296000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23100000000000012 " "
y[1] (analytic) = 1.207105980686679 " "
y[1] (numeric) = 1.2071059806866786 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.67895791219124200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23200000000000012 " "
y[1] (analytic) = 1.2078996929301336 " "
y[1] (numeric) = 1.207899692930133 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.676540464819451600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23300000000000012 " "
y[1] (analytic) = 1.2086925319651765 " "
y[1] (numeric) = 1.2086925319651758 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.51119327007048800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23400000000000012 " "
y[1] (analytic) = 1.2094844980222184 " "
y[1] (numeric) = 1.2094844980222177 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.50758456073123600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23500000000000013 " "
y[1] (analytic) = 1.2102755913326433 " "
y[1] (numeric) = 1.2102755913326426 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.503984543236216000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23600000000000013 " "
y[1] (analytic) = 1.2110658121288078 " "
y[1] (numeric) = 1.2110658121288072 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.500393191714048000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23700000000000013 " "
y[1] (analytic) = 1.211855160644041 " "
y[1] (numeric) = 1.2118551606440406 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.664540320264438000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23800000000000013 " "
y[1] (analytic) = 1.212643637112645 " "
y[1] (numeric) = 1.2126436371126446 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.662157589079158600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23900000000000013 " "
y[1] (analytic) = 1.2134312417698927 " "
y[1] (numeric) = 1.2134312417698923 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.659780583878166600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000013 " "
y[1] (analytic) = 1.2142179748520296 " "
y[1] (numeric) = 1.2142179748520292 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.657409287687257000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24100000000000013 " "
y[1] (analytic) = 1.2150038365962728 " "
y[1] (numeric) = 1.2150038365962723 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.655043683599714700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24200000000000013 " "
y[1] (analytic) = 1.2157888272408102 " "
y[1] (numeric) = 1.2157888272408097 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.65268375477596200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24300000000000013 " "
y[1] (analytic) = 1.216572947024801 " "
y[1] (numeric) = 1.2165729470248008 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.825164742221616300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24400000000000013 " "
y[1] (analytic) = 1.2173561961883759 " "
y[1] (numeric) = 1.2173561961883756 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.823990427947612000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24500000000000013 " "
y[1] (analytic) = 1.2181385749726354 " "
y[1] (numeric) = 1.2181385749726352 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.82281892624588600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24600000000000014 " "
y[1] (analytic) = 1.218920083619651 " "
y[1] (numeric) = 1.2189200836196505 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.64330045765851200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24700000000000014 " "
y[1] (analytic) = 1.2197007223724636 " "
y[1] (numeric) = 1.2197007223724632 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.64096865488655330000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24800000000000014 " "
y[1] (analytic) = 1.2204804914750846 " "
y[1] (numeric) = 1.2204804914750842 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.638642427732147000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24900000000000014 " "
y[1] (analytic) = 1.221259391172495 " "
y[1] (numeric) = 1.2212593911724945 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.636321759816362000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (analytic) = 1.2220374217106449 " "
y[1] (numeric) = 1.2220374217106444 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.634006634824759600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2510000000000001 " "
y[1] (analytic) = 1.2228145833364539 " "
y[1] (numeric) = 1.2228145833364534 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.63169703650706900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2520000000000001 " "
y[1] (analytic) = 1.2235908762978103 " "
y[1] (numeric) = 1.2235908762978098 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.62939294867687100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2530000000000001 " "
y[1] (analytic) = 1.224366300843571 " "
y[1] (numeric) = 1.2243663008435706 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.62709435521127500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2540000000000001 " "
y[1] (analytic) = 1.2251408572235616 " "
y[1] (numeric) = 1.2251408572235611 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.62480124005060400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2550000000000001 " "
y[1] (analytic) = 1.2259145456885756 " "
y[1] (numeric) = 1.2259145456885752 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.6225135871980800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2560000000000001 " "
y[1] (analytic) = 1.2266873664903746 " "
y[1] (numeric) = 1.2266873664903741 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.62023138071950800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2570000000000001 " "
y[1] (analytic) = 1.2274593198816879 " "
y[1] (numeric) = 1.2274593198816872 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.42693190711445400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2580000000000001 " "
y[1] (analytic) = 1.2282304061162117 " "
y[1] (numeric) = 1.228230406116211 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.423524865187763000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2590000000000001 " "
y[1] (analytic) = 1.2290006254486099 " "
y[1] (numeric) = 1.2290006254486094 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.61341728111782800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (analytic) = 1.2297699781345135 " "
y[1] (numeric) = 1.2297699781345128 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.41673505305096600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2610000000000001 " "
y[1] (analytic) = 1.230538464430519 " "
y[1] (numeric) = 1.2305384644305186 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.60890149058105800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2620000000000001 " "
y[1] (analytic) = 1.231306084594191 " "
y[1] (numeric) = 1.2313060845941906 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.606651631193910600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2630000000000001 " "
y[1] (analytic) = 1.2320728388840587 " "
y[1] (numeric) = 1.2320728388840583 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.60440710836782400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2640000000000001 " "
y[1] (analytic) = 1.232838727559618 " "
y[1] (numeric) = 1.2328387275596175 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.60216790665823130000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2650000000000001 " "
y[1] (analytic) = 1.2336037508813305 " "
y[1] (numeric) = 1.2336037508813298 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.39990101602061600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2660000000000001 " "
y[1] (analytic) = 1.234367909110622 " "
y[1] (numeric) = 1.2343679091106217 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.59770540510919950000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2670000000000001 " "
y[1] (analytic) = 1.2351312025098853 " "
y[1] (numeric) = 1.2351312025098848 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.595482074678688600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2680000000000001 " "
y[1] (analytic) = 1.2358936313424762 " "
y[1] (numeric) = 1.2358936313424758 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.59326400418194140000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.26900000000000013 " "
y[1] (analytic) = 1.236655195872716 " "
y[1] (numeric) = 1.2366551958727157 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.59105117847069550000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (analytic) = 1.2374158963658908 " "
y[1] (numeric) = 1.2374158963658901 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.383265373682619000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27100000000000013 " "
y[1] (analytic) = 1.238175733088249 " "
y[1] (numeric) = 1.2381757330882486 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.58664120110332400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27200000000000013 " "
y[1] (analytic) = 1.2389347063070046 " "
y[1] (numeric) = 1.2389347063070042 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.584444019441477300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27300000000000013 " "
y[1] (analytic) = 1.2396928162903342 " "
y[1] (numeric) = 1.2396928162903338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.582252022553122400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27400000000000013 " "
y[1] (analytic) = 1.2404500633073776 " "
y[1] (numeric) = 1.2404500633073774 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.79003259778954700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27500000000000013 " "
y[1] (analytic) = 1.241206447628238 " "
y[1] (numeric) = 1.2412064476282378 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.78894176185859900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27600000000000013 " "
y[1] (analytic) = 1.241961969523981 " "
y[1] (numeric) = 1.2419619695239807 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.787853496110968200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27700000000000014 " "
y[1] (analytic) = 1.2427166292666347 " "
y[1] (numeric) = 1.2427166292666343 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.573535586404225600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27800000000000014 " "
y[1] (analytic) = 1.2434704271291892 " "
y[1] (numeric) = 1.2434704271291888 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.57136929163112570000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27900000000000014 " "
y[1] (analytic) = 1.2442233633855968 " "
y[1] (numeric) = 1.2442233633855964 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.56920809332556430000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (analytic) = 1.244975438310771 " "
y[1] (numeric) = 1.2449754383107707 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.783525988483031200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28100000000000014 " "
y[1] (analytic) = 1.2457266521805872 " "
y[1] (numeric) = 1.2457266521805868 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.5649009280864696000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28200000000000014 " "
y[1] (analytic) = 1.246477005271881 " "
y[1] (numeric) = 1.2464770052718808 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.781377466137845400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28300000000000014 " "
y[1] (analytic) = 1.2472264978624499 " "
y[1] (numeric) = 1.2472264978624494 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.560613975177417400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28400000000000014 " "
y[1] (analytic) = 1.2479751302310507 " "
y[1] (numeric) = 1.2479751302310502 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.558478042489867700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28500000000000014 " "
y[1] (analytic) = 1.2487229026574012 " "
y[1] (numeric) = 1.248722902657401 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.778173559982757200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28600000000000014 " "
y[1] (analytic) = 1.249469815422179 " "
y[1] (numeric) = 1.2494698154221788 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.777110596705415000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28700000000000014 " "
y[1] (analytic) = 1.2502158688070217 " "
y[1] (numeric) = 1.2502158688070213 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.55210024868601650000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28800000000000014 " "
y[1] (analytic) = 1.2509610630945254 " "
y[1] (numeric) = 1.250961063094525 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.54998427170475640000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28900000000000015 " "
y[1] (analytic) = 1.2517053985682456 " "
y[1] (numeric) = 1.2517053985682454 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.77393662421697200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (analytic) = 1.2524488755126972 " "
y[1] (numeric) = 1.252448875512697 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.77288358244671700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29100000000000015 " "
y[1] (analytic) = 1.2531914942133533 " "
y[1] (numeric) = 1.253191494213353 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.771833003577892600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29200000000000015 " "
y[1] (analytic) = 1.253933254956645 " "
y[1] (numeric) = 1.2539332549566446 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.54156976134600600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29300000000000015 " "
y[1] (analytic) = 1.2546741580299616 " "
y[1] (numeric) = 1.2546741580299612 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.53947841364130300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29400000000000015 " "
y[1] (analytic) = 1.2554142037216498 " "
y[1] (numeric) = 1.2554142037216494 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.53739195027082900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29500000000000015 " "
y[1] (analytic) = 1.2561533923210142 " "
y[1] (numeric) = 1.2561533923210138 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.53531035751543040000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29600000000000015 " "
y[1] (analytic) = 1.2568917241183155 " "
y[1] (numeric) = 1.2568917241183155 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29700000000000015 " "
y[1] (analytic) = 1.2576291994047728 " "
y[1] (numeric) = 1.2576291994047728 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29800000000000015 " "
y[1] (analytic) = 1.2583658184725606 " "
y[1] (numeric) = 1.2583658184725603 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.764547333259220400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29900000000000015 " "
y[1] (analytic) = 1.2591015816148095 " "
y[1] (numeric) = 1.259101581614809 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.52703242005711800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (analytic) = 1.2598364891256062 " "
y[1] (numeric) = 1.2598364891256058 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.52497497638192900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30100000000000016 " "
y[1] (analytic) = 1.2605705412999932 " "
y[1] (numeric) = 1.260570541299993 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.7614611610393700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30200000000000016 " "
y[1] (analytic) = 1.261303738433969 " "
y[1] (numeric) = 1.2613037384339685 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.52087444378340200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30300000000000016 " "
y[1] (analytic) = 1.2620360808244857 " "
y[1] (numeric) = 1.2620360808244853 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.51883132818152100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30400000000000016 " "
y[1] (analytic) = 1.262767568769451 " "
y[1] (numeric) = 1.2627675687694506 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.51679296200821170000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30500000000000016 " "
y[1] (analytic) = 1.2634982025677273 " "
y[1] (numeric) = 1.2634982025677268 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.51475933204786700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30600000000000016 " "
y[1] (analytic) = 1.26422798251913 " "
y[1] (numeric) = 1.2642279825191298 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.756365212566961800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30700000000000016 " "
y[1] (analytic) = 1.2649569089244301 " "
y[1] (numeric) = 1.26495690892443 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.75535311407431100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30800000000000016 " "
y[1] (analytic) = 1.2656849820853509 " "
y[1] (numeric) = 1.2656849820853504 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.50868672802278400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30900000000000016 " "
y[1] (analytic) = 1.2664122023045685 " "
y[1] (numeric) = 1.2664122023045683 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.753335955867789400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (analytic) = 1.2671385698857136 " "
y[1] (numeric) = 1.2671385698857132 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.504661766314288700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31100000000000017 " "
y[1] (analytic) = 1.2678640851333678 " "
y[1] (numeric) = 1.2678640851333676 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.751328139417043500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31200000000000017 " "
y[1] (analytic) = 1.2685887483530665 " "
y[1] (numeric) = 1.2685887483530662 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.750327718208904700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31300000000000017 " "
y[1] (analytic) = 1.2693125598512962 " "
y[1] (numeric) = 1.2693125598512958 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.49865922623572700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31400000000000017 " "
y[1] (analytic) = 1.2700355199354951 " "
y[1] (numeric) = 1.2700355199354947 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.49666763550532670000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31500000000000017 " "
y[1] (analytic) = 1.2707576289140534 " "
y[1] (numeric) = 1.270757628914053 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.49468065149108160000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31600000000000017 " "
y[1] (analytic) = 1.271478887096312 " "
y[1] (numeric) = 1.2714788870963116 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.49269826150423300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31700000000000017 " "
y[1] (analytic) = 1.2721992947925627 " "
y[1] (numeric) = 1.2721992947925624 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.745360226451285700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31800000000000017 " "
y[1] (analytic) = 1.272918852314048 " "
y[1] (numeric) = 1.2729188523140476 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.48874721309021200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3190000000000002 " "
y[1] (analytic) = 1.27363755997296 " "
y[1] (numeric) = 1.2736375599729595 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.48677852951738400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (analytic) = 1.274355418082441 " "
y[1] (numeric) = 1.2743554180824406 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.484814389680206400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3210000000000002 " "
y[1] (analytic) = 1.2750724269565832 " "
y[1] (numeric) = 1.2750724269565827 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.48285478112047700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3220000000000002 " "
y[1] (analytic) = 1.2757885869104273 " "
y[1] (numeric) = 1.275788586910427 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.740449845712728500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3230000000000002 " "
y[1] (analytic) = 1.276503898259964 " "
y[1] (numeric) = 1.2765038982599635 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.478949108227654700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3240000000000002 " "
y[1] (analytic) = 1.277218361322131 " "
y[1] (numeric) = 1.2772183613221306 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.477003019204619000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3250000000000002 " "
y[1] (analytic) = 1.2779319764148158 " "
y[1] (numeric) = 1.2779319764148154 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.47506141207872540000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3260000000000002 " "
y[1] (analytic) = 1.2786447438568533 " "
y[1] (numeric) = 1.2786447438568527 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.20968641192544500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3270000000000002 " "
y[1] (analytic) = 1.2793566639680258 " "
y[1] (numeric) = 1.2793566639680252 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.20678739194609900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3280000000000002 " "
y[1] (analytic) = 1.2800677370690632 " "
y[1] (numeric) = 1.2800677370690625 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.20389503996345300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3290000000000002 " "
y[1] (analytic) = 1.2807779634816425 " "
y[1] (numeric) = 1.2807779634816419 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.20100933782689700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (analytic) = 1.2814873435283871 " "
y[1] (numeric) = 1.2814873435283864 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.198130267451510000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3310000000000002 " "
y[1] (analytic) = 1.282195877532867 " "
y[1] (numeric) = 1.2821958775328663 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.19525781081774400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3320000000000002 " "
y[1] (analytic) = 1.2829035658195984 " "
y[1] (numeric) = 1.2829035658195975 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.92318926662817100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3330000000000002 " "
y[1] (analytic) = 1.2836104087140425 " "
y[1] (numeric) = 1.2836104087140416 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.9193768893626200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3340000000000002 " "
y[1] (analytic) = 1.2843164065426067 " "
y[1] (numeric) = 1.2843164065426058 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.91557325886002600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3350000000000002 " "
y[1] (analytic) = 1.285021559632643 " "
y[1] (numeric) = 1.2850215596326422 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.91177835143897600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3360000000000002 " "
y[1] (analytic) = 1.2857258683124486 " "
y[1] (numeric) = 1.2857258683124477 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.90799214350322200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3370000000000002 " "
y[1] (analytic) = 1.2864293329112644 " "
y[1] (numeric) = 1.2864293329112635 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.90421461154128000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3380000000000002 " "
y[1] (analytic) = 1.287131953759276 " "
y[1] (numeric) = 1.2871319537592751 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.90044573212604300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3390000000000002 " "
y[1] (analytic) = 1.2878337311876127 " "
y[1] (numeric) = 1.2878337311876116 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.62085685239299200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (analytic) = 1.2885346655283465 " "
y[1] (numeric) = 1.2885346655283454 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.61616729705851100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3410000000000002 " "
y[1] (analytic) = 1.2892347571144933 " "
y[1] (numeric) = 1.2892347571144922 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.61148847018371800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3420000000000002 " "
y[1] (analytic) = 1.2899340062800115 " "
y[1] (numeric) = 1.2899340062800104 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.60682034290175600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3430000000000002 " "
y[1] (analytic) = 1.290632413359802 " "
y[1] (numeric) = 1.290632413359801 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.88173030915905900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3440000000000002 " "
y[1] (analytic) = 1.2913299786897077 " "
y[1] (numeric) = 1.2913299786897068 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.87801285773095700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3450000000000002 " "
y[1] (analytic) = 1.292026702606513 " "
y[1] (numeric) = 1.2920267026065122 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.87430389718981000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3460000000000002 " "
y[1] (analytic) = 1.2927225854479443 " "
y[1] (numeric) = 1.2927225854479434 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.87060340476963600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3470000000000002 " "
y[1] (analytic) = 1.2934176275526685 " "
y[1] (numeric) = 1.2934176275526676 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.86691135778538900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3480000000000002 " "
y[1] (analytic) = 1.2941118292602936 " "
y[1] (numeric) = 1.2941118292602927 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.86322773363259200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3490000000000002 " "
y[1] (analytic) = 1.2948051909113676 " "
y[1] (numeric) = 1.2948051909113667 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.85955250978695800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3500000000000002 " "
y[1] (analytic) = 1.295497712847379 " "
y[1] (numeric) = 1.2954977128473781 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.85588566380402700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3510000000000002 " "
y[1] (analytic) = 1.296189395410756 " "
y[1] (numeric) = 1.296189395410755 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.85222717331880300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3520000000000002 " "
y[1] (analytic) = 1.2968802389448655 " "
y[1] (numeric) = 1.2968802389448648 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.136432762034039000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3530000000000002 " "
y[1] (analytic) = 1.2975702437940146 " "
y[1] (numeric) = 1.2975702437940138 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.84493516977660400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3540000000000002 " "
y[1] (analytic) = 1.2982594103034482 " "
y[1] (numeric) = 1.2982594103034473 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.84130161238366900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3550000000000002 " "
y[1] (analytic) = 1.2989477388193493 " "
y[1] (numeric) = 1.2989477388193484 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.8376763218158100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3560000000000002 " "
y[1] (analytic) = 1.29963522968884 " "
y[1] (numeric) = 1.299635229688839 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.54257409512488500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3570000000000002 " "
y[1] (analytic) = 1.300321883259979 " "
y[1] (numeric) = 1.3003218832599779 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.53806306667519900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3580000000000002 " "
y[1] (analytic) = 1.3010076998817628 " "
y[1] (numeric) = 1.3010076998817617 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.53356228964713300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3590000000000002 " "
y[1] (analytic) = 1.3016926799041248 " "
y[1] (numeric) = 1.3016926799041237 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.52907173686287500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3600000000000002 " "
y[1] (analytic) = 1.302376823677935 " "
y[1] (numeric) = 1.3023768236779338 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.52459138123993400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3610000000000002 " "
y[1] (analytic) = 1.3030601315549994 " "
y[1] (numeric) = 1.3030601315549983 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.52012119579069700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3620000000000002 " "
y[1] (analytic) = 1.3037426038880602 " "
y[1] (numeric) = 1.303742603888059 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.51566115362201300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3630000000000002 " "
y[1] (analytic) = 1.3044242410307951 " "
y[1] (numeric) = 1.304424241030794 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.51121122793474700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3640000000000002 " "
y[1] (analytic) = 1.305105043337817 " "
y[1] (numeric) = 1.3051050433378157 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.02081256704280480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3650000000000002 " "
y[1] (analytic) = 1.3057850111646734 " "
y[1] (numeric) = 1.305785011164672 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.02028099431306360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3660000000000002 " "
y[1] (analytic) = 1.3064641448678462 " "
y[1] (numeric) = 1.3064641448678451 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.49792188317161900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3670000000000002 " "
y[1] (analytic) = 1.3071424448047522 " "
y[1] (numeric) = 1.307142444804751 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.49351215728436200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3680000000000002 " "
y[1] (analytic) = 1.307819911333741 " "
y[1] (numeric) = 1.3078199113337399 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.48911241527840600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3690000000000002 " "
y[1] (analytic) = 1.3084965448140964 " "
y[1] (numeric) = 1.3084965448140953 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.48472263090989300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (analytic) = 1.3091723456060347 " "
y[1] (numeric) = 1.3091723456060336 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.48034277802605400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3710000000000002 " "
y[1] (analytic) = 1.309847314070705 " "
y[1] (numeric) = 1.3098473140707039 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.47597283056479400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3720000000000002 " "
y[1] (analytic) = 1.3105214505701888 " "
y[1] (numeric) = 1.3105214505701879 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.77729021004342800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3730000000000002 " "
y[1] (analytic) = 1.3111947554674996 " "
y[1] (numeric) = 1.3111947554674988 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.77381003849004800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3740000000000002 " "
y[1] (analytic) = 1.311867229126583 " "
y[1] (numeric) = 1.3118672291265818 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.46292216144710400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3750000000000002 " "
y[1] (analytic) = 1.3125388719123143 " "
y[1] (numeric) = 1.3125388719123134 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.76687326148357400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3760000000000002 " "
y[1] (analytic) = 1.3132096841905017 " "
y[1] (numeric) = 1.3132096841905005 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.45427076871983500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3770000000000002 " "
y[1] (analytic) = 1.3138796663278822 " "
y[1] (numeric) = 1.3138796663278811 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.44995971151666600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3780000000000002 " "
y[1] (analytic) = 1.3145488186921237 " "
y[1] (numeric) = 1.3145488186921228 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.75652670384501500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3790000000000002 " "
y[1] (analytic) = 1.3152171416518241 " "
y[1] (numeric) = 1.3152171416518232 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.75309339858993200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000002 " "
y[1] (analytic) = 1.3158846355765104 " "
y[1] (numeric) = 1.3158846355765095 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.74966783323676300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3810000000000002 " "
y[1] (analytic) = 1.3165513008366383 " "
y[1] (numeric) = 1.3165513008366374 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.74624998764353600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38200000000000023 " "
y[1] (analytic) = 1.3172171378035928 " "
y[1] (numeric) = 1.317217137803592 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.74283984173731100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38300000000000023 " "
y[1] (analytic) = 1.317882146849687 " "
y[1] (numeric) = 1.317882146849686 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.4242967193923500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38400000000000023 " "
y[1] (analytic) = 1.3185463283481615 " "
y[1] (numeric) = 1.3185463283481604 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.42005321129681700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38500000000000023 " "
y[1] (analytic) = 1.319209682673185 " "
y[1] (numeric) = 1.3192096826731838 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.4158192530504500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38600000000000023 " "
y[1] (analytic) = 1.3198722101998528 " "
y[1] (numeric) = 1.319872210199852 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.7292758559227410000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38700000000000023 " "
y[1] (analytic) = 1.3205339113041878 " "
y[1] (numeric) = 1.320533911304187 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.72590390975223800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38800000000000023 " "
y[1] (analytic) = 1.3211947863631386 " "
y[1] (numeric) = 1.3211947863631377 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.72253954426371700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38900000000000023 " "
y[1] (analytic) = 1.3218548357545803 " "
y[1] (numeric) = 1.3218548357545794 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.71918273985894200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39000000000000024 " "
y[1] (analytic) = 1.3225140598573133 " "
y[1] (numeric) = 1.3225140598573124 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.71583347700629600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39100000000000024 " "
y[1] (analytic) = 1.3231724590510634 " "
y[1] (numeric) = 1.3231724590510625 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.71249173624047600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39200000000000024 " "
y[1] (analytic) = 1.3238300337164817 " "
y[1] (numeric) = 1.3238300337164808 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.70915749816220200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39300000000000024 " "
y[1] (analytic) = 1.324486784235143 " "
y[1] (numeric) = 1.3244867842351422 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.70583074343792200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39400000000000024 " "
y[1] (analytic) = 1.3251427109895473 " "
y[1] (numeric) = 1.3251427109895464 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.70251145279952600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39500000000000024 " "
y[1] (analytic) = 1.3257978143631175 " "
y[1] (numeric) = 1.3257978143631166 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.69919960704404600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39600000000000024 " "
y[1] (analytic) = 1.3264520947402 " "
y[1] (numeric) = 1.3264520947401994 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.02192139027503600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39700000000000024 " "
y[1] (analytic) = 1.3271055525060649 " "
y[1] (numeric) = 1.3271055525060642 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.019448630270498000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39800000000000024 " "
y[1] (analytic) = 1.3277581880469043 " "
y[1] (numeric) = 1.3277581880469034 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.68930854801664800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39900000000000024 " "
y[1] (analytic) = 1.3284100017498321 " "
y[1] (numeric) = 1.3284100017498313 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.68602629105609600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (analytic) = 1.3290609940028852 " "
y[1] (numeric) = 1.3290609940028844 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.6827513839308200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40100000000000025 " "
y[1] (analytic) = 1.3297111651950209 " "
y[1] (numeric) = 1.3297111651950202 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.00961285586705600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40200000000000025 " "
y[1] (analytic) = 1.3303605157161185 " "
y[1] (numeric) = 1.3303605157161176 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.67622354397693900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40300000000000025 " "
y[1] (analytic) = 1.3310090459569768 " "
y[1] (numeric) = 1.331009045956976 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.67297057370137900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40400000000000025 " "
y[1] (analytic) = 1.3316567563093156 " "
y[1] (numeric) = 1.331656756309315 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.002293658774973000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40500000000000025 " "
y[1] (analytic) = 1.3323036471657748 " "
y[1] (numeric) = 1.332303647165774 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.999864829554195300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40600000000000025 " "
y[1] (analytic) = 1.3329497189199135 " "
y[1] (numeric) = 1.3329497189199129 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.997441428734917000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40700000000000025 " "
y[1] (analytic) = 1.33359497196621 " "
y[1] (numeric) = 1.3335949719662092 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.99502344248469600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40800000000000025 " "
y[1] (analytic) = 1.334239406700061 " "
y[1] (numeric) = 1.3342394067000602 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.992610857017220600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40900000000000025 " "
y[1] (analytic) = 1.3348830235177815 " "
y[1] (numeric) = 1.3348830235177809 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.99020365859211600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (analytic) = 1.3355258228166051 " "
y[1] (numeric) = 1.3355258228166045 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.987801833514735600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41100000000000025 " "
y[1] (analytic) = 1.3361678049946826 " "
y[1] (numeric) = 1.3361678049946817 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.6472071575146200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41200000000000025 " "
y[1] (analytic) = 1.3368089704510813 " "
y[1] (numeric) = 1.3368089704510804 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.64401899846936200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41300000000000026 " "
y[1] (analytic) = 1.3374493195857857 " "
y[1] (numeric) = 1.337449319585785 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.980628462104258500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41400000000000026 " "
y[1] (analytic) = 1.338088852799697 " "
y[1] (numeric) = 1.3380888527996964 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.97824799437896300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41500000000000026 " "
y[1] (analytic) = 1.338727570494632 " "
y[1] (numeric) = 1.338727570494631 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.63449710960955100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41600000000000026 " "
y[1] (analytic) = 1.3393654730733224 " "
y[1] (numeric) = 1.3393654730733218 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.97350296216443500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41700000000000026 " "
y[1] (analytic) = 1.3400025609394162 " "
y[1] (numeric) = 1.3400025609394155 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.97113837087070300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41800000000000026 " "
y[1] (analytic) = 1.3406388344974751 " "
y[1] (numeric) = 1.3406388344974745 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.96877904499005100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41900000000000026 " "
y[1] (analytic) = 1.3412742941529758 " "
y[1] (numeric) = 1.3412742941529752 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.96642497123052800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (analytic) = 1.3419089403123086 " "
y[1] (numeric) = 1.3419089403123077 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.61876818179194400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42100000000000026 " "
y[1] (analytic) = 1.3425427733827768 " "
y[1] (numeric) = 1.3425427733827762 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.961732527125750600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42200000000000026 " "
y[1] (analytic) = 1.3431757937725979 " "
y[1] (numeric) = 1.3431757937725972 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.959394130414709000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42300000000000026 " "
y[1] (analytic) = 1.3438080018909013 " "
y[1] (numeric) = 1.3438080018909004 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.60941457745712300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42400000000000027 " "
y[1] (analytic) = 1.3444393981477285 " "
y[1] (numeric) = 1.3444393981477278 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.95473292208518300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42500000000000027 " "
y[1] (analytic) = 1.3450699829540338 " "
y[1] (numeric) = 1.3450699829540331 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.952410084359591000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42600000000000027 " "
y[1] (analytic) = 1.345699756721682 " "
y[1] (numeric) = 1.3456997567216813 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.95009240692657670000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42700000000000027 " "
y[1] (analytic) = 1.3463287198634495 " "
y[1] (numeric) = 1.3463287198634486 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.59703983578548400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42800000000000027 " "
y[1] (analytic) = 1.3469568727930228 " "
y[1] (numeric) = 1.346956872793022 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.59396330825660600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42900000000000027 " "
y[1] (analytic) = 1.347584215924999 " "
y[1] (numeric) = 1.3475842159249982 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.59089360949859600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000027 " "
y[1] (analytic) = 1.3482107496748852 " "
y[1] (numeric) = 1.3482107496748845 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.94087304181285500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43100000000000027 " "
y[1] (analytic) = 1.3488364744590977 " "
y[1] (numeric) = 1.3488364744590968 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.58477462997356400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4320000000000003 " "
y[1] (analytic) = 1.349461390694961 " "
y[1] (numeric) = 1.3494613906949604 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.93629398638845600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4330000000000003 " "
y[1] (analytic) = 1.3500854988007096 " "
y[1] (numeric) = 1.350085498800709 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.934012070841626300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4340000000000003 " "
y[1] (analytic) = 1.350708799195485 " "
y[1] (numeric) = 1.3507087991954843 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.93173521318480700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4350000000000003 " "
y[1] (analytic) = 1.3513312922993368 " "
y[1] (numeric) = 1.3513312922993361 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.92946340080413770000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4360000000000003 " "
y[1] (analytic) = 1.3519529785332218 " "
y[1] (numeric) = 1.3519529785332212 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.927196621126604400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4370000000000003 " "
y[1] (analytic) = 1.352573858319004 " "
y[1] (numeric) = 1.3525738583190032 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.924934861619857000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4380000000000003 " "
y[1] (analytic) = 1.3531939320794533 " "
y[1] (numeric) = 1.3531939320794524 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.56357081305605200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4390000000000003 " "
y[1] (analytic) = 1.3538132002382457 " "
y[1] (numeric) = 1.353813200238245 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.92042635319161370000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (analytic) = 1.3544316632199636 " "
y[1] (numeric) = 1.354431663219963 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.918179579407188600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4410000000000003 " "
y[1] (analytic) = 1.3550493214500936 " "
y[1] (numeric) = 1.355049321450093 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.91593777606734600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4420000000000003 " "
y[1] (analytic) = 1.3556661753550276 " "
y[1] (numeric) = 1.3556661753550268 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.55160124112062600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4430000000000003 " "
y[1] (analytic) = 1.3562822253620612 " "
y[1] (numeric) = 1.3562822253620606 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.9114690314345800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4440000000000003 " "
y[1] (analytic) = 1.3568974718993951 " "
y[1] (numeric) = 1.3568974718993945 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.90924206559715140000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4450000000000003 " "
y[1] (analytic) = 1.3575119153961324 " "
y[1] (numeric) = 1.3575119153961317 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.9070200211149595000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4460000000000003 " "
y[1] (analytic) = 1.3581255562822792 " "
y[1] (numeric) = 1.3581255562822787 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.26986859054260400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4470000000000003 " "
y[1] (analytic) = 1.358738394988745 " "
y[1] (numeric) = 1.3587383949887446 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.26839376503923140000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4480000000000003 " "
y[1] (analytic) = 1.359350431947341 " "
y[1] (numeric) = 1.3593504319473406 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.26692219616895600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4490000000000003 " "
y[1] (analytic) = 1.3599616675907804 " "
y[1] (numeric) = 1.3599616675907797 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.89818081383994630000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (analytic) = 1.3605721023526771 " "
y[1] (numeric) = 1.3605721023526764 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.895983194299127000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4510000000000003 " "
y[1] (analytic) = 1.3611817366675465 " "
y[1] (numeric) = 1.3611817366675458 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.89379042365001800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4520000000000003 " "
y[1] (analytic) = 1.361790570970804 " "
y[1] (numeric) = 1.3617905709708036 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.26106832663319700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4530000000000003 " "
y[1] (analytic) = 1.3623986056987658 " "
y[1] (numeric) = 1.3623986056987654 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.25961292086240750000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4540000000000003 " "
y[1] (analytic) = 1.3630058412886468 " "
y[1] (numeric) = 1.3630058412886463 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.258160723876288000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4550000000000003 " "
y[1] (analytic) = 1.3636122781785613 " "
y[1] (numeric) = 1.363612278178561 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.256711727788581500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4560000000000003 " "
y[1] (analytic) = 1.3642179168075224 " "
y[1] (numeric) = 1.3642179168075221 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.627632962369014200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4570000000000003 " "
y[1] (analytic) = 1.3648227576154417 " "
y[1] (numeric) = 1.3648227576154413 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.253823306888256600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4580000000000003 " "
y[1] (analytic) = 1.365426801043128 " "
y[1] (numeric) = 1.3654268010431276 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.25238386642767900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4590000000000003 " "
y[1] (analytic) = 1.3660300475322882 " "
y[1] (numeric) = 1.3660300475322877 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.25094759556938600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (analytic) = 1.3666324975255253 " "
y[1] (numeric) = 1.366632497525525 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.624757243275521400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4610000000000003 " "
y[1] (analytic) = 1.3672341514663398 " "
y[1] (numeric) = 1.3672341514663395 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.624042265817391400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4620000000000003 " "
y[1] (analytic) = 1.3678350097991274 " "
y[1] (numeric) = 1.3678350097991272 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.623328861553555000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4630000000000003 " "
y[1] (analytic) = 1.3684350729691799 " "
y[1] (numeric) = 1.3684350729691797 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.62261702663939400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4640000000000003 " "
y[1] (analytic) = 1.3690343414226838 " "
y[1] (numeric) = 1.3690343414226835 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.621906757242373200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4650000000000003 " "
y[1] (analytic) = 1.3696328156067208 " "
y[1] (numeric) = 1.3696328156067206 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.621198049541985300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4660000000000003 " "
y[1] (analytic) = 1.3702304959692668 " "
y[1] (numeric) = 1.3702304959692666 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.62049089972970200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4670000000000003 " "
y[1] (analytic) = 1.3708273829591913 " "
y[1] (numeric) = 1.370827382959191 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.619785304008925200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4680000000000003 " "
y[1] (analytic) = 1.371423477026257 " "
y[1] (numeric) = 1.371423477026257 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4690000000000003 " "
y[1] (analytic) = 1.3720187786211202 " "
y[1] (numeric) = 1.3720187786211202 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (analytic) = 1.3726132881953292 " "
y[1] (numeric) = 1.3726132881953292 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4710000000000003 " "
y[1] (analytic) = 1.3732070062013242 " "
y[1] (numeric) = 1.3732070062013242 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4720000000000003 " "
y[1] (analytic) = 1.373799933092437 " "
y[1] (numeric) = 1.3737999330924373 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.616280504725362300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4730000000000003 " "
y[1] (analytic) = 1.3743920693228915 " "
y[1] (numeric) = 1.3743920693228915 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4740000000000003 " "
y[1] (analytic) = 1.3749834153478004 " "
y[1] (numeric) = 1.3749834153478007 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.614889332093255600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4750000000000003 " "
y[1] (analytic) = 1.3755739716231683 " "
y[1] (numeric) = 1.3755739716231685 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.614196033841932300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4760000000000003 " "
y[1] (analytic) = 1.376163738605889 " "
y[1] (numeric) = 1.376163738605889 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4770000000000003 " "
y[1] (analytic) = 1.3767527167537446 " "
y[1] (numeric) = 1.3767527167537448 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.612813995011333200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4780000000000003 " "
y[1] (analytic) = 1.3773409065254076 " "
y[1] (numeric) = 1.3773409065254079 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.612125247083375500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4790000000000003 " "
y[1] (analytic) = 1.3779283083804383 " "
y[1] (numeric) = 1.3779283083804383 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000003 " "
y[1] (analytic) = 1.3785149227792843 " "
y[1] (numeric) = 1.3785149227792846 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.610752275915573500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4810000000000003 " "
y[1] (analytic) = 1.3791007501832817 " "
y[1] (numeric) = 1.379100750183282 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.610068045394955300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4820000000000003 " "
y[1] (analytic) = 1.3796857910546527 " "
y[1] (numeric) = 1.379685791054653 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.609385313414709300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4830000000000003 " "
y[1] (analytic) = 1.3802700458565065 " "
y[1] (numeric) = 1.3802700458565067 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.608704076362424700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4840000000000003 " "
y[1] (analytic) = 1.380853515052838 " "
y[1] (numeric) = 1.3808535150528385 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.216048661273601000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4850000000000003 " "
y[1] (analytic) = 1.3814361991085287 " "
y[1] (numeric) = 1.3814361991085289 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.60734607264759380000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4860000000000003 " "
y[1] (analytic) = 1.3820180984893435 " "
y[1] (numeric) = 1.382018098489344 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.213338597631157400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4870000000000003 " "
y[1] (analytic) = 1.3825992136619338 " "
y[1] (numeric) = 1.3825992136619343 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.21198801114499300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4880000000000003 " "
y[1] (analytic) = 1.3831795450938338 " "
y[1] (numeric) = 1.3831795450938345 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.81596056808303860000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4890000000000003 " "
y[1] (analytic) = 1.3837590932534627 " "
y[1] (numeric) = 1.3837590932534631 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.20929569326934100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000003 " "
y[1] (analytic) = 1.3843378586101216 " "
y[1] (numeric) = 1.3843378586101223 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.81193092157353700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4910000000000003 " "
y[1] (analytic) = 1.3849158416339957 " "
y[1] (numeric) = 1.3849158416339962 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.206615135011403600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4920000000000003 " "
y[1] (analytic) = 1.3854930427961514 " "
y[1] (numeric) = 1.385493042796152 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.80791887219243650000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4930000000000003 " "
y[1] (analytic) = 1.3860694625685377 " "
y[1] (numeric) = 1.3860694625685386 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.40789256011912800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4940000000000003 " "
y[1] (analytic) = 1.3866451014239853 " "
y[1] (numeric) = 1.3866451014239858 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.202616223819741400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.49500000000000033 " "
y[1] (analytic) = 1.3872199598362045 " "
y[1] (numeric) = 1.387219959836205 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.201289072444562500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.49600000000000033 " "
y[1] (analytic) = 1.387794038279787 " "
y[1] (numeric) = 1.3877940382797878 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.79994722848634700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.49700000000000033 " "
y[1] (analytic) = 1.3883673372302048 " "
y[1] (numeric) = 1.3883673372302054 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.797965184804995300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = (0.1 * x + 1.0) - sin(x);"
Iterations = 398
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds
"Expected Time Remaining "= 0 Years 0 Days 0 Hours 33 Minutes 54 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 33 Minutes 47 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 36 Minutes 47 Seconds
"Time to Timeout " Unknown
Percent Done = 8.14285714285715 "%"
(%o57) true
(%o57) diffeq.max