(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
array_tmp2 : array_tmp1 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp2 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
array_tmp2 : array_tmp1 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp2 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_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
array_tmp2 : array_tmp1 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp2 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_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
array_tmp2 : array_tmp1 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp2 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_tmp1_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------, array_tmp2 : array_tmp1 ,
kkk kkk - 1 kkk kkk
order_d : 1, if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp2 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
array_tmp2 : array_tmp1 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp2 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
array_tmp2 : array_tmp1 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp2 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_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
array_tmp2 : array_tmp1 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp2 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_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
array_tmp2 : array_tmp1 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp2 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_tmp1_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------, array_tmp2 : array_tmp1 ,
kkk kkk - 1 kkk kkk
order_d : 1, if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp2 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole() := 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(2.0 - cos(x))
(%o55) exact_soln_y(x) := block(2.0 - 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/sinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x);"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* # Comment 1 */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:20,"), omniout_str(ALWAYS,
"/* # Comment 2 */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* # Comment 3 */"), omniout_str(ALWAYS, "x_start:0.1,"),
omniout_str(ALWAYS, "x_end:1.0,"), omniout_str(ALWAYS,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.0005,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* # Comment 4 */"),
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, "/* # Comment 5 */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, "/* # Comment 6 */"),
omniout_str(ALWAYS, " (2.0 - cos(x)) "),
omniout_str(ALWAYS, "/* # Comment 7 */"), 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 : 20,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 1.0, array_y_init : exact_soln_y(x_start), glob_h : 5.0E-4,
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, omniout_str(ALWAYS, "START of Optimize"),
1, 20
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = sin(x);"),
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,
"2013-01-13T02:09:34-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sin"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = 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, "sin diffeq.max"),
logitem_str(html_log_file,
"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/sinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x);"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* # Comment 1 */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:20,"), omniout_str(ALWAYS,
"/* # Comment 2 */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* # Comment 3 */"), omniout_str(ALWAYS, "x_start:0.1,"),
omniout_str(ALWAYS, "x_end:1.0,"), omniout_str(ALWAYS,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.0005,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* # Comment 4 */"),
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, "/* # Comment 5 */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, "/* # Comment 6 */"),
omniout_str(ALWAYS, " (2.0 - cos(x)) "),
omniout_str(ALWAYS, "/* # Comment 7 */"), 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 : 20,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 1.0, array_y_init : exact_soln_y(x_start), glob_h : 5.0E-4,
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, omniout_str(ALWAYS, "START of Optimize"),
1, 20
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = sin(x);"),
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,
"2013-01-13T02:09:34-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sin"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = 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, "sin diffeq.max"),
logitem_str(html_log_file,
"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/sinpostode.ode#################"
"diff ( y , x , 1 ) = sin(x);"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"/* # Comment 1 */"
"Digits:32,"
"max_terms:20,"
"/* # Comment 2 */"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"/* # Comment 3 */"
"x_start:0.1,"
"x_end:1.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.0005,"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"/* # Comment 4 */"
"/* 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 */"
"/* # Comment 5 */"
"exact_soln_y (x) := (block("
"/* # Comment 6 */"
" (2.0 - cos(x)) "
"/* # Comment 7 */"
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 0.9 ""
estimated_steps = 900. ""
step_error = 1.11111111111111100000000000000E-13 ""
est_needed_step_err = 1.11111111111111100000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 4.755585815822891400000000000000000000000000000000000000000000000000000000000000E-62 ""
max_value3 = 4.755585815822891400000000000000000000000000000000000000000000000000000000000000E-62 ""
value3 = 4.755585815822891400000000000000000000000000000000000000000000000000000000000000E-62 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = 0.1 " "
y[1] (analytic) = 1.0049958347219743 " "
y[1] (numeric) = 1.0049958347219743 " "
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) = 1.0049958347219743 " "
y[1] (numeric) = 1.0049958347219743 " "
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) = 1.0050961656240234 " "
y[1] (numeric) = 1.0050961656240234 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10200000000000001 " "
y[1] (analytic) = 1.0051974914298238 " "
y[1] (numeric) = 1.0051974914298238 " "
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) = 1.00529981203805 " "
y[1] (numeric) = 1.00529981203805 " "
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) = 1.0054031273463815 " "
y[1] (numeric) = 1.0054031273463815 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10500000000000001 " "
y[1] (analytic) = 1.0055074372515027 " "
y[1] (numeric) = 1.0055074372515025 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208284063337985500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10600000000000001 " "
y[1] (analytic) = 1.0056127416491036 " "
y[1] (numeric) = 1.0056127416491034 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20805281922840900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10700000000000001 " "
y[1] (analytic) = 1.0057190404338798 " "
y[1] (numeric) = 1.0057190404338798 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10800000000000001 " "
y[1] (analytic) = 1.0058263334995332 " "
y[1] (numeric) = 1.005826333499533 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.207583929051449300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10900000000000001 " "
y[1] (analytic) = 1.00593462073877 " "
y[1] (numeric) = 1.0059346207387698 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.207346286202568300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000001 " "
y[1] (analytic) = 1.0060439020433032 " "
y[1] (numeric) = 1.006043902043303 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.2071065136824800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11100000000000002 " "
y[1] (analytic) = 1.0061541773038516 " "
y[1] (numeric) = 1.0061541773038514 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.206864613135481600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11200000000000002 " "
y[1] (analytic) = 1.0062654464101397 " "
y[1] (numeric) = 1.0062654464101397 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11300000000000002 " "
y[1] (analytic) = 1.0063777092508988 " "
y[1] (numeric) = 1.0063777092508988 " "
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) = 1.0064909657138656 " "
y[1] (numeric) = 1.0064909657138656 " "
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) = 1.0066052156857843 " "
y[1] (numeric) = 1.006605215685784 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20587576405270070000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11600000000000002 " "
y[1] (analytic) = 1.0067204590524041 " "
y[1] (numeric) = 1.0067204590524041 " "
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) = 1.0068366956984822 " "
y[1] (numeric) = 1.0068366956984822 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11800000000000002 " "
y[1] (analytic) = 1.006953925507782 " "
y[1] (numeric) = 1.006953925507782 " "
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) = 1.0070721483630733 " "
y[1] (numeric) = 1.0070721483630733 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000002 " "
y[1] (analytic) = 1.0071913641461339 " "
y[1] (numeric) = 1.0071913641461336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.204592025203412600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12100000000000002 " "
y[1] (analytic) = 1.007311572737747 " "
y[1] (numeric) = 1.007311572737747 " "
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) = 1.0074327740177051 " "
y[1] (numeric) = 1.0074327740177051 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12300000000000003 " "
y[1] (analytic) = 1.0075549678648064 " "
y[1] (numeric) = 1.0075549678648064 " "
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) = 1.0076781541568571 " "
y[1] (numeric) = 1.0076781541568571 " "
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) = 1.0078023327706709 " "
y[1] (numeric) = 1.0078023327706709 " "
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) = 1.0079275035820694 " "
y[1] (numeric) = 1.0079275035820692 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20298190232837100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12700000000000003 " "
y[1] (analytic) = 1.0080536664658815 " "
y[1] (numeric) = 1.0080536664658812 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.202706188287512400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12800000000000003 " "
y[1] (analytic) = 1.0081808212959444 " "
y[1] (numeric) = 1.0081808212959442 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.202428376286793800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12900000000000003 " "
y[1] (analytic) = 1.0083089679451036 " "
y[1] (numeric) = 1.0083089679451032 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.40429693643506900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13000000000000003 " "
y[1] (analytic) = 1.008438106285212 " "
y[1] (numeric) = 1.0084381062852117 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20186646598449200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13100000000000003 " "
y[1] (analytic) = 1.0085682361871315 " "
y[1] (numeric) = 1.0085682361871313 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20158237150582600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13200000000000003 " "
y[1] (analytic) = 1.0086993575207321 " "
y[1] (numeric) = 1.0086993575207321 " "
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) = 1.0088314701548928 " "
y[1] (numeric) = 1.0088314701548928 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13400000000000004 " "
y[1] (analytic) = 1.0089645739575008 " "
y[1] (numeric) = 1.0089645739575006 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20071755397810600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13500000000000004 " "
y[1] (analytic) = 1.0090986687954522 " "
y[1] (numeric) = 1.009098668795452 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.200425109965540300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13600000000000004 " "
y[1] (analytic) = 1.0092337545346521 " "
y[1] (numeric) = 1.009233754534652 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.200130583498110500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13700000000000004 " "
y[1] (analytic) = 1.009369831040015 " "
y[1] (numeric) = 1.0093698310400148 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.19983397657373300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13800000000000004 " "
y[1] (analytic) = 1.0095068981754642 " "
y[1] (numeric) = 1.009506898175464 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.199535291203501300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13900000000000004 " "
y[1] (analytic) = 1.0096449558039327 " "
y[1] (numeric) = 1.0096449558039327 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14000000000000004 " "
y[1] (analytic) = 1.0097840037873629 " "
y[1] (numeric) = 1.0097840037873629 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14100000000000004 " "
y[1] (analytic) = 1.0099240419867068 " "
y[1] (numeric) = 1.0099240419867068 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14200000000000004 " "
y[1] (analytic) = 1.010065070261926 " "
y[1] (numeric) = 1.0100650702619263 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.1983198059452900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14300000000000004 " "
y[1] (analytic) = 1.0102070884719927 " "
y[1] (numeric) = 1.010207088471993 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.198010758971103400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14400000000000004 " "
y[1] (analytic) = 1.0103500964748884 " "
y[1] (numeric) = 1.0103500964748886 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.197699645892497700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14500000000000005 " "
y[1] (analytic) = 1.0104940941276053 " "
y[1] (numeric) = 1.0104940941276053 " "
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) = 1.0106390812861454 " "
y[1] (numeric) = 1.0106390812861454 " "
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) = 1.010785057805522 " "
y[1] (numeric) = 1.010785057805522 " "
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) = 1.010932023539758 " "
y[1] (numeric) = 1.010932023539758 " "
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) = 1.0110799783418882 " "
y[1] (numeric) = 1.0110799783418882 " "
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) = 1.0112289220639576 " "
y[1] (numeric) = 1.0112289220639576 " "
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) = 1.0113788545570226 " "
y[1] (numeric) = 1.0113788545570226 " "
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) = 1.0115297756711508 " "
y[1] (numeric) = 1.0115297756711508 " "
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) = 1.0116816852554207 " "
y[1] (numeric) = 1.011681685255421 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.194807004625880800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15400000000000005 " "
y[1] (analytic) = 1.0118345831579232 " "
y[1] (numeric) = 1.0118345831579234 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.19447534825339570000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15500000000000005 " "
y[1] (analytic) = 1.0119884692257601 " "
y[1] (numeric) = 1.0119884692257604 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.194141649607040700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15600000000000006 " "
y[1] (analytic) = 1.0121433433050455 " "
y[1] (numeric) = 1.0121433433050457 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.19380591092926100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15700000000000006 " "
y[1] (analytic) = 1.0122992052409052 " "
y[1] (numeric) = 1.0122992052409054 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.193468134475019300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15800000000000006 " "
y[1] (analytic) = 1.0124560548774775 " "
y[1] (numeric) = 1.0124560548774777 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.193128322511756500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15900000000000006 " "
y[1] (analytic) = 1.0126138920579124 " "
y[1] (numeric) = 1.0126138920579126 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.192786477319356700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000006 " "
y[1] (analytic) = 1.0127727166243732 " "
y[1] (numeric) = 1.0127727166243734 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.192442601190108300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16100000000000006 " "
y[1] (analytic) = 1.0129325284180348 " "
y[1] (numeric) = 1.0129325284180353 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.38419339285733840000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16200000000000006 " "
y[1] (analytic) = 1.013093327279086 " "
y[1] (numeric) = 1.0130933272790863 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.191748765352026200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16300000000000006 " "
y[1] (analytic) = 1.0132551130467276 " "
y[1] (numeric) = 1.0132551130467278 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.19139881028946220000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16400000000000006 " "
y[1] (analytic) = 1.0134178855591738 " "
y[1] (numeric) = 1.013417885559174 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.19104683358251280000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16500000000000006 " "
y[1] (analytic) = 1.0135816446536523 " "
y[1] (numeric) = 1.0135816446536525 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.190692837584933300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16600000000000006 " "
y[1] (analytic) = 1.0137463901664039 " "
y[1] (numeric) = 1.013746390166404 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.19033682466265780000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16700000000000007 " "
y[1] (analytic) = 1.0139121219326834 " "
y[1] (numeric) = 1.0139121219326834 " "
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) = 1.0140788397867584 " "
y[1] (numeric) = 1.0140788397867586 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.189618757568426400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16900000000000007 " "
y[1] (analytic) = 1.014246543561912 " "
y[1] (numeric) = 1.014246543561912 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000007 " "
y[1] (analytic) = 1.0144152330904395 " "
y[1] (numeric) = 1.0144152330904395 " "
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) = 1.0145849082036515 " "
y[1] (numeric) = 1.0145849082036518 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.188526589836300200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17200000000000007 " "
y[1] (analytic) = 1.0147555687318737 " "
y[1] (numeric) = 1.0147555687318737 " "
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) = 1.0149272145044448 " "
y[1] (numeric) = 1.0149272145044448 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17400000000000007 " "
y[1] (analytic) = 1.0150998453497193 " "
y[1] (numeric) = 1.0150998453497193 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17500000000000007 " "
y[1] (analytic) = 1.0152734610950667 " "
y[1] (numeric) = 1.0152734610950664 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.187042343109565600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17600000000000007 " "
y[1] (analytic) = 1.0154480615668704 " "
y[1] (numeric) = 1.0154480615668704 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17700000000000007 " "
y[1] (analytic) = 1.015623646590531 " "
y[1] (numeric) = 1.0156236465905308 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.1862882542213300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17800000000000007 " "
y[1] (analytic) = 1.0158002159904627 " "
y[1] (numeric) = 1.0158002159904627 " "
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) = 1.0159777695900964 " "
y[1] (numeric) = 1.0159777695900964 " "
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) = 1.0161563072118787 " "
y[1] (numeric) = 1.0161563072118787 " "
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) = 1.0163358286772715 " "
y[1] (numeric) = 1.0163358286772717 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.18475624552186900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18200000000000008 " "
y[1] (analytic) = 1.016516333806754 " "
y[1] (numeric) = 1.016516333806754 " "
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) = 1.0166978224198204 " "
y[1] (numeric) = 1.0166978224198207 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.183978366320759600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18400000000000008 " "
y[1] (analytic) = 1.0168802943349826 " "
y[1] (numeric) = 1.0168802943349828 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.18358646698177600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18500000000000008 " "
y[1] (analytic) = 1.0170637493697685 " "
y[1] (numeric) = 1.0170637493697687 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.183192597933246400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18600000000000008 " "
y[1] (analytic) = 1.0172481873407233 " "
y[1] (numeric) = 1.0172481873407233 " "
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) = 1.0174336080634085 " "
y[1] (numeric) = 1.0174336080634088 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.182398961124085700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18800000000000008 " "
y[1] (analytic) = 1.017620011352404 " "
y[1] (numeric) = 1.0176200113524043 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.181999198600043700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18900000000000008 " "
y[1] (analytic) = 1.0178073970213064 " "
y[1] (numeric) = 1.0178073970213066 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.18159747683955100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000009 " "
y[1] (analytic) = 1.0179957648827296 " "
y[1] (numeric) = 1.01799576488273 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.36238759697807300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1910000000000001 " "
y[1] (analytic) = 1.0181851147483063 " "
y[1] (numeric) = 1.0181851147483068 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.36157633241221300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1920000000000001 " "
y[1] (analytic) = 1.0183754464286865 " "
y[1] (numeric) = 1.018375446428687 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.3607611653190100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1930000000000001 " "
y[1] (analytic) = 1.0185667597335382 " "
y[1] (numeric) = 1.0185667597335388 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.53991315158721300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1940000000000001 " "
y[1] (analytic) = 1.0187590544715488 " "
y[1] (numeric) = 1.0187590544715492 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.359119145011386400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1950000000000001 " "
y[1] (analytic) = 1.0189523304504227 " "
y[1] (numeric) = 1.0189523304504233 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.53743845387382300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1960000000000001 " "
y[1] (analytic) = 1.0191465874768846 " "
y[1] (numeric) = 1.0191465874768852 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.53619236879604100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1970000000000001 " "
y[1] (analytic) = 1.0193418253566775 " "
y[1] (numeric) = 1.019341825356678 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.356626980303408600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1980000000000001 " "
y[1] (analytic) = 1.019538043894563 " "
y[1] (numeric) = 1.0195380438945636 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.53368276705506800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1990000000000001 " "
y[1] (analytic) = 1.019735242894323 " "
y[1] (numeric) = 1.0197352428943236 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.53241926683244500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2000000000000001 " "
y[1] (analytic) = 1.0199334221587584 " "
y[1] (numeric) = 1.019933422158759 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.5311499780561800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2010000000000001 " "
y[1] (analytic) = 1.02013258148969 " "
y[1] (numeric) = 1.0201325814896907 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.52987490902746200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2020000000000001 " "
y[1] (analytic) = 1.0203327206879584 " "
y[1] (numeric) = 1.020332720687959 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.52859406807961400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2030000000000001 " "
y[1] (analytic) = 1.0205338395534245 " "
y[1] (numeric) = 1.0205338395534251 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.52730746357795900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2040000000000001 " "
y[1] (analytic) = 1.0207359378849694 " "
y[1] (numeric) = 1.02073593788497 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.52601510391968800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2050000000000001 " "
y[1] (analytic) = 1.020939015480495 " "
y[1] (numeric) = 1.0209390154804956 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.52471699753373300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2060000000000001 " "
y[1] (analytic) = 1.0211430721369235 " "
y[1] (numeric) = 1.021143072136924 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.34894210192041900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2070000000000001 " "
y[1] (analytic) = 1.021348107650198 " "
y[1] (numeric) = 1.0213481076501987 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.52210357845239600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2080000000000001 " "
y[1] (analytic) = 1.0215541218152835 " "
y[1] (numeric) = 1.0215541218152842 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.5207882827723910000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2090000000000001 " "
y[1] (analytic) = 1.0217611144261656 " "
y[1] (numeric) = 1.0217611144261662 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.51946727439518400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2100000000000001 " "
y[1] (analytic) = 1.0219690852758516 " "
y[1] (numeric) = 1.0219690852758525 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.69085408254190600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2110000000000001 " "
y[1] (analytic) = 1.0221780341563713 " "
y[1] (numeric) = 1.022178034156372 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.51680815392272200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2120000000000001 " "
y[1] (analytic) = 1.022387960858775 " "
y[1] (numeric) = 1.0223879608587758 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.68729341212197200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2130000000000001 " "
y[1] (analytic) = 1.0225988651731364 " "
y[1] (numeric) = 1.0225988651731373 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.6855017147877200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2140000000000001 " "
y[1] (analytic) = 1.0228107468885512 " "
y[1] (numeric) = 1.0228107468885521 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.68370245817239200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2150000000000001 " "
y[1] (analytic) = 1.0230236057931377 " "
y[1] (numeric) = 1.0230236057931386 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.68189565392805800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2160000000000001 " "
y[1] (analytic) = 1.0232374416740369 " "
y[1] (numeric) = 1.0232374416740377 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.68008131374715600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2170000000000001 " "
y[1] (analytic) = 1.0234522543174132 " "
y[1] (numeric) = 1.023452254317414 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.67825944936231300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2180000000000001 " "
y[1] (analytic) = 1.0236680435084535 " "
y[1] (numeric) = 1.0236680435084546 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.08455375906827190000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2190000000000001 " "
y[1] (analytic) = 1.0238848090313692 " "
y[1] (numeric) = 1.0238848090313704 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.08432414938890080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2200000000000001 " "
y[1] (analytic) = 1.0241025506693946 " "
y[1] (numeric) = 1.0241025506693957 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.0840936036136910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2210000000000001 " "
y[1] (analytic) = 1.0243212682047877 " "
y[1] (numeric) = 1.024321268204789 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.30063454787490930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22200000000000011 " "
y[1] (analytic) = 1.0245409614188317 " "
y[1] (numeric) = 1.0245409614188328 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.08362970972645970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22300000000000011 " "
y[1] (analytic) = 1.0247616300918327 " "
y[1] (numeric) = 1.0247616300918339 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.08339636460204430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22400000000000012 " "
y[1] (analytic) = 1.0249832740031222 " "
y[1] (numeric) = 1.0249832740031235 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2997945072283490000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22500000000000012 " "
y[1] (analytic) = 1.0252058929310568 " "
y[1] (numeric) = 1.025205892931058 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.08292688549715260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22600000000000012 " "
y[1] (analytic) = 1.025429486653017 " "
y[1] (numeric) = 1.0254294866530183 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.29922890544008550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22700000000000012 " "
y[1] (analytic) = 1.0256540549454094 " "
y[1] (numeric) = 1.0256540549454107 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.29894443757753970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22800000000000012 " "
y[1] (analytic) = 1.0258795975836656 " "
y[1] (numeric) = 1.025879597583667 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2986588608333590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22900000000000012 " "
y[1] (analytic) = 1.0261061143422432 " "
y[1] (numeric) = 1.0261061143422445 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.29837217703765550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000012 " "
y[1] (analytic) = 1.0263336049946252 " "
y[1] (numeric) = 1.0263336049946266 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.29808438802621550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23100000000000012 " "
y[1] (analytic) = 1.026562069313321 " "
y[1] (numeric) = 1.0265620693133224 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.29779549564047000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23200000000000012 " "
y[1] (analytic) = 1.0267915070698665 " "
y[1] (numeric) = 1.0267915070698679 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.29750550172746560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23300000000000012 " "
y[1] (analytic) = 1.0270219180348237 " "
y[1] (numeric) = 1.0270219180348252 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.5134168094964810000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23400000000000012 " "
y[1] (analytic) = 1.0272533019777819 " "
y[1] (numeric) = 1.0272533019777834 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.51307591952509170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23500000000000013 " "
y[1] (analytic) = 1.027485658667357 " "
y[1] (numeric) = 1.0274856586673586 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.51273375094223030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23600000000000013 " "
y[1] (analytic) = 1.0277189878711925 " "
y[1] (numeric) = 1.027718987871194 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.51239030592867300000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23700000000000013 " "
y[1] (analytic) = 1.0279532893559589 " "
y[1] (numeric) = 1.0279532893559606 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7280520990532430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23800000000000013 " "
y[1] (analytic) = 1.028188562887355 " "
y[1] (numeric) = 1.0281885628873568 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7276566804165690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23900000000000013 " "
y[1] (analytic) = 1.0284248082301075 " "
y[1] (numeric) = 1.028424808230109 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.51135233420725270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000013 " "
y[1] (analytic) = 1.0286620251479706 " "
y[1] (numeric) = 1.0286620251479721 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.51100380540599320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24100000000000013 " "
y[1] (analytic) = 1.0289002134037273 " "
y[1] (numeric) = 1.028900213403729 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.72646172705499370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24200000000000013 " "
y[1] (analytic) = 1.02913937275919 " "
y[1] (numeric) = 1.0291393727591918 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.72606051854543420000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24300000000000013 " "
y[1] (analytic) = 1.029379502975199 " "
y[1] (numeric) = 1.0293795029752006 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.50995063529321820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24400000000000013 " "
y[1] (analytic) = 1.0296206038116242 " "
y[1] (numeric) = 1.0296206038116258 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.50959705810198660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24500000000000013 " "
y[1] (analytic) = 1.0298626750273647 " "
y[1] (numeric) = 1.0298626750273663 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.50924222439066360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24600000000000014 " "
y[1] (analytic) = 1.030105716380349 " "
y[1] (numeric) = 1.0301057163803509 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7244412987456530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24700000000000014 " "
y[1] (analytic) = 1.0303497276275366 " "
y[1] (numeric) = 1.0303497276275382 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.50852879638659040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24800000000000014 " "
y[1] (analytic) = 1.0305947085249154 " "
y[1] (numeric) = 1.0305947085249172 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.72362309325529150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24900000000000014 " "
y[1] (analytic) = 1.0308406588275052 " "
y[1] (numeric) = 1.0308406588275068 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.50781036929909130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (analytic) = 1.0310875782893554 " "
y[1] (numeric) = 1.0310875782893567 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2920993886479660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2510000000000001 " "
y[1] (analytic) = 1.0313354666635464 " "
y[1] (numeric) = 1.0313354666635477 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2917888239218430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2520000000000001 " "
y[1] (analytic) = 1.03158432370219 " "
y[1] (numeric) = 1.0315843237021913 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.29147719574575740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2530000000000001 " "
y[1] (analytic) = 1.0318341491564291 " "
y[1] (numeric) = 1.0318341491564305 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.29116450607820700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2540000000000001 " "
y[1] (analytic) = 1.0320849427764385 " "
y[1] (numeric) = 1.0320849427764398 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.29085075688268460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2550000000000001 " "
y[1] (analytic) = 1.0323367043114244 " "
y[1] (numeric) = 1.0323367043114258 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.29053595012764670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2560000000000001 " "
y[1] (analytic) = 1.0325894335096255 " "
y[1] (numeric) = 1.0325894335096268 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.29022008778648700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2570000000000001 " "
y[1] (analytic) = 1.0328431301183123 " "
y[1] (numeric) = 1.0328431301183136 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2899031718375050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2580000000000001 " "
y[1] (analytic) = 1.0330977938837886 " "
y[1] (numeric) = 1.0330977938837898 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07465433688656530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2590000000000001 " "
y[1] (analytic) = 1.0333534245513902 " "
y[1] (numeric) = 1.0333534245513916 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28926618705363570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (analytic) = 1.0336100218654867 " "
y[1] (numeric) = 1.0336100218654882 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.50377047589956150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2610000000000001 " "
y[1] (analytic) = 1.033867585569481 " "
y[1] (numeric) = 1.0338675855694823 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28862501169948200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2620000000000001 " "
y[1] (analytic) = 1.034126115405809 " "
y[1] (numeric) = 1.0341261154058103 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28830285755561130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2630000000000001 " "
y[1] (analytic) = 1.0343856111159413 " "
y[1] (numeric) = 1.0343856111159426 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2879796617751460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2640000000000001 " "
y[1] (analytic) = 1.034646072440382 " "
y[1] (numeric) = 1.0346460724403832 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07304618864160360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2650000000000001 " "
y[1] (analytic) = 1.0349074991186697 " "
y[1] (numeric) = 1.0349074991186709 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07277512779705030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2660000000000001 " "
y[1] (analytic) = 1.035169890889378 " "
y[1] (numeric) = 1.0351698908893792 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07250320396326040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2670000000000001 " "
y[1] (analytic) = 1.035433247490115 " "
y[1] (numeric) = 1.035433247490116 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07223041882838090000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2680000000000001 " "
y[1] (analytic) = 1.035697568657524 " "
y[1] (numeric) = 1.0356975686575252 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07195677408438130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.26900000000000013 " "
y[1] (analytic) = 1.035962854127284 " "
y[1] (numeric) = 1.0359628541272852 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07168227142702980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (analytic) = 1.0362291036341094 " "
y[1] (numeric) = 1.0362291036341107 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28568829506704260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27100000000000013 " "
y[1] (analytic) = 1.0364963169117511 " "
y[1] (numeric) = 1.0364963169117523 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07113069917418980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27200000000000013 " "
y[1] (analytic) = 1.0367644936929956 " "
y[1] (numeric) = 1.0367644936929967 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07085363298901060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27300000000000013 " "
y[1] (analytic) = 1.0370336337096662 " "
y[1] (numeric) = 1.0370336337096673 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07057571571104990000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27400000000000013 " "
y[1] (analytic) = 1.0373037366926225 " "
y[1] (numeric) = 1.0373037366926239 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28435633886564320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27500000000000013 " "
y[1] (analytic) = 1.0375748023717621 " "
y[1] (numeric) = 1.0375748023717635 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28402080168561920000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27600000000000013 " "
y[1] (analytic) = 1.037846830476019 " "
y[1] (numeric) = 1.0378468304760204 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28368424937919750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27700000000000014 " "
y[1] (analytic) = 1.0381198207333653 " "
y[1] (numeric) = 1.0381198207333668 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.49723779801949730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27800000000000014 " "
y[1] (analytic) = 1.038393772870811 " "
y[1] (numeric) = 1.0383937728708124 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28300810767278980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27900000000000014 " "
y[1] (analytic) = 1.0386686866144035 " "
y[1] (numeric) = 1.0386686866144048 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28266852242632430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (analytic) = 1.0389445616892292 " "
y[1] (numeric) = 1.0389445616892306 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2823279303604440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28100000000000014 " "
y[1] (analytic) = 1.039221397819413 " "
y[1] (numeric) = 1.0392213978194145 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.49565072248956380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28200000000000014 " "
y[1] (analytic) = 1.0394991947281191 " "
y[1] (numeric) = 1.0394991947281205 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28164373412395230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28300000000000014 " "
y[1] (analytic) = 1.0397779521375505 " "
y[1] (numeric) = 1.0397779521375519 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28130013414050950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28400000000000014 " "
y[1] (analytic) = 1.0400576697689496 " "
y[1] (numeric) = 1.040057669768951 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28095553571193150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28500000000000014 " "
y[1] (analytic) = 1.040338347342599 " "
y[1] (numeric) = 1.0403383473426004 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.49404493109909470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28600000000000014 " "
y[1] (analytic) = 1.040619984577821 " "
y[1] (numeric) = 1.0406199845778226 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.49364057726202800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28700000000000014 " "
y[1] (analytic) = 1.0409025811929786 " "
y[1] (numeric) = 1.0409025811929802 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.49323506594999660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28800000000000014 " "
y[1] (analytic) = 1.041186136905475 " "
y[1] (numeric) = 1.0411861369054767 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.70608959957898350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28900000000000015 " "
y[1] (analytic) = 1.0414706514317547 " "
y[1] (numeric) = 1.0414706514317562 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.49242058078011050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (analytic) = 1.041756124487303 " "
y[1] (numeric) = 1.0417561244873046 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.49201161187333450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29100000000000015 " "
y[1] (analytic) = 1.0420425557866468 " "
y[1] (numeric) = 1.0420425557866486 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7046874233070680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29200000000000015 " "
y[1] (analytic) = 1.0423299450433552 " "
y[1] (numeric) = 1.042329945043357 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.70421741008924350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29300000000000015 " "
y[1] (analytic) = 1.0426182919700386 " "
y[1] (numeric) = 1.0426182919700404 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.70374609104910760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29400000000000015 " "
y[1] (analytic) = 1.0429075962783503 " "
y[1] (numeric) = 1.042907596278352 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.70327346903909580000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29500000000000015 " "
y[1] (analytic) = 1.0431978576789862 " "
y[1] (numeric) = 1.0431978576789878 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.4899496035521131000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29600000000000015 " "
y[1] (analytic) = 1.0434890758816846 " "
y[1] (numeric) = 1.0434890758816862 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.48953378660137900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29700000000000015 " "
y[1] (analytic) = 1.0437812505952273 " "
y[1] (numeric) = 1.0437812505952289 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.48911683706605800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29800000000000015 " "
y[1] (analytic) = 1.0440743815274396 " "
y[1] (numeric) = 1.0440743815274414 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7013700085251690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29900000000000015 " "
y[1] (analytic) = 1.0443684683851908 " "
y[1] (numeric) = 1.0443684683851926 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7008909146279230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (analytic) = 1.044663510874394 " "
y[1] (numeric) = 1.0446635108743958 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7004105349802268000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30100000000000016 " "
y[1] (analytic) = 1.0449595087000068 " "
y[1] (numeric) = 1.0449595087000085 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.6999288724690840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30200000000000016 " "
y[1] (analytic) = 1.0452564615660314 " "
y[1] (numeric) = 1.045256461566033 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.48701518873799320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30300000000000016 " "
y[1] (analytic) = 1.0455543691755145 " "
y[1] (numeric) = 1.0455543691755163 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.69896171042833470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30400000000000016 " "
y[1] (analytic) = 1.045853231230549 " "
y[1] (numeric) = 1.0458532312305509 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.69847621669647870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30500000000000016 " "
y[1] (analytic) = 1.046153047432273 " "
y[1] (numeric) = 1.0461530474322747 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.48574077023452320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30600000000000016 " "
y[1] (analytic) = 1.04645381748087 " "
y[1] (numeric) = 1.0464538174808715 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.4853137410468029000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30700000000000016 " "
y[1] (analytic) = 1.0467555410755698 " "
y[1] (numeric) = 1.0467555410755716 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.69701211953938700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30800000000000016 " "
y[1] (analytic) = 1.0470582179146493 " "
y[1] (numeric) = 1.047058217914651 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.69652155821678470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30900000000000016 " "
y[1] (analytic) = 1.0473618476954316 " "
y[1] (numeric) = 1.0473618476954332 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.48402602013359450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (analytic) = 1.0476664301142866 " "
y[1] (numeric) = 1.0476664301142882 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.4835945772412160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31100000000000017 " "
y[1] (analytic) = 1.0479719648666324 " "
y[1] (numeric) = 1.0479719648666337 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.27128174628195870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31200000000000017 " "
y[1] (analytic) = 1.0482784516469337 " "
y[1] (numeric) = 1.048278451646935 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2709100596860340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31300000000000017 " "
y[1] (analytic) = 1.0485858901487042 " "
y[1] (numeric) = 1.0485858901487055 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.27053743719673120000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31400000000000017 " "
y[1] (analytic) = 1.0488942800645051 " "
y[1] (numeric) = 1.0488942800645065 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2701638810236010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31500000000000017 " "
y[1] (analytic) = 1.0492036210859468 " "
y[1] (numeric) = 1.0492036210859481 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2697893933793940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31600000000000017 " "
y[1] (analytic) = 1.0495139129036881 " "
y[1] (numeric) = 1.0495139129036894 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.26941397648003100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31700000000000017 " "
y[1] (analytic) = 1.0498251552074374 " "
y[1] (numeric) = 1.0498251552074387 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.26903763254457540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31800000000000017 " "
y[1] (analytic) = 1.0501373476859523 " "
y[1] (numeric) = 1.0501373476859535 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.05721696982933420000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3190000000000002 " "
y[1] (analytic) = 1.0504504900270404 " "
y[1] (numeric) = 1.0504504900270415 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.05690181038097050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (analytic) = 1.050764581917559 " "
y[1] (numeric) = 1.0507645819175604 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2679030607587752000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3210000000000002 " "
y[1] (analytic) = 1.051079623043417 " "
y[1] (numeric) = 1.0510796230434183 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.26752303093136430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3220000000000002 " "
y[1] (analytic) = 1.0513956130895727 " "
y[1] (numeric) = 1.051395613089574 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.26714208520925850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3230000000000002 " "
y[1] (analytic) = 1.0517125517400363 " "
y[1] (numeric) = 1.0517125517400376 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2667602258297470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3240000000000002 " "
y[1] (analytic) = 1.0520304386778692 " "
y[1] (numeric) = 1.0520304386778705 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.26637745503305450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3250000000000002 " "
y[1] (analytic) = 1.0523492735851843 " "
y[1] (numeric) = 1.0523492735851856 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.26599377506231070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3260000000000002 " "
y[1] (analytic) = 1.0526690561431469 " "
y[1] (numeric) = 1.0526690561431482 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.26560918816352100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3270000000000002 " "
y[1] (analytic) = 1.0529897860319744 " "
y[1] (numeric) = 1.0529897860319757 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.26522369658553650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3280000000000002 " "
y[1] (analytic) = 1.053311462930937 " "
y[1] (numeric) = 1.0533114629309381 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.05403108548335530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3290000000000002 " "
y[1] (analytic) = 1.0536340865183578 " "
y[1] (numeric) = 1.0536340865183589 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.05370834033453880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (analytic) = 1.053957656471613 " "
y[1] (numeric) = 1.0539576564716142 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.0533848469225090000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3310000000000002 " "
y[1] (analytic) = 1.0542821724671332 " "
y[1] (numeric) = 1.0542821724671343 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.0530606071305519000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3320000000000002 " "
y[1] (analytic) = 1.0546076341804018 " "
y[1] (numeric) = 1.0546076341804032 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.26328274741304340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3330000000000002 " "
y[1] (analytic) = 1.0549340412859576 " "
y[1] (numeric) = 1.054934041285959 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2628918751414660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3340000000000002 " "
y[1] (analytic) = 1.0552613934573936 " "
y[1] (numeric) = 1.0552613934573947 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.05208342834156950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3350000000000002 " "
y[1] (analytic) = 1.055589690367357 " "
y[1] (numeric) = 1.0555896903673583 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.26210746628886070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3360000000000002 " "
y[1] (analytic) = 1.0559189316875517 " "
y[1] (numeric) = 1.0559189316875528 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.05142827854295310000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3370000000000002 " "
y[1] (analytic) = 1.0562491170887358 " "
y[1] (numeric) = 1.056249117088737 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.05109960014469430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3380000000000002 " "
y[1] (analytic) = 1.056580246240724 " "
y[1] (numeric) = 1.0565802462407254 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.26092422633335230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3390000000000002 " "
y[1] (analytic) = 1.0569123188123877 " "
y[1] (numeric) = 1.056912318812389 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2605280550114190000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (analytic) = 1.057245334471654 " "
y[1] (numeric) = 1.0572453344716553 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2601310084910170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3410000000000002 " "
y[1] (analytic) = 1.057579292885507 " "
y[1] (numeric) = 1.0575792928855083 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.25973308905776630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3420000000000002 " "
y[1] (analytic) = 1.0579141937199887 " "
y[1] (numeric) = 1.05791419371999 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.25933429899969330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3430000000000002 " "
y[1] (analytic) = 1.0582500366401981 " "
y[1] (numeric) = 1.0582500366401995 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.25893464060720360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3440000000000002 " "
y[1] (analytic) = 1.0585868213102925 " "
y[1] (numeric) = 1.0585868213102938 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.25853411617305040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3450000000000002 " "
y[1] (analytic) = 1.0589245473934872 " "
y[1] (numeric) = 1.0589245473934883 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.04844393999358980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3460000000000002 " "
y[1] (analytic) = 1.0592632145520557 " "
y[1] (numeric) = 1.059263214552057 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.25773047836234080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3470000000000002 " "
y[1] (analytic) = 1.0596028224473315 " "
y[1] (numeric) = 1.0596028224473328 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.25732736958277520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3480000000000002 " "
y[1] (analytic) = 1.0599433707397066 " "
y[1] (numeric) = 1.059943370739708 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2569234039554710000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3490000000000002 " "
y[1] (analytic) = 1.0602848590886325 " "
y[1] (numeric) = 1.0602848590886338 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.25651858378449170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3500000000000002 " "
y[1] (analytic) = 1.060627287152621 " "
y[1] (numeric) = 1.0606272871526223 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.25611291137607580000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3510000000000002 " "
y[1] (analytic) = 1.0609706545892443 " "
y[1] (numeric) = 1.0609706545892454 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.04642199086550630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3520000000000002 " "
y[1] (analytic) = 1.0613149610551345 " "
y[1] (numeric) = 1.0613149610551358 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.25529901908259050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3530000000000002 " "
y[1] (analytic) = 1.0616602062059854 " "
y[1] (numeric) = 1.0616602062059868 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.25489080382061390000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3540000000000002 " "
y[1] (analytic) = 1.0620063896965521 " "
y[1] (numeric) = 1.0620063896965533 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.04540145463944090000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3550000000000002 " "
y[1] (analytic) = 1.0623535111806508 " "
y[1] (numeric) = 1.062353511180652 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.04505987219951450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3560000000000002 " "
y[1] (analytic) = 1.0627015703111602 " "
y[1] (numeric) = 1.0627015703111613 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.04471759112963580000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3570000000000002 " "
y[1] (analytic) = 1.0630505667400212 " "
y[1] (numeric) = 1.0630505667400223 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.04437461336368570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3580000000000002 " "
y[1] (analytic) = 1.0634005001182374 " "
y[1] (numeric) = 1.0634005001182385 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.04403094083716630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3590000000000002 " "
y[1] (analytic) = 1.0637513700958754 " "
y[1] (numeric) = 1.0637513700958765 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.04368657548717670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3600000000000002 " "
y[1] (analytic) = 1.0641031763220652 " "
y[1] (numeric) = 1.0641031763220663 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.04334151925238930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3610000000000002 " "
y[1] (analytic) = 1.0644559184450006 " "
y[1] (numeric) = 1.0644559184450018 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.04299577407302530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3620000000000002 " "
y[1] (analytic) = 1.06480959611194 " "
y[1] (numeric) = 1.0648095961119408 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.34119473512665400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3630000000000002 " "
y[1] (analytic) = 1.065164208969205 " "
y[1] (numeric) = 1.065164208969206 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.33841779719246400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3640000000000002 " "
y[1] (analytic) = 1.0655197566621832 " "
y[1] (numeric) = 1.0655197566621841 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.3356353943394490000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3650000000000002 " "
y[1] (analytic) = 1.065876238835327 " "
y[1] (numeric) = 1.0658762388353278 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.33284754213706400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3660000000000002 " "
y[1] (analytic) = 1.066233655132154 " "
y[1] (numeric) = 1.0662336551321547 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.24754069212465600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3670000000000002 " "
y[1] (analytic) = 1.0665920051952482 " "
y[1] (numeric) = 1.0665920051952489 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.2454416640142810000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3680000000000002 " "
y[1] (analytic) = 1.0669512886662593 " "
y[1] (numeric) = 1.06695128866626 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.24333858397409500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3690000000000002 " "
y[1] (analytic) = 1.067311505185904 " "
y[1] (numeric) = 1.0673115051859046 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.24123146371468200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (analytic) = 1.0676726543939656 " "
y[1] (numeric) = 1.0676726543939663 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.23912031495464400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3710000000000002 " "
y[1] (analytic) = 1.0680347359292952 " "
y[1] (numeric) = 1.0680347359292959 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.23700514942046400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3720000000000002 " "
y[1] (analytic) = 1.0683977494298116 " "
y[1] (numeric) = 1.068397749429812 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.156590652564240400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3730000000000002 " "
y[1] (analytic) = 1.0687616945325005 " "
y[1] (numeric) = 1.0687616945325011 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.23276281497415900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3740000000000002 " "
y[1] (analytic) = 1.0691265708734172 " "
y[1] (numeric) = 1.0691265708734181 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.30751422607084500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3750000000000002 " "
y[1] (analytic) = 1.069492378087686 " "
y[1] (numeric) = 1.0694923780876866 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.22850455433987900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3760000000000002 " "
y[1] (analytic) = 1.0698591158094986 " "
y[1] (numeric) = 1.0698591158094994 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.30182597479756500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3770000000000002 " "
y[1] (analytic) = 1.0702267836721182 " "
y[1] (numeric) = 1.0702267836721189 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.2242304615988300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3780000000000002 " "
y[1] (analytic) = 1.0705953813078763 " "
y[1] (numeric) = 1.0705953813078772 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.29611667682608300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3790000000000002 " "
y[1] (analytic) = 1.070964908348176 " "
y[1] (numeric) = 1.070964908348177 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.29325417459312300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000002 " "
y[1] (analytic) = 1.07133536442349 " "
y[1] (numeric) = 1.0713353644234906 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.21778984336576700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3810000000000002 " "
y[1] (analytic) = 1.0717067491633618 " "
y[1] (numeric) = 1.0717067491633627 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.28751354223989300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38200000000000023 " "
y[1] (analytic) = 1.0720790621964074 " "
y[1] (numeric) = 1.0720790621964083 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.2846354435882910000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38300000000000023 " "
y[1] (analytic) = 1.0724523031503133 " "
y[1] (numeric) = 1.0724523031503141 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.28175217761306400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38400000000000023 " "
y[1] (analytic) = 1.0728264716518388 " "
y[1] (numeric) = 1.0728264716518396 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.27886376006914200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38500000000000023 " "
y[1] (analytic) = 1.0732015673268154 " "
y[1] (numeric) = 1.0732015673268163 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.27597020671936600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38600000000000023 " "
y[1] (analytic) = 1.0735775898001474 " "
y[1] (numeric) = 1.0735775898001483 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.27307153333430400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38700000000000023 " "
y[1] (analytic) = 1.0739545386958125 " "
y[1] (numeric) = 1.0739545386958134 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.27016775569206300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38800000000000023 " "
y[1] (analytic) = 1.0743324136368617 " "
y[1] (numeric) = 1.0743324136368626 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.2672588895781100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38900000000000023 " "
y[1] (analytic) = 1.07471121424542 " "
y[1] (numeric) = 1.074711214245421 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.26434495078509200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39000000000000024 " "
y[1] (analytic) = 1.0750909401426871 " "
y[1] (numeric) = 1.075090940142688 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.26142595511264600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39100000000000024 " "
y[1] (analytic) = 1.0754715909489367 " "
y[1] (numeric) = 1.0754715909489379 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.03231273979590400000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39200000000000024 " "
y[1] (analytic) = 1.0758531662835187 " "
y[1] (numeric) = 1.0758531662835196 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.25557285636192700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39300000000000024 " "
y[1] (analytic) = 1.076235665764857 " "
y[1] (numeric) = 1.0762356657648582 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.03157984811453480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39400000000000024 " "
y[1] (analytic) = 1.076619089010453 " "
y[1] (numeric) = 1.076619089010454 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.24969971985609000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39500000000000024 " "
y[1] (analytic) = 1.077003435636883 " "
y[1] (numeric) = 1.0770034356368836 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.18506675775994700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39600000000000024 " "
y[1] (analytic) = 1.0773887052598001 " "
y[1] (numeric) = 1.0773887052598008 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.18285500416920800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39700000000000024 " "
y[1] (analytic) = 1.0777748974939354 " "
y[1] (numeric) = 1.0777748974939358 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.12042636066833670000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39800000000000024 " "
y[1] (analytic) = 1.0781620119530961 " "
y[1] (numeric) = 1.0781620119530966 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.11894692009777500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39900000000000024 " "
y[1] (analytic) = 1.0785500482501682 " "
y[1] (numeric) = 1.0785500482501686 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.11746502232835400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (analytic) = 1.078939005997115 " "
y[1] (numeric) = 1.0789390059971156 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.17397101293486100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40100000000000025 " "
y[1] (analytic) = 1.0793288848049793 " "
y[1] (numeric) = 1.0793288848049798 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.114493886914772400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40200000000000025 " "
y[1] (analytic) = 1.0797196842838819 " "
y[1] (numeric) = 1.0797196842838825 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.16950699770657200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40300000000000025 " "
y[1] (analytic) = 1.0801114040430235 " "
y[1] (numeric) = 1.0801114040430242 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.16726952684373400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40400000000000025 " "
y[1] (analytic) = 1.0805040436906848 " "
y[1] (numeric) = 1.0805040436906852 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.11001895312843200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40500000000000025 " "
y[1] (analytic) = 1.0808976028342254 " "
y[1] (numeric) = 1.0808976028342259 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.108522478777034700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40600000000000025 " "
y[1] (analytic) = 1.0812920810800866 " "
y[1] (numeric) = 1.0812920810800872 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.16053540417777500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40700000000000025 " "
y[1] (analytic) = 1.0816874780337904 " "
y[1] (numeric) = 1.0816874780337908 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.105522333098413600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40800000000000025 " "
y[1] (analytic) = 1.0820837932999394 " "
y[1] (numeric) = 1.0820837932999399 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.10401867766415130000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40900000000000025 " "
y[1] (analytic) = 1.0824810264822187 " "
y[1] (numeric) = 1.082481026482219 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.102512644431624600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (analytic) = 1.082879177183395 " "
y[1] (numeric) = 1.0828791771833954 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.10100424135177830000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41100000000000025 " "
y[1] (analytic) = 1.0832782450053178 " "
y[1] (numeric) = 1.0832782450053182 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.09949347637718500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41200000000000025 " "
y[1] (analytic) = 1.083678229548919 " "
y[1] (numeric) = 1.0836782295489196 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.14697053619294500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41300000000000026 " "
y[1] (analytic) = 1.0840791304142146 " "
y[1] (numeric) = 1.084079130414215 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.09646489256168100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41400000000000026 " "
y[1] (analytic) = 1.0844809472003032 " "
y[1] (numeric) = 1.0844809472003036 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.094947089633281000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41500000000000026 " "
y[1] (analytic) = 1.0848836795053685 " "
y[1] (numeric) = 1.084883679505369 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.09342695663498600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41600000000000026 " "
y[1] (analytic) = 1.0852873269266778 " "
y[1] (numeric) = 1.0852873269266783 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.091904501526215700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41700000000000026 " "
y[1] (analytic) = 1.085691889060584 " "
y[1] (numeric) = 1.0856918890605847 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.13556959840124700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41800000000000026 " "
y[1] (analytic) = 1.0860973655025252 " "
y[1] (numeric) = 1.0860973655025257 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.0888526568203900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41900000000000026 " "
y[1] (analytic) = 1.0865037558470245 " "
y[1] (numeric) = 1.086503755847025 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.08732328314738600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (analytic) = 1.0869110596876919 " "
y[1] (numeric) = 1.0869110596876923 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.08579161921183500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42100000000000026 " "
y[1] (analytic) = 1.0873192766172235 " "
y[1] (numeric) = 1.087319276617224 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.08425767297785500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42200000000000026 " "
y[1] (analytic) = 1.0877284062274024 " "
y[1] (numeric) = 1.0877284062274029 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.08272145241024900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42300000000000026 " "
y[1] (analytic) = 1.088138448109099 " "
y[1] (numeric) = 1.0881384481090994 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.081182965474420000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42400000000000027 " "
y[1] (analytic) = 1.0885494018522717 " "
y[1] (numeric) = 1.0885494018522721 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.079642220136284000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42500000000000027 " "
y[1] (analytic) = 1.0889612670459665 " "
y[1] (numeric) = 1.088961267045967 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.07809922436219200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42600000000000027 " "
y[1] (analytic) = 1.089374043278318 " "
y[1] (numeric) = 1.0893740432783188 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.11483097917826100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42700000000000027 " "
y[1] (analytic) = 1.089787730136551 " "
y[1] (numeric) = 1.0897877301365515 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.075006513373186000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42800000000000027 " "
y[1] (analytic) = 1.0902023272069776 " "
y[1] (numeric) = 1.090202327206978 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.07345681409237300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42900000000000027 " "
y[1] (analytic) = 1.0906178340750012 " "
y[1] (numeric) = 1.0906178340750017 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.07190489624363550000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000027 " "
y[1] (analytic) = 1.091034250325115 " "
y[1] (numeric) = 1.0910342503251154 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.070350767794223600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43100000000000027 " "
y[1] (analytic) = 1.0914515755409027 " "
y[1] (numeric) = 1.091451575540903 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.068794436711316600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4320000000000003 " "
y[1] (analytic) = 1.0918698093050392 " "
y[1] (numeric) = 1.0918698093050396 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.06723591096194500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4330000000000003 " "
y[1] (analytic) = 1.0922889511992906 " "
y[1] (numeric) = 1.092288951199291 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.06567519851290300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4340000000000003 " "
y[1] (analytic) = 1.0927090008045153 " "
y[1] (numeric) = 1.0927090008045157 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.06411230733066730000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4350000000000003 " "
y[1] (analytic) = 1.0931299577006635 " "
y[1] (numeric) = 1.093129957700664 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.06254724538131700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4360000000000003 " "
y[1] (analytic) = 1.0935518214667783 " "
y[1] (numeric) = 1.0935518214667788 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.06098002063045200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4370000000000003 " "
y[1] (analytic) = 1.0939745916809964 " "
y[1] (numeric) = 1.0939745916809966 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.02970532052155400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4380000000000003 " "
y[1] (analytic) = 1.094398267920547 " "
y[1] (numeric) = 1.0943982679205475 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.057839114583680600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4390000000000003 " "
y[1] (analytic) = 1.0948228497617545 " "
y[1] (numeric) = 1.094822849761755 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.056265449215837300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (analytic) = 1.0952483367800367 " "
y[1] (numeric) = 1.0952483367800372 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.05468965290244400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4410000000000003 " "
y[1] (analytic) = 1.0956747285499067 " "
y[1] (numeric) = 1.095674728549907 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.0531117336054800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4420000000000003 " "
y[1] (analytic) = 1.0961020246449729 " "
y[1] (numeric) = 1.0961020246449733 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.05153169928595850000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4430000000000003 " "
y[1] (analytic) = 1.096530224637939 " "
y[1] (numeric) = 1.0965302246379394 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.049949557903846400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4440000000000003 " "
y[1] (analytic) = 1.0969593281006051 " "
y[1] (numeric) = 1.0969593281006056 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.04836531741798500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4450000000000003 " "
y[1] (analytic) = 1.097389334603868 " "
y[1] (numeric) = 1.0973893346038683 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.04677898578601100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4460000000000003 " "
y[1] (analytic) = 1.0978202437177211 " "
y[1] (numeric) = 1.0978202437177214 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.022595285482136600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4470000000000003 " "
y[1] (analytic) = 1.0982520550112551 " "
y[1] (numeric) = 1.0982520550112556 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.043600080907761600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4480000000000003 " "
y[1] (analytic) = 1.0986847680526592 " "
y[1] (numeric) = 1.0986847680526595 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.02100376178500800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4490000000000003 " "
y[1] (analytic) = 1.0991183824092199 " "
y[1] (numeric) = 1.0991183824092203 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.04041290690306100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (analytic) = 1.0995528976473232 " "
y[1] (numeric) = 1.0995528976473237 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.03881623885731700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4510000000000003 " "
y[1] (analytic) = 1.099988313332454 " "
y[1] (numeric) = 1.0999883133324544 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.03721752738152700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4520000000000003 " "
y[1] (analytic) = 1.1004246290291961 " "
y[1] (numeric) = 1.1004246290291968 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.05342517063401900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4530000000000003 " "
y[1] (analytic) = 1.1008618443012343 " "
y[1] (numeric) = 1.100861844301235 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.0510210088888890000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4540000000000003 " "
y[1] (analytic) = 1.1012999587113534 " "
y[1] (numeric) = 1.101299958711354 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.04861381775176300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4550000000000003 " "
y[1] (analytic) = 1.101738971821439 " "
y[1] (numeric) = 1.1017389718214396 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.0462036091345200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4560000000000003 " "
y[1] (analytic) = 1.1021788831924777 " "
y[1] (numeric) = 1.1021788831924784 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.04379039494593900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4570000000000003 " "
y[1] (analytic) = 1.1026196923845586 " "
y[1] (numeric) = 1.1026196923845593 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.04137418709158700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4580000000000003 " "
y[1] (analytic) = 1.1030613989568723 " "
y[1] (numeric) = 1.103061398956873 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.03895499747370400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4590000000000003 " "
y[1] (analytic) = 1.1035040024677123 " "
y[1] (numeric) = 1.103504002467713 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.03653283799108400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (analytic) = 1.103947502474475 " "
y[1] (numeric) = 1.1039475024744758 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.04547696071862200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4610000000000003 " "
y[1] (analytic) = 1.1043918985336605 " "
y[1] (numeric) = 1.1043918985336614 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.0422395426785610000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4620000000000003 " "
y[1] (analytic) = 1.104837190200873 " "
y[1] (numeric) = 1.1048371902008738 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.03899821238497100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4630000000000003 " "
y[1] (analytic) = 1.1052833770308206 " "
y[1] (numeric) = 1.1052833770308215 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.03575298568304300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4640000000000003 " "
y[1] (analytic) = 1.1057304585773164 " "
y[1] (numeric) = 1.1057304585773176 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.00406298480157670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4650000000000003 " "
y[1] (analytic) = 1.1061784343932795 " "
y[1] (numeric) = 1.1061784343932806 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.00365636330100340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4660000000000003 " "
y[1] (analytic) = 1.1066273040307335 " "
y[1] (numeric) = 1.1066273040307346 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.00324926068724850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4670000000000003 " "
y[1] (analytic) = 1.1070770670408092 " "
y[1] (numeric) = 1.10707706704081 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.02273343150540600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4680000000000003 " "
y[1] (analytic) = 1.1075277229737432 " "
y[1] (numeric) = 1.1075277229737441 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.01946896024725200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4690000000000003 " "
y[1] (analytic) = 1.10797927137888 " "
y[1] (numeric) = 1.107979271378881 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.01620068753440900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (analytic) = 1.1084317118046711 " "
y[1] (numeric) = 1.108431711804672 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.01292862917152700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4710000000000003 " "
y[1] (analytic) = 1.1088850437986761 " "
y[1] (numeric) = 1.108885043798677 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.00965280095687500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4720000000000003 " "
y[1] (analytic) = 1.109339266907563 " "
y[1] (numeric) = 1.109339266907564 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.00637321868219600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4730000000000003 " "
y[1] (analytic) = 1.109794380677109 " "
y[1] (numeric) = 1.1097943806771098 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.00308989813256200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4740000000000003 " "
y[1] (analytic) = 1.1102503846521998 " "
y[1] (numeric) = 1.1102503846522007 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.99980285508622900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4750000000000003 " "
y[1] (analytic) = 1.110707278376832 " "
y[1] (numeric) = 1.1107072783768328 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.99651210531449400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4760000000000003 " "
y[1] (analytic) = 1.1111650613941115 " "
y[1] (numeric) = 1.1111650613941124 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.99321766458154800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4770000000000003 " "
y[1] (analytic) = 1.1116237332462557 " "
y[1] (numeric) = 1.1116237332462566 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.98991954864433300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4780000000000003 " "
y[1] (analytic) = 1.1120832934745928 " "
y[1] (numeric) = 1.1120832934745934 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.98996332993930300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4790000000000003 " "
y[1] (analytic) = 1.112543741619562 " "
y[1] (numeric) = 1.112543741619563 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.98331235414778600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000003 " "
y[1] (analytic) = 1.1130050772207158 " "
y[1] (numeric) = 1.1130050772207167 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.98000330706482400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4810000000000003 " "
y[1] (analytic) = 1.1134672998167185 " "
y[1] (numeric) = 1.1134672998167194 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.97669064773005100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4820000000000003 " "
y[1] (analytic) = 1.1139304089453477 " "
y[1] (numeric) = 1.1139304089453486 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.97337439186204700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4830000000000003 " "
y[1] (analytic) = 1.114394404143494 " "
y[1] (numeric) = 1.1143944041434948 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.97754091637846900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4840000000000003 " "
y[1] (analytic) = 1.1148592849471624 " "
y[1] (numeric) = 1.114859284947163 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.97504836502002800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4850000000000003 " "
y[1] (analytic) = 1.1153250508914718 " "
y[1] (numeric) = 1.1153250508914727 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.96340420212215500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4860000000000003 " "
y[1] (analytic) = 1.1157917015106569 " "
y[1] (numeric) = 1.1157917015106578 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.96007371714300500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4870000000000003 " "
y[1] (analytic) = 1.1162592363380666 " "
y[1] (numeric) = 1.1162592363380675 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.95673971409930100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4880000000000003 " "
y[1] (analytic) = 1.1167276549061664 " "
y[1] (numeric) = 1.1167276549061673 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.95340220865896600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4890000000000003 " "
y[1] (analytic) = 1.1171969567465376 " "
y[1] (numeric) = 1.1171969567465385 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.95006121648100300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000003 " "
y[1] (analytic) = 1.1176671413898787 " "
y[1] (numeric) = 1.1176671413898795 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.94671675321534500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4910000000000003 " "
y[1] (analytic) = 1.1181382083660047 " "
y[1] (numeric) = 1.1181382083660056 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.94336883450273900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4920000000000003 " "
y[1] (analytic) = 1.118610157203849 " "
y[1] (numeric) = 1.1186101572038498 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.94001747597459700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4930000000000003 " "
y[1] (analytic) = 1.1190829874314625 " "
y[1] (numeric) = 1.1190829874314634 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.93666269325286400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4940000000000003 " "
y[1] (analytic) = 1.119556698576015 " "
y[1] (numeric) = 1.1195566985760161 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.91663062743736000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.49500000000000033 " "
y[1] (analytic) = 1.1200312901637959 " "
y[1] (numeric) = 1.120031290163797 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.91242864708534300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.49600000000000033 " "
y[1] (analytic) = 1.1205067617202134 " "
y[1] (numeric) = 1.1205067617202142 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.92657795600077200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.49700000000000033 " "
y[1] (analytic) = 1.1209831127697956 " "
y[1] (numeric) = 1.1209831127697965 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.92320963253012900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.49800000000000033 " "
y[1] (analytic) = 1.1214603428361918 " "
y[1] (numeric) = 1.1214603428361927 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.91983796282896100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.49900000000000033 " "
y[1] (analytic) = 1.1219384514421717 " "
y[1] (numeric) = 1.1219384514421729 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.89557870307452300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000003 " "
y[1] (analytic) = 1.1224174381096275 " "
y[1] (numeric) = 1.1224174381096284 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.91308464697406100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5010000000000003 " "
y[1] (analytic) = 1.1228973023595716 " "
y[1] (numeric) = 1.1228973023595727 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.88712878989216300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5020000000000003 " "
y[1] (analytic) = 1.1233780437121408 " "
y[1] (numeric) = 1.1233780437121417 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.90631813280940200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5030000000000003 " "
y[1] (analytic) = 1.1238596616865928 " "
y[1] (numeric) = 1.1238596616865937 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.90292996518108600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5040000000000003 " "
y[1] (analytic) = 1.12434215580131 " "
y[1] (numeric) = 1.1243421558013111 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.87442318067233800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5050000000000003 " "
y[1] (analytic) = 1.1248255255737987 " "
y[1] (numeric) = 1.1248255255737998 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.87017985797225800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5060000000000003 " "
y[1] (analytic) = 1.125309770520689 " "
y[1] (numeric) = 1.1253097705206898 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.89274600618777900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5070000000000003 " "
y[1] (analytic) = 1.1257948901577357 " "
y[1] (numeric) = 1.1257948901577366 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.88934491944338200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5080000000000003 " "
y[1] (analytic) = 1.1262808839998195 " "
y[1] (numeric) = 1.1262808839998204 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.8859406416087900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5090000000000003 " "
y[1] (analytic) = 1.1267677515609464 " "
y[1] (numeric) = 1.1267677515609473 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.88253318813663200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000003 " "
y[1] (analytic) = 1.1272554923542488 " "
y[1] (numeric) = 1.12725549235425 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.84890321808483500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5110000000000003 " "
y[1] (analytic) = 1.1277441058919864 " "
y[1] (numeric) = 1.1277441058919875 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.84463602003956800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5120000000000003 " "
y[1] (analytic) = 1.1282335916855453 " "
y[1] (numeric) = 1.1282335916855464 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.84036491030654800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5130000000000003 " "
y[1] (analytic) = 1.12872394924544 " "
y[1] (numeric) = 1.128723949245441 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.83608990814227600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5140000000000003 " "
y[1] (analytic) = 1.1292151780813127 " "
y[1] (numeric) = 1.1292151780813138 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.83181103278804400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5150000000000003 " "
y[1] (analytic) = 1.1297072777019346 " "
y[1] (numeric) = 1.129707277701936 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.17930339641637450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5160000000000003 " "
y[1] (analytic) = 1.1302002476152064 " "
y[1] (numeric) = 1.1302002476152078 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.1787890087277510000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5170000000000003 " "
y[1] (analytic) = 1.1306940873281583 " "
y[1] (numeric) = 1.1306940873281595 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.8189513597672100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5180000000000003 " "
y[1] (analytic) = 1.1311887963469505 " "
y[1] (numeric) = 1.1311887963469514 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.8517257470052700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5190000000000003 " "
y[1] (analytic) = 1.1316843741768736 " "
y[1] (numeric) = 1.1316843741768745 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.84828738442322700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000004 " "
y[1] (analytic) = 1.1321808203223502 " "
y[1] (numeric) = 1.1321808203223511 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.84484601538512600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5210000000000004 " "
y[1] (analytic) = 1.1326781342869343 " "
y[1] (numeric) = 1.1326781342869352 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.84140165519544200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5220000000000004 " "
y[1] (analytic) = 1.1331763155733119 " "
y[1] (numeric) = 1.1331763155733128 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.83795431914552500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5230000000000004 " "
y[1] (analytic) = 1.1336753636833015 " "
y[1] (numeric) = 1.1336753636833026 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.79313002814184400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5240000000000004 " "
y[1] (analytic) = 1.1341752781178553 " "
y[1] (numeric) = 1.1341752781178565 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.78881347570503300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5250000000000004 " "
y[1] (analytic) = 1.134676058377059 " "
y[1] (numeric) = 1.13467605837706 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.7844932606855400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5260000000000004 " "
y[1] (analytic) = 1.135177703960132 " "
y[1] (numeric) = 1.1351777039601332 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.78016940213043500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5270000000000004 " "
y[1] (analytic) = 1.135680214365429 " "
y[1] (numeric) = 1.13568021436543 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.77584191906964900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5280000000000004 " "
y[1] (analytic) = 1.1361835890904395 " "
y[1] (numeric) = 1.1361835890904408 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.17258129966189840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5290000000000004 " "
y[1] (analytic) = 1.136687827631789 " "
y[1] (numeric) = 1.1366878276317904 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.17206113865569920000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000004 " "
y[1] (analytic) = 1.1371929294852392 " "
y[1] (numeric) = 1.1371929294852405 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.17154054954707740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5310000000000004 " "
y[1] (analytic) = 1.1376988941456878 " "
y[1] (numeric) = 1.1376988941456891 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.17101953461122410000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5320000000000004 " "
y[1] (analytic) = 1.1382057211071703 " "
y[1] (numeric) = 1.1382057211071717 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.1704980961211890000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5330000000000004 " "
y[1] (analytic) = 1.1387134098628602 " "
y[1] (numeric) = 1.1387134098628613 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.74980196956550500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5340000000000004 " "
y[1] (analytic) = 1.1392219599050681 " "
y[1] (numeric) = 1.1392219599050692 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.7454496463329400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5350000000000004 " "
y[1] (analytic) = 1.1397313707252446 " "
y[1] (numeric) = 1.1397313707252457 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.74109385019988400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5360000000000004 " "
y[1] (analytic) = 1.1402416418139785 " "
y[1] (numeric) = 1.1402416418139796 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.73673460003560100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5370000000000004 " "
y[1] (analytic) = 1.140752772660999 " "
y[1] (numeric) = 1.140752772661 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.732371914690800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5380000000000004 " "
y[1] (analytic) = 1.1412647627551753 " "
y[1] (numeric) = 1.1412647627551764 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.72800581299750700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5390000000000004 " "
y[1] (analytic) = 1.141777611584517 " "
y[1] (numeric) = 1.1417776115845184 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.16683635765227140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000004 " "
y[1] (analytic) = 1.142291318636176 " "
y[1] (numeric) = 1.1422913186361772 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.7192634357993100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5410000000000004 " "
y[1] (analytic) = 1.1428058833964447 " "
y[1] (numeric) = 1.1428058833964458 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.71488719786381200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5420000000000004 " "
y[1] (analytic) = 1.1433213053507587 " "
y[1] (numeric) = 1.1433213053507598 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.71050761871836300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5430000000000004 " "
y[1] (analytic) = 1.1438375839836958 " "
y[1] (numeric) = 1.143837583983697 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.70612471709953500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5440000000000004 " "
y[1] (analytic) = 1.1443547187789775 " "
y[1] (numeric) = 1.1443547187789789 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.16420862140692930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5450000000000004 " "
y[1] (analytic) = 1.1448727092194693 " "
y[1] (numeric) = 1.1448727092194706 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.1636818825548541000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5460000000000004 " "
y[1] (analytic) = 1.1453915547871807 " "
y[1] (numeric) = 1.1453915547871818 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.69295626447535100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5470000000000004 " "
y[1] (analytic) = 1.145911254963266 " "
y[1] (numeric) = 1.145911254963267 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.6885602599369400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5480000000000004 " "
y[1] (analytic) = 1.1464318092280252 " "
y[1] (numeric) = 1.1464318092280261 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.74732882105041700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5490000000000004 " "
y[1] (analytic) = 1.1469532170609038 " "
y[1] (numeric) = 1.146953217060905 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.67975858222125800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000004 " "
y[1] (analytic) = 1.1474754779404943 " "
y[1] (numeric) = 1.1474754779404954 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.67535294625904300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5510000000000004 " "
y[1] (analytic) = 1.147998591344536 " "
y[1] (numeric) = 1.147998591344537 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.73675530960269300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5520000000000004 " "
y[1] (analytic) = 1.1485225567499153 " "
y[1] (numeric) = 1.1485225567499162 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.73322573840856100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5530000000000004 " "
y[1] (analytic) = 1.149047373632667 " "
y[1] (numeric) = 1.1490473736326678 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.72969365825348800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5540000000000004 " "
y[1] (analytic) = 1.1495730414679741 " "
y[1] (numeric) = 1.1495730414679748 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.79461931296213200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5550000000000004 " "
y[1] (analytic) = 1.1500995597301689 " "
y[1] (numeric) = 1.1500995597301695 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.79196652271894800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5560000000000004 " "
y[1] (analytic) = 1.1506269278927328 " "
y[1] (numeric) = 1.1506269278927337 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.71908251205924900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5570000000000004 " "
y[1] (analytic) = 1.1511551454282984 " "
y[1] (numeric) = 1.151155145428299 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.78665540800977300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5580000000000004 " "
y[1] (analytic) = 1.1516842118086477 " "
y[1] (numeric) = 1.1516842118086483 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.78399710567337400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5590000000000004 " "
y[1] (analytic) = 1.1522141265047146 " "
y[1] (numeric) = 1.1522141265047152 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.7813369880808200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000004 " "
y[1] (analytic) = 1.1527448889865841 " "
y[1] (numeric) = 1.1527448889865848 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.77867506626478300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5610000000000004 " "
y[1] (analytic) = 1.153276498723494 " "
y[1] (numeric) = 1.153276498723495 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.70134846832660600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5620000000000004 " "
y[1] (analytic) = 1.1538089551838349 " "
y[1] (numeric) = 1.1538089551838357 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.69779447203729600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5630000000000004 " "
y[1] (analytic) = 1.1543422578351499 " "
y[1] (numeric) = 1.1543422578351508 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.69423811414313600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5640000000000004 " "
y[1] (analytic) = 1.1548764061441368 " "
y[1] (numeric) = 1.1548764061441374 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.76800955696341200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5650000000000004 " "
y[1] (analytic) = 1.1554113995766468 " "
y[1] (numeric) = 1.1554113995766477 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.68711837208428000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5660000000000004 " "
y[1] (analytic) = 1.1559472375976871 " "
y[1] (numeric) = 1.155947237597688 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.68355501714728300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5670000000000004 " "
y[1] (analytic) = 1.1564839196714196 " "
y[1] (numeric) = 1.1564839196714203 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.75999201929548700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5680000000000004 " "
y[1] (analytic) = 1.1570214452611618 " "
y[1] (numeric) = 1.1570214452611627 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.67642141239349600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5690000000000004 " "
y[1] (analytic) = 1.1575598138293888 " "
y[1] (numeric) = 1.1575598138293894 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.75463839377266500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000004 " "
y[1] (analytic) = 1.1580990248377314 " "
y[1] (numeric) = 1.1580990248377323 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.66927871150373900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5710000000000004 " "
y[1] (analytic) = 1.1586390777469793 " "
y[1] (numeric) = 1.1586390777469802 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.66570398632872100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5720000000000004 " "
y[1] (analytic) = 1.1591799720170792 " "
y[1] (numeric) = 1.1591799720170801 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.66212703066818400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5730000000000004 " "
y[1] (analytic) = 1.159721707107137 " "
y[1] (numeric) = 1.159721707107138 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.65854785900005400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5740000000000004 " "
y[1] (analytic) = 1.160264282475418 " "
y[1] (numeric) = 1.1602642824754186 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.74122486433781000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5750000000000004 " "
y[1] (analytic) = 1.160807697579346 " "
y[1] (numeric) = 1.1608076975793469 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.65138292546009400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5760000000000004 " "
y[1] (analytic) = 1.1613519518755069 " "
y[1] (numeric) = 1.1613519518755075 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.7358478943384200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5770000000000004 " "
y[1] (analytic) = 1.161897044819646 " "
y[1] (numeric) = 1.1618970448196466 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.73315697587038600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5780000000000004 " "
y[1] (analytic) = 1.1624429758666701 " "
y[1] (numeric) = 1.162442975866671 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.64061926597247100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5790000000000004 " "
y[1] (analytic) = 1.1629897444706487 " "
y[1] (numeric) = 1.1629897444706496 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.63702710125266200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000004 " "
y[1] (analytic) = 1.1635373500848134 " "
y[1] (numeric) = 1.163537350084814 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.72507461601071600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5810000000000004 " "
y[1] (analytic) = 1.164085792161558 " "
y[1] (numeric) = 1.1640857921615588 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.62983644058477700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5820000000000004 " "
y[1] (analytic) = 1.1646350701524408 " "
y[1] (numeric) = 1.1646350701524417 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.62623797327235100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5830000000000004 " "
y[1] (analytic) = 1.165185183508184 " "
y[1] (numeric) = 1.1651851835081848 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.62263743369928400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5840000000000004 " "
y[1] (analytic) = 1.1657361316786738 " "
y[1] (numeric) = 1.1657361316786747 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.61903483613515300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5850000000000004 " "
y[1] (analytic) = 1.1662879141129627 " "
y[1] (numeric) = 1.1662879141129636 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.61543019483008400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5860000000000004 " "
y[1] (analytic) = 1.1668405302592677 " "
y[1] (numeric) = 1.1668405302592688 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.51477940501834500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5870000000000004 " "
y[1] (analytic) = 1.1673939795649733 " "
y[1] (numeric) = 1.1673939795649744 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.51026854737488600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5880000000000004 " "
y[1] (analytic) = 1.1679482614766301 " "
y[1] (numeric) = 1.167948261476631 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.60460415067707200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5890000000000004 " "
y[1] (analytic) = 1.1685033754399559 " "
y[1] (numeric) = 1.1685033754399567 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.60099147651768800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000004 " "
y[1] (analytic) = 1.1690593208998368 " "
y[1] (numeric) = 1.1690593208998377 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.59737682957341600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5910000000000004 " "
y[1] (analytic) = 1.1696160973003276 " "
y[1] (numeric) = 1.1696160973003285 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.59376022397598500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5920000000000004 " "
y[1] (analytic) = 1.170173704084652 " "
y[1] (numeric) = 1.170173704084653 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.5901416738371100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5930000000000004 " "
y[1] (analytic) = 1.1707321406952031 " "
y[1] (numeric) = 1.170732140695204 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.58652119324842200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5940000000000004 " "
y[1] (analytic) = 1.1712914065735445 " "
y[1] (numeric) = 1.1712914065735454 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.58289879628137800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5950000000000004 " "
y[1] (analytic) = 1.1718515011604103 " "
y[1] (numeric) = 1.1718515011604111 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.5792744969871910000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5960000000000004 " "
y[1] (analytic) = 1.1724124238957057 " "
y[1] (numeric) = 1.1724124238957068 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.46956038674594100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5970000000000004 " "
y[1] (analytic) = 1.1729741742185085 " "
y[1] (numeric) = 1.1729741742185094 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.57202024752055800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5980000000000004 " "
y[1] (analytic) = 1.173536751567068 " "
y[1] (numeric) = 1.173536751567069 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.56839032534862600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5990000000000004 " "
y[1] (analytic) = 1.174100155378807 " "
y[1] (numeric) = 1.174100155378808 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.56475855685043300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000004 " "
y[1] (analytic) = 1.1746643850903218 " "
y[1] (numeric) = 1.174664385090323 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.4514061949685300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6010000000000004 " "
y[1] (analytic) = 1.1752294401373828 " "
y[1] (numeric) = 1.175229440137384 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.4468619208124400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6020000000000004 " "
y[1] (analytic) = 1.1757953199549351 " "
y[1] (numeric) = 1.175795319954936 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.55385231278320200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6030000000000004 " "
y[1] (analytic) = 1.1763620239770987 " "
y[1] (numeric) = 1.1763620239770995 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.55021329826111700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6040000000000004 " "
y[1] (analytic) = 1.1769295516371696 " "
y[1] (numeric) = 1.1769295516371705 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.54657250694931800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6050000000000004 " "
y[1] (analytic) = 1.1774979023676202 " "
y[1] (numeric) = 1.177497902367621 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.5429299526924500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6060000000000004 " "
y[1] (analytic) = 1.1780670756001 " "
y[1] (numeric) = 1.1780670756001008 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.53928564931409100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6070000000000004 " "
y[1] (analytic) = 1.1786370707654357 " "
y[1] (numeric) = 1.1786370707654366 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.53563961061669700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6080000000000004 " "
y[1] (analytic) = 1.1792078872936322 " "
y[1] (numeric) = 1.1792078872936331 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.53199185038152300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6090000000000004 " "
y[1] (analytic) = 1.179779524613873 " "
y[1] (numeric) = 1.1797795246138738 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.52834238236856100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000004 " "
y[1] (analytic) = 1.1803519821545208 " "
y[1] (numeric) = 1.1803519821545216 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.5246912203164600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6110000000000004 " "
y[1] (analytic) = 1.180925259343118 " "
y[1] (numeric) = 1.180925259343119 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.52103837794246700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6120000000000004 " "
y[1] (analytic) = 1.181499355606388 " "
y[1] (numeric) = 1.1814993556063886 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.63803790170676900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6130000000000004 " "
y[1] (analytic) = 1.1820742703702338 " "
y[1] (numeric) = 1.1820742703702345 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.63529578024277800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = sin(x);"
Iterations = 514
"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 2 Minutes 14 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 2 Minutes 14 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 5 Minutes 14 Seconds
"Time to Timeout " Unknown
Percent Done = 57.22222222222227 "%"
(%o57) true
(%o57) diffeq.max