(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr # 0.0 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr # 0.0 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
elseif (omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 5
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
elseif (omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 5
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : sinh(array_const_0D1 ),
1 1
array_tmp2 : cosh(array_const_0D05 ), array_tmp3 : array_tmp1 array_tmp2 ,
1 1 1 1 1
array_tmp3
1
array_tmp4 : tanh(array_const_0D02 ), array_tmp5 : -----------,
1 1 1 array_tmp4
1
array_tmp6 : array_tmp5 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1),
1
temporary
array_y : temporary, array_y_higher : temporary, temporary : ---------,
2 1, 2 glob_h
array_y_higher : temporary, 0)), kkk : 2,
2, 1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(1, 2),
2
temporary
array_y : temporary, array_y_higher : temporary, temporary : ---------,
3 1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (order_d : 1,
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
array_tmp6 expt(glob_h, order_d)
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y : temporary, array_y_higher : temporary,
order_d + kkk 1, order_d + kkk
term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2,
while term >= 1 do (if adj3 <= 1 + order_d
temporary convfp(adj2)
then (if adj2 > 1 then temporary : ----------------------
glob_h
temporary
else temporary : ---------, array_y_higher : temporary),
glob_h adj3, term
term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : sinh(array_const_0D1 ),
1 1
array_tmp2 : cosh(array_const_0D05 ), array_tmp3 : array_tmp1 array_tmp2 ,
1 1 1 1 1
array_tmp3
1
array_tmp4 : tanh(array_const_0D02 ), array_tmp5 : -----------,
1 1 1 array_tmp4
1
array_tmp6 : array_tmp5 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1),
1
temporary
array_y : temporary, array_y_higher : temporary, temporary : ---------,
2 1, 2 glob_h
array_y_higher : temporary, 0)), kkk : 2,
2, 1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(1, 2),
2
temporary
array_y : temporary, array_y_higher : temporary, temporary : ---------,
3 1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (order_d : 1,
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
array_tmp6 expt(glob_h, order_d)
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y : temporary, array_y_higher : temporary,
order_d + kkk 1, order_d + kkk
term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2,
while term >= 1 do (if adj3 <= 1 + order_d
temporary convfp(adj2)
then (if adj2 > 1 then temporary : ----------------------
glob_h
temporary
else temporary : ---------, array_y_higher : temporary),
glob_h adj3, term
term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error # 0.0
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error # 0.0
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i32) log_revs(file, revs) := printf(file, revs)
(%o32) log_revs(file, revs) := printf(file, revs)
(%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i35) logstart(file) := printf(file, "")
(%o35) logstart(file) := printf(file, "
")
(%i36) logend(file) := printf(file, "
~%")
(%o36) logend(file) := printf(file, "~%")
(%i37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i40) factorial_2(nnn) := nnn!
(%o40) factorial_2(nnn) := nnn!
(%i41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i46) arcsin(x) := asin(x)
(%o46) arcsin(x) := asin(x)
(%i47) arccos(x) := acos(x)
(%o47) arccos(x) := acos(x)
(%i48) arctan(x) := atan(x)
(%o48) arctan(x) := atan(x)
(%i49) omniabs(x) := abs(x)
(%o49) omniabs(x) := abs(x)
y
(%i50) expt(x, y) := x
y
(%o50) expt(x, y) := x
(%i51) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%o51) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(sinh(0.1) cosh(0.05)) x
(%i52) exact_soln_y(x) := block(------------------------)
tanh(0.02)
(sinh(0.1) cosh(0.05)) x
(%o52) exact_soln_y(x) := block(------------------------)
tanh(0.02)
(%i53) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h], define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\
########temp/mult_div_sinh_cosh_tanhpostode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = sinh(0.1) * cosh(0.05) / tanh(0.02);"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS,
"glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " ((sinh(0.1) * cosh(0.05) / tanh(0.02)) * x) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2_g, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4_g, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_tmp6, 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_g : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp4_g : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
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_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2_g : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_g : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D05, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D05 : 0.0, term : 1 + term),
term
array_const_0D05 : 0.05, array(array_const_0D02, 1 + 1 + max_terms),
1
term : 1, while term <= 1 + max_terms do (array_const_0D02 : 0.0,
term
term : 1 + term), array_const_0D02 : 0.02,
1
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05,
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"),
if glob_iter >= glob_max_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = sinh(0.1) * cosh(0.05) / tanh(0.02);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-12-15T01:55:31-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file,
"mult_div_sinh_cosh_tanh"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sinh(0.1) * cosh(0.05) / tanh(0.02);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 151 | "), logitem_str(html_log_file, "mult_div_sinh_cosh_tanh diffeq.m\
ax"), logitem_str(html_log_file, "mult_div_sinh_cosh_tanh maxima results"),
logitem_str(html_log_file, "Languages compared"), logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%o53) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h], define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\
########temp/mult_div_sinh_cosh_tanhpostode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = sinh(0.1) * cosh(0.05) / tanh(0.02);"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS,
"glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " ((sinh(0.1) * cosh(0.05) / tanh(0.02)) * x) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2_g, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4_g, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_tmp6, 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_g : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp4_g : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
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_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2_g : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_g : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D05, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D05 : 0.0, term : 1 + term),
term
array_const_0D05 : 0.05, array(array_const_0D02, 1 + 1 + max_terms),
1
term : 1, while term <= 1 + max_terms do (array_const_0D02 : 0.0,
term
term : 1 + term), array_const_0D02 : 0.02,
1
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05,
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"),
if glob_iter >= glob_max_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = sinh(0.1) * cosh(0.05) / tanh(0.02);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-12-15T01:55:31-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file,
"mult_div_sinh_cosh_tanh"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sinh(0.1) * cosh(0.05) / tanh(0.02);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 151 | "), logitem_str(html_log_file, "mult_div_sinh_cosh_tanh diffeq.m\
ax"), logitem_str(html_log_file, "mult_div_sinh_cosh_tanh maxima results"),
logitem_str(html_log_file, "Languages compared"), logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i54) main()
"##############ECHO OF PROBLEM#################"
"##############temp/mult_div_sinh_cosh_tanhpostode.ode#################"
"diff ( y , x , 1 ) = sinh(0.1) * cosh(0.05) / tanh(0.02);"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.1,"
"x_end:5.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.05,"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" ((sinh(0.1) * cosh(0.05) / tanh(0.02)) * x) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 4.9 ""
estimated_steps = 4900. ""
step_error = 2.040816326530612300000000000000E-14 ""
est_needed_step_err = 2.040816326530612300000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_value3 = 0.0 ""
value3 = 0.0 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = 0.1 " "
y[1] (analytic) = 0.5015267822632982 " "
y[1] (numeric) = 0.5015267822632982 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.101 " "
y[1] (analytic) = 0.5065420500859312 " "
y[1] (numeric) = 0.5065420500859311 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.191768727664001600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10200000000000001 " "
y[1] (analytic) = 0.5115573179085642 " "
y[1] (numeric) = 0.5115573179085641 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.170280798961413700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10300000000000001 " "
y[1] (analytic) = 0.5165725857311971 " "
y[1] (numeric) = 0.516572585731197 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.149210111592856400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10400000000000001 " "
y[1] (analytic) = 0.5215878535538302 " "
y[1] (numeric) = 0.52158785355383 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 4.25708925950123400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10500000000000001 " "
y[1] (analytic) = 0.5266031213764631 " "
y[1] (numeric) = 0.5266031213764629 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 4.21654555226788900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10600000000000001 " "
y[1] (analytic) = 0.5316183891990961 " "
y[1] (numeric) = 0.5316183891990959 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 4.17676682064272050000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10700000000000001 " "
y[1] (analytic) = 0.5366336570217292 " "
y[1] (numeric) = 0.5366336570217288 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 6.20659742506721800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10800000000000001 " "
y[1] (analytic) = 0.5416489248443621 " "
y[1] (numeric) = 0.5416489248443618 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 6.14912893039067200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10900000000000001 " "
y[1] (analytic) = 0.5466641926669951 " "
y[1] (numeric) = 0.5466641926669947 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 6.09271490350635400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11000000000000001 " "
y[1] (analytic) = 0.5516794604896281 " "
y[1] (numeric) = 0.5516794604896277 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 8.04976878160233300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11100000000000002 " "
y[1] (analytic) = 0.5566947283122611 " "
y[1] (numeric) = 0.5566947283122606 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 7.97724834212843900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11200000000000002 " "
y[1] (analytic) = 0.561709996134894 " "
y[1] (numeric) = 0.5617099961348936 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 7.90602291050229200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11300000000000002 " "
y[1] (analytic) = 0.5667252639575271 " "
y[1] (numeric) = 0.5667252639575265 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 9.79507263248071500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11400000000000002 " "
y[1] (analytic) = 0.57174053178016 " "
y[1] (numeric) = 0.5717405317801595 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 9.70915094272211200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11500000000000002 " "
y[1] (analytic) = 0.576755799602793 " "
y[1] (numeric) = 0.5767557996027924 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 9.62472354322018200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11600000000000002 " "
y[1] (analytic) = 0.581771067425426 " "
y[1] (numeric) = 0.5817710674254254 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 9.5417517885372490000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11700000000000002 " "
y[1] (analytic) = 0.586786335248059 " "
y[1] (numeric) = 0.5867863352480583 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 1.13522380253366240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11800000000000002 " "
y[1] (analytic) = 0.591801603070692 " "
y[1] (numeric) = 0.5918016030706913 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 1.12560326183422460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11900000000000002 " "
y[1] (analytic) = 0.5968168708933249 " "
y[1] (numeric) = 0.5968168708933242 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 1.11614441089444130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12000000000000002 " "
y[1] (analytic) = 0.601832138715958 " "
y[1] (numeric) = 0.6018321387159572 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 1.29131707538204080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12100000000000002 " "
y[1] (analytic) = 0.6068474065385909 " "
y[1] (numeric) = 0.6068474065385902 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 1.2806450334367350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12200000000000003 " "
y[1] (analytic) = 0.6118626743612239 " "
y[1] (numeric) = 0.6118626743612231 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 1.27014794299872900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12300000000000003 " "
y[1] (analytic) = 0.6168779421838569 " "
y[1] (numeric) = 0.616877942183856 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.43979604223781560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12400000000000003 " "
y[1] (analytic) = 0.6218932100064899 " "
y[1] (numeric) = 0.621893210006489 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.4281847838326720000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12500000000000003 " "
y[1] (analytic) = 0.6269084778291228 " "
y[1] (numeric) = 0.626908477829122 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.41675930556201060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12600000000000003 " "
y[1] (analytic) = 0.6319237456517559 " "
y[1] (numeric) = 0.6319237456517549 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 1.5812045821004580000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12700000000000003 " "
y[1] (analytic) = 0.6369390134743889 " "
y[1] (numeric) = 0.6369390134743879 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 1.56875415232013980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12800000000000003 " "
y[1] (analytic) = 0.6419542812970218 " "
y[1] (numeric) = 0.6419542812970208 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 1.55649826050513860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12900000000000003 " "
y[1] (analytic) = 0.6469695491196549 " "
y[1] (numeric) = 0.6469695491196538 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.71603598057414040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13000000000000003 " "
y[1] (analytic) = 0.6519848169422878 " "
y[1] (numeric) = 0.6519848169422867 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.70283570380049350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13100000000000003 " "
y[1] (analytic) = 0.6570000847649208 " "
y[1] (numeric) = 0.6570000847649197 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.68983695796995540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13200000000000003 " "
y[1] (analytic) = 0.6620153525875537 " "
y[1] (numeric) = 0.6620153525875526 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.67703516283381950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13300000000000003 " "
y[1] (analytic) = 0.6670306204101868 " "
y[1] (numeric) = 0.6670306204101856 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.8308684634847410000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13400000000000004 " "
y[1] (analytic) = 0.6720458882328197 " "
y[1] (numeric) = 0.6720458882328185 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.8172052659960490000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13500000000000004 " "
y[1] (analytic) = 0.6770611560554527 " "
y[1] (numeric) = 0.6770611560554515 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.803744486247930200000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13600000000000004 " "
y[1] (analytic) = 0.6820764238780858 " "
y[1] (numeric) = 0.6820764238780844 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.95325271906527180000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13700000000000004 " "
y[1] (analytic) = 0.6870916917007187 " "
y[1] (numeric) = 0.6870916917007174 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.9389953999480070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13800000000000004 " "
y[1] (analytic) = 0.6921069595233517 " "
y[1] (numeric) = 0.6921069595233503 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.9249447086440360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13900000000000004 " "
y[1] (analytic) = 0.6971222273459847 " "
y[1] (numeric) = 0.6971222273459833 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 2.07035420102362120000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14000000000000004 " "
y[1] (analytic) = 0.7021374951686177 " "
y[1] (numeric) = 0.7021374951686162 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 2.05556595673059560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14100000000000004 " "
y[1] (analytic) = 0.7071527629912506 " "
y[1] (numeric) = 0.7071527629912492 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 2.04098747476796740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14200000000000004 " "
y[1] (analytic) = 0.7121680308138837 " "
y[1] (numeric) = 0.7121680308138821 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 2.18250773304006880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14300000000000004 " "
y[1] (analytic) = 0.7171832986365166 " "
y[1] (numeric) = 0.7171832986365151 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 2.16724544120062780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14400000000000004 " "
y[1] (analytic) = 0.7221985664591496 " "
y[1] (numeric) = 0.722198566459148 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 2.15219512563673470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14500000000000005 " "
y[1] (analytic) = 0.7272138342817825 " "
y[1] (numeric) = 0.727213834281781 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 2.13735240063234360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14600000000000005 " "
y[1] (analytic) = 0.7322291021044156 " "
y[1] (numeric) = 0.7322291021044139 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 2.2743353578157272000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14700000000000005 " "
y[1] (analytic) = 0.7372443699270486 " "
y[1] (numeric) = 0.7372443699270469 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 2.258863688714940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14800000000000005 " "
y[1] (analytic) = 0.7422596377496815 " "
y[1] (numeric) = 0.7422596377496798 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 2.24360109622362330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14900000000000005 " "
y[1] (analytic) = 0.7472749055723146 " "
y[1] (numeric) = 0.7472749055723128 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.37711292879531940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15000000000000005 " "
y[1] (analytic) = 0.7522901733949475 " "
y[1] (numeric) = 0.7522901733949457 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.36126550927001740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15100000000000005 " "
y[1] (analytic) = 0.7573054412175805 " "
y[1] (numeric) = 0.7573054412175787 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.3456279893410772000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15200000000000005 " "
y[1] (analytic) = 0.7623207090402135 " "
y[1] (numeric) = 0.7623207090402117 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.4758334903941380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15300000000000005 " "
y[1] (analytic) = 0.7673359768628465 " "
y[1] (numeric) = 0.7673359768628446 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.45965157215626840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15400000000000005 " "
y[1] (analytic) = 0.7723512446854794 " "
y[1] (numeric) = 0.7723512446854776 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.4436798087007080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15500000000000005 " "
y[1] (analytic) = 0.7773665125081125 " "
y[1] (numeric) = 0.7773665125081105 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 2.5707326108988093000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15600000000000006 " "
y[1] (analytic) = 0.7823817803307455 " "
y[1] (numeric) = 0.7823817803307435 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 2.554253555700740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15700000000000006 " "
y[1] (analytic) = 0.7873970481533784 " "
y[1] (numeric) = 0.7873970481533764 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 2.537984424772710000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15800000000000006 " "
y[1] (analytic) = 0.7924123159760115 " "
y[1] (numeric) = 0.7924123159760094 " "
absolute error = 2.1094237467877974000000000000000E-15 " "
relative error = 2.66202796733368300000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15900000000000006 " "
y[1] (analytic) = 0.7974275837986444 " "
y[1] (numeric) = 0.7974275837986423 " "
absolute error = 2.1094237467877974000000000000000E-15 " "
relative error = 2.6452856530737220000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16000000000000006 " "
y[1] (analytic) = 0.8024428516212774 " "
y[1] (numeric) = 0.8024428516212753 " "
absolute error = 2.1094237467877974000000000000000E-15 " "
relative error = 2.62875261774201100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16100000000000006 " "
y[1] (analytic) = 0.8074581194439103 " "
y[1] (numeric) = 0.8074581194439082 " "
absolute error = 2.1094237467877974000000000000000E-15 " "
relative error = 2.61242496173119200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16200000000000006 " "
y[1] (analytic) = 0.8124733872665434 " "
y[1] (numeric) = 0.8124733872665412 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.73294619128474250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16300000000000006 " "
y[1] (analytic) = 0.8174886550891763 " "
y[1] (numeric) = 0.8174886550891741 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.71617965023391500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16400000000000006 " "
y[1] (analytic) = 0.8225039229118093 " "
y[1] (numeric) = 0.8225039229118071 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.6996175791959043000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16500000000000006 " "
y[1] (analytic) = 0.8275191907344424 " "
y[1] (numeric) = 0.82751919073444 " "
absolute error = 2.3314683517128287000000000000000E-15 " "
relative error = 2.8174190735608160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16600000000000006 " "
y[1] (analytic) = 0.8325344585570753 " "
y[1] (numeric) = 0.832534458557073 " "
absolute error = 2.3314683517128287000000000000000E-15 " "
relative error = 2.80044666950322100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16700000000000007 " "
y[1] (analytic) = 0.8375497263797083 " "
y[1] (numeric) = 0.8375497263797059 " "
absolute error = 2.3314683517128287000000000000000E-15 " "
relative error = 2.78367752776966850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16800000000000007 " "
y[1] (analytic) = 0.8425649942023413 " "
y[1] (numeric) = 0.8425649942023389 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.8988750671841730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16900000000000007 " "
y[1] (analytic) = 0.8475802620249743 " "
y[1] (numeric) = 0.8475802620249718 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.8817219602777580000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17000000000000007 " "
y[1] (analytic) = 0.8525955298476072 " "
y[1] (numeric) = 0.8525955298476048 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.8647706546290650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17100000000000007 " "
y[1] (analytic) = 0.8576107976702403 " "
y[1] (numeric) = 0.8576107976702377 " "
absolute error = 2.55351295663786000000000000000E-15 " "
relative error = 2.9774729557681140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17200000000000007 " "
y[1] (analytic) = 0.8626260654928732 " "
y[1] (numeric) = 0.8626260654928707 " "
absolute error = 2.55351295663786000000000000000E-15 " "
relative error = 2.96016206649039200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17300000000000007 " "
y[1] (analytic) = 0.8676413333155062 " "
y[1] (numeric) = 0.8676413333155036 " "
absolute error = 2.55351295663786000000000000000E-15 " "
relative error = 2.94305130310027400000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17400000000000007 " "
y[1] (analytic) = 0.8726566011381393 " "
y[1] (numeric) = 0.8726566011381366 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.05336057233191850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17500000000000007 " "
y[1] (analytic) = 0.8776718689607722 " "
y[1] (numeric) = 0.8776718689607695 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.0359127976328790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17600000000000007 " "
y[1] (analytic) = 0.8826871367834052 " "
y[1] (numeric) = 0.8826871367834025 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.01866329310087440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17700000000000007 " "
y[1] (analytic) = 0.8877024046060381 " "
y[1] (numeric) = 0.8877024046060354 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.0016086982245980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17800000000000007 " "
y[1] (analytic) = 0.8927176724286712 " "
y[1] (numeric) = 0.8927176724286684 " "
absolute error = 2.7755575615628914000000000000000E-15 " "
relative error = 3.1091101333435966000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17900000000000008 " "
y[1] (analytic) = 0.8977329402513041 " "
y[1] (numeric) = 0.8977329402513013 " "
absolute error = 2.7755575615628914000000000000000E-15 " "
relative error = 3.09174080298972250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18000000000000008 " "
y[1] (analytic) = 0.9027482080739371 " "
y[1] (numeric) = 0.9027482080739343 " "
absolute error = 2.7755575615628914000000000000000E-15 " "
relative error = 3.0745644651953350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18100000000000008 " "
y[1] (analytic) = 0.9077634758965701 " "
y[1] (numeric) = 0.9077634758965673 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 3.179881038036279600000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18200000000000008 " "
y[1] (analytic) = 0.9127787437192031 " "
y[1] (numeric) = 0.9127787437192002 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 3.16240916420091560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18300000000000008 " "
y[1] (analytic) = 0.917794011541836 " "
y[1] (numeric) = 0.9177940115418332 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 3.14512823980637500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18400000000000008 " "
y[1] (analytic) = 0.9228092793644691 " "
y[1] (numeric) = 0.9228092793644661 " "
absolute error = 2.9976021664879227000000000000000E-15 " "
relative error = 3.248344195836810000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18500000000000008 " "
y[1] (analytic) = 0.9278245471871021 " "
y[1] (numeric) = 0.9278245471870991 " "
absolute error = 2.9976021664879227000000000000000E-15 " "
relative error = 3.2307855785620165000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18600000000000008 " "
y[1] (analytic) = 0.932839815009735 " "
y[1] (numeric) = 0.932839815009732 " "
absolute error = 2.9976021664879227000000000000000E-15 " "
relative error = 3.21341576362351170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18700000000000008 " "
y[1] (analytic) = 0.9378550828323681 " "
y[1] (numeric) = 0.937855082832365 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.31461067477743070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18800000000000008 " "
y[1] (analytic) = 0.942870350655001 " "
y[1] (numeric) = 0.9428703506549979 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.29697976693287000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18900000000000008 " "
y[1] (analytic) = 0.947885618477634 " "
y[1] (numeric) = 0.9478856184776309 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.27953542954169060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.19000000000000009 " "
y[1] (analytic) = 0.952900886300267 " "
y[1] (numeric) = 0.9529008863002638 " "
absolute error = 3.219646771412954000000000000000E-15 " "
relative error = 3.3787845280672940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1910000000000001 " "
y[1] (analytic) = 0.9579161541229 " "
y[1] (numeric) = 0.9579161541228968 " "
absolute error = 3.219646771412954000000000000000E-15 " "
relative error = 3.3610945567161560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1920000000000001 " "
y[1] (analytic) = 0.9629314219455329 " "
y[1] (numeric) = 0.9629314219455297 " "
absolute error = 3.219646771412954000000000000000E-15 " "
relative error = 3.34358885589992660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1930000000000001 " "
y[1] (analytic) = 0.9679466897681659 " "
y[1] (numeric) = 0.9679466897681627 " "
absolute error = 3.219646771412954000000000000000E-15 " "
relative error = 3.32626456130977200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1940000000000001 " "
y[1] (analytic) = 0.972961957590799 " "
y[1] (numeric) = 0.9729619575907956 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.42322641485666160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1950000000000001 " "
y[1] (analytic) = 0.9779772254134319 " "
y[1] (numeric) = 0.9779772254134286 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.4056714076009864000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1960000000000001 " "
y[1] (analytic) = 0.9829924932360649 " "
y[1] (numeric) = 0.9829924932360615 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.388295533072409600000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1970000000000001 " "
y[1] (analytic) = 0.9880077610586979 " "
y[1] (numeric) = 0.9880077610586945 " "
absolute error = 3.4416913763379850000000000000000E-15 " "
relative error = 3.4834659321400950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1980000000000001 " "
y[1] (analytic) = 0.9930230288813309 " "
y[1] (numeric) = 0.9930230288813274 " "
absolute error = 3.4416913763379850000000000000000E-15 " "
relative error = 3.4658726698565590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1990000000000001 " "
y[1] (analytic) = 0.9980382967039638 " "
y[1] (numeric) = 0.9980382967039604 " "
absolute error = 3.4416913763379850000000000000000E-15 " "
relative error = 3.4484562242793910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2000000000000001 " "
y[1] (analytic) = 1.0030535645265968 " "
y[1] (numeric) = 1.0030535645265934 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.3205296224109620000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2010000000000001 " "
y[1] (analytic) = 1.0080688323492297 " "
y[1] (numeric) = 1.0080688323492264 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.30400957453827100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2020000000000001 " "
y[1] (analytic) = 1.013084100171863 " "
y[1] (numeric) = 1.0130841001718593 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.5068299642624010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2030000000000001 " "
y[1] (analytic) = 1.0180993679944959 " "
y[1] (numeric) = 1.0180993679944923 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.4895549398079070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2040000000000001 " "
y[1] (analytic) = 1.0231146358171288 " "
y[1] (numeric) = 1.0231146358171253 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.472449278338260400000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2050000000000001 " "
y[1] (analytic) = 1.0281299036397618 " "
y[1] (numeric) = 1.0281299036397582 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.4555105013707565000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2060000000000001 " "
y[1] (analytic) = 1.0331451714623947 " "
y[1] (numeric) = 1.0331451714623912 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.4387361785485690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2070000000000001 " "
y[1] (analytic) = 1.0381604392850277 " "
y[1] (numeric) = 1.038160439285024 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.42212392647828540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2080000000000001 " "
y[1] (analytic) = 1.0431757071076608 " "
y[1] (numeric) = 1.043175707107657 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.61852587057604760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2090000000000001 " "
y[1] (analytic) = 1.0481909749302938 " "
y[1] (numeric) = 1.04819097493029 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.60121234966420070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2100000000000001 " "
y[1] (analytic) = 1.0532062427529267 " "
y[1] (numeric) = 1.053206242752923 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.5840637194277040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2110000000000001 " "
y[1] (analytic) = 1.0582215105755597 " "
y[1] (numeric) = 1.058221510575556 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.5670776354493740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2120000000000001 " "
y[1] (analytic) = 1.0632367783981926 " "
y[1] (numeric) = 1.0632367783981889 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.55025179754631100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2130000000000001 " "
y[1] (analytic) = 1.0682520462208256 " "
y[1] (numeric) = 1.0682520462208218 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.53358394873153960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2140000000000001 " "
y[1] (analytic) = 1.0732673140434588 " "
y[1] (numeric) = 1.0732673140434548 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.72395845504033040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2150000000000001 " "
y[1] (analytic) = 1.0782825818660917 " "
y[1] (numeric) = 1.0782825818660877 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.70663771804014200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2160000000000001 " "
y[1] (analytic) = 1.0832978496887247 " "
y[1] (numeric) = 1.0832978496887207 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.6894773582344010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2170000000000001 " "
y[1] (analytic) = 1.0883131175113576 " "
y[1] (numeric) = 1.0883131175113536 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.672475158426870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2180000000000001 " "
y[1] (analytic) = 1.0933283853339906 " "
y[1] (numeric) = 1.0933283853339866 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.65562894210381100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2190000000000001 " "
y[1] (analytic) = 1.0983436531566235 " "
y[1] (numeric) = 1.0983436531566195 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.6389365725051630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2200000000000001 " "
y[1] (analytic) = 1.1033589209792565 " "
y[1] (numeric) = 1.1033589209792525 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.6223959517210490000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2210000000000001 " "
y[1] (analytic) = 1.1083741888018896 " "
y[1] (numeric) = 1.1083741888018854 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.8063386320246310000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22200000000000011 " "
y[1] (analytic) = 1.1133894566245226 " "
y[1] (numeric) = 1.1133894566245184 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.78919296251100660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22300000000000011 " "
y[1] (analytic) = 1.1184047244471556 " "
y[1] (numeric) = 1.1184047244471513 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.7722010658181320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22400000000000012 " "
y[1] (analytic) = 1.1234199922697885 " "
y[1] (numeric) = 1.1234199922697843 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.7553608824885870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22500000000000012 " "
y[1] (analytic) = 1.1284352600924215 " "
y[1] (numeric) = 1.1284352600924172 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.7386703896775270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22600000000000012 " "
y[1] (analytic) = 1.1334505279150544 " "
y[1] (numeric) = 1.1334505279150502 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.7221276003426710000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22700000000000012 " "
y[1] (analytic) = 1.1384657957376876 " "
y[1] (numeric) = 1.1384657957376831 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 3.9007690131112610000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22800000000000012 " "
y[1] (analytic) = 1.1434810635603205 " "
y[1] (numeric) = 1.143481063560316 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 3.88366037708884340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22900000000000012 " "
y[1] (analytic) = 1.1484963313829535 " "
y[1] (numeric) = 1.148496331382949 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 3.86670116146836830000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23000000000000012 " "
y[1] (analytic) = 1.1535115992055864 " "
y[1] (numeric) = 1.153511599205582 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 3.8498894172880710000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23100000000000012 " "
y[1] (analytic) = 1.1585268670282194 " "
y[1] (numeric) = 1.158526867028215 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 3.83322322933444300000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23200000000000012 " "
y[1] (analytic) = 1.1635421348508523 " "
y[1] (numeric) = 1.163542134850848 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 3.8167007154148980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23300000000000012 " "
y[1] (analytic) = 1.1685574026734853 " "
y[1] (numeric) = 1.1685574026734808 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 3.80032002564916900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23400000000000012 " "
y[1] (analytic) = 1.1735726704961185 " "
y[1] (numeric) = 1.1735726704961138 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.97328330886781660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23500000000000013 " "
y[1] (analytic) = 1.1785879383187514 " "
y[1] (numeric) = 1.1785879383187468 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.9563757203194433000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23600000000000013 " "
y[1] (analytic) = 1.1836032061413844 " "
y[1] (numeric) = 1.1836032061413797 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.93961141641978430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23700000000000013 " "
y[1] (analytic) = 1.1886184739640173 " "
y[1] (numeric) = 1.1886184739640127 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.92298858343911040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23800000000000013 " "
y[1] (analytic) = 1.1936337417866503 " "
y[1] (numeric) = 1.1936337417866456 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.90650543813054250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23900000000000013 " "
y[1] (analytic) = 1.1986490096092832 " "
y[1] (numeric) = 1.1986490096092786 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.890160227092339700000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24000000000000013 " "
y[1] (analytic) = 1.2036642774319164 " "
y[1] (numeric) = 1.2036642774319115 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.0584250940578410000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24100000000000013 " "
y[1] (analytic) = 1.2086795452545493 " "
y[1] (numeric) = 1.2086795452545445 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.04158515590822400000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24200000000000013 " "
y[1] (analytic) = 1.2136948130771823 " "
y[1] (numeric) = 1.2136948130771774 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.0248843908011650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24300000000000013 " "
y[1] (analytic) = 1.2187100808998153 " "
y[1] (numeric) = 1.2187100808998104 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.0083210805509550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24400000000000013 " "
y[1] (analytic) = 1.2237253487224482 " "
y[1] (numeric) = 1.2237253487224433 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 3.9918935351388607000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24500000000000013 " "
y[1] (analytic) = 1.2287406165450812 " "
y[1] (numeric) = 1.2287406165450763 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 3.9756000921382940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24600000000000014 " "
y[1] (analytic) = 1.2337558843677143 " "
y[1] (numeric) = 1.2337558843677092 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.13941362143371850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24700000000000014 " "
y[1] (analytic) = 1.2387711521903473 " "
y[1] (numeric) = 1.2387711521903422 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.1226548618327720000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24800000000000014 " "
y[1] (analytic) = 1.2437864200129802 " "
y[1] (numeric) = 1.2437864200129751 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.10603125351893030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24900000000000014 " "
y[1] (analytic) = 1.2488016878356132 " "
y[1] (numeric) = 1.248801687835608 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.0895411681634330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2500000000000001 " "
y[1] (analytic) = 1.2538169556582461 " "
y[1] (numeric) = 1.253816955658241 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.0731830034907790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2510000000000001 " "
y[1] (analytic) = 1.258832223480879 " "
y[1] (numeric) = 1.258832223480874 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.05695518275974050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2520000000000001 " "
y[1] (analytic) = 1.263847491303512 " "
y[1] (numeric) = 1.263847491303507 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.04085615425672560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2530000000000001 " "
y[1] (analytic) = 1.268862759126145 " "
y[1] (numeric) = 1.2688627591261399 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.02488439080116560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2540000000000001 " "
y[1] (analytic) = 1.273878026948778 " "
y[1] (numeric) = 1.2738780269487728 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.0090383892625780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2550000000000001 " "
y[1] (analytic) = 1.278893294771411 " "
y[1] (numeric) = 1.2788932947714058 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 3.99331667008899940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2560000000000001 " "
y[1] (analytic) = 1.2839085625940438 " "
y[1] (numeric) = 1.2839085625940387 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 3.9777177768464650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2570000000000001 " "
y[1] (analytic) = 1.288923830416677 " "
y[1] (numeric) = 1.2889238304166717 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.13451159210703360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2580000000000001 " "
y[1] (analytic) = 1.29393909823931 " "
y[1] (numeric) = 1.2939390982393046 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.1184863533779370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2590000000000001 " "
y[1] (analytic) = 1.298954366061943 " "
y[1] (numeric) = 1.2989543660619376 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.1025848616660530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2600000000000001 " "
y[1] (analytic) = 1.3039696338845759 " "
y[1] (numeric) = 1.3039696338845705 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.08680568912118350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2610000000000001 " "
y[1] (analytic) = 1.3089849017072088 " "
y[1] (numeric) = 1.3089849017072035 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.0711474297758920000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2620000000000001 " "
y[1] (analytic) = 1.3140001695298418 " "
y[1] (numeric) = 1.3140001695298364 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.05560869912789200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2630000000000001 " "
y[1] (analytic) = 1.319015437352475 " "
y[1] (numeric) = 1.3190154373524694 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.20852930597080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2640000000000001 " "
y[1] (analytic) = 1.324030705175108 " "
y[1] (numeric) = 1.3240307051751024 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.1925879070845470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2650000000000001 " "
y[1] (analytic) = 1.3290459729977409 " "
y[1] (numeric) = 1.3290459729977353 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.17676682064271900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2660000000000001 " "
y[1] (analytic) = 1.3340612408203738 " "
y[1] (numeric) = 1.3340612408203683 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.16106468973804660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2670000000000001 " "
y[1] (analytic) = 1.3390765086430068 " "
y[1] (numeric) = 1.3390765086430012 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.1454801777914630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2680000000000001 " "
y[1] (analytic) = 1.3440917764656397 " "
y[1] (numeric) = 1.3440917764656342 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.1300119681728380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.26900000000000013 " "
y[1] (analytic) = 1.3491070442882727 " "
y[1] (numeric) = 1.349107044288267 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.11465876383018850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27000000000000013 " "
y[1] (analytic) = 1.3541223121109058 " "
y[1] (numeric) = 1.3541223121109 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.26339605840419740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27100000000000013 " "
y[1] (analytic) = 1.3591375799335388 " "
y[1] (numeric) = 1.359137579933533 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.2476639696277980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27200000000000013 " "
y[1] (analytic) = 1.3641528477561717 " "
y[1] (numeric) = 1.364152847756166 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.2320475579747546000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27300000000000013 " "
y[1] (analytic) = 1.3691681155788047 " "
y[1] (numeric) = 1.369168115578799 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.21654555226788800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27400000000000013 " "
y[1] (analytic) = 1.3741833834014376 " "
y[1] (numeric) = 1.3741833834014319 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.2011566998873480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27500000000000013 " "
y[1] (analytic) = 1.3791986512240706 " "
y[1] (numeric) = 1.3791986512240648 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.18587976643321260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27600000000000013 " "
y[1] (analytic) = 1.3842139190467038 " "
y[1] (numeric) = 1.3842139190466978 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.331125594449080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27700000000000014 " "
y[1] (analytic) = 1.3892291868693367 " "
y[1] (numeric) = 1.3892291868693307 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.31548976197814460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27800000000000014 " "
y[1] (analytic) = 1.3942444546919697 " "
y[1] (numeric) = 1.3942444546919637 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.29996641751059700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27900000000000014 " "
y[1] (analytic) = 1.3992597225146026 " "
y[1] (numeric) = 1.3992597225145966 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.28455435149801500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28000000000000014 " "
y[1] (analytic) = 1.4042749903372356 " "
y[1] (numeric) = 1.4042749903372296 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.26925237167123600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28100000000000014 " "
y[1] (analytic) = 1.4092902581598685 " "
y[1] (numeric) = 1.4092902581598625 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.25405930273290500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28200000000000014 " "
y[1] (analytic) = 1.4143055259825017 " "
y[1] (numeric) = 1.4143055259824955 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.3959730225771587000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28300000000000014 " "
y[1] (analytic) = 1.4193207938051347 " "
y[1] (numeric) = 1.4193207938051284 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.3804395489991480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28400000000000014 " "
y[1] (analytic) = 1.4243360616277676 " "
y[1] (numeric) = 1.4243360616277614 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.3650154660801370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28500000000000014 " "
y[1] (analytic) = 1.4293513294504006 " "
y[1] (numeric) = 1.4293513294503943 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.3496996223395050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28600000000000014 " "
y[1] (analytic) = 1.4343665972730335 " "
y[1] (numeric) = 1.4343665972730273 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.3344908824012550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28700000000000014 " "
y[1] (analytic) = 1.4393818650956665 " "
y[1] (numeric) = 1.4393818650956602 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.31938812671344600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28800000000000014 " "
y[1] (analytic) = 1.4443971329182994 " "
y[1] (numeric) = 1.4443971329182932 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.30439025127346900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28900000000000015 " "
y[1] (analytic) = 1.4494124007409326 " "
y[1] (numeric) = 1.4494124007409261 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 4.4426924590504210000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29000000000000015 " "
y[1] (analytic) = 1.4544276685635655 " "
y[1] (numeric) = 1.454427668563559 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 4.42737282988128140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29100000000000015 " "
y[1] (analytic) = 1.4594429363861985 " "
y[1] (numeric) = 1.459442936386192 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 4.4121584902596966000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29200000000000015 " "
y[1] (analytic) = 1.4644582042088314 " "
y[1] (numeric) = 1.464458204208825 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 4.39704835844373860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29300000000000015 " "
y[1] (analytic) = 1.4694734720314644 " "
y[1] (numeric) = 1.469473472031458 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 4.38204136745928950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29400000000000015 " "
y[1] (analytic) = 1.4744887398540973 " "
y[1] (numeric) = 1.474488739854091 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 4.36713646484888360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29500000000000015 " "
y[1] (analytic) = 1.4795040076767305 " "
y[1] (numeric) = 1.4795040076767239 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 4.50241304733689600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29600000000000015 " "
y[1] (analytic) = 1.4845192754993635 " "
y[1] (numeric) = 1.4845192754993568 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 4.4872021924472450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29700000000000015 " "
y[1] (analytic) = 1.4895345433219964 " "
y[1] (numeric) = 1.4895345433219898 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 4.472093767556850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29800000000000015 " "
y[1] (analytic) = 1.4945498111446294 " "
y[1] (numeric) = 1.4945498111446227 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 4.45708674149122350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29900000000000015 " "
y[1] (analytic) = 1.4995650789672623 " "
y[1] (numeric) = 1.4995650789672557 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 4.44218009687085140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30000000000000016 " "
y[1] (analytic) = 1.5045803467898953 " "
y[1] (numeric) = 1.5045803467898886 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 4.4273728298812820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30100000000000016 " "
y[1] (analytic) = 1.5095956146125282 " "
y[1] (numeric) = 1.5095956146125216 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 4.41266395004778930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30200000000000016 " "
y[1] (analytic) = 1.5146108824351614 " "
y[1] (numeric) = 1.5146108824351545 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 4.54465422934833550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30300000000000016 " "
y[1] (analytic) = 1.5196261502577944 " "
y[1] (numeric) = 1.5196261502577875 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 4.52965537050560140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30400000000000016 " "
y[1] (analytic) = 1.5246414180804273 " "
y[1] (numeric) = 1.5246414180804204 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 4.51475518836578050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30500000000000016 " "
y[1] (analytic) = 1.5296566859030603 " "
y[1] (numeric) = 1.5296566859030534 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 4.4999527123383520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30600000000000016 " "
y[1] (analytic) = 1.5346719537256932 " "
y[1] (numeric) = 1.5346719537256863 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 4.48524698452025250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30700000000000016 " "
y[1] (analytic) = 1.5396872215483262 " "
y[1] (numeric) = 1.5396872215483193 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 4.47063705948924250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30800000000000016 " "
y[1] (analytic) = 1.5447024893709593 " "
y[1] (numeric) = 1.5447024893709522 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.5998678752013317000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30900000000000016 " "
y[1] (analytic) = 1.5497177571935923 " "
y[1] (numeric) = 1.5497177571935852 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.5849815713980910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31000000000000016 " "
y[1] (analytic) = 1.5547330250162252 " "
y[1] (numeric) = 1.5547330250162181 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.5701913082645484000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31100000000000017 " "
y[1] (analytic) = 1.5597482928388582 " "
y[1] (numeric) = 1.559748292838851 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.5554961593633770000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31200000000000017 " "
y[1] (analytic) = 1.5647635606614911 " "
y[1] (numeric) = 1.564763560661484 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.5408952101346480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31300000000000017 " "
y[1] (analytic) = 1.569778828484124 " "
y[1] (numeric) = 1.569778828484117 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.5263875577061030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31400000000000017 " "
y[1] (analytic) = 1.574794096306757 " "
y[1] (numeric) = 1.57479409630675 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.5119723107070390000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31500000000000017 " "
y[1] (analytic) = 1.5798093641293902 " "
y[1] (numeric) = 1.5798093641293829 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 4.6382001074946755000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31600000000000017 " "
y[1] (analytic) = 1.5848246319520232 " "
y[1] (numeric) = 1.5848246319520158 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 4.6235222590532377000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31700000000000017 " "
y[1] (analytic) = 1.5898398997746561 " "
y[1] (numeric) = 1.5898398997746488 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 4.6089370153338260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31800000000000017 " "
y[1] (analytic) = 1.594855167597289 " "
y[1] (numeric) = 1.5948551675972817 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 4.5944435027069910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3190000000000002 " "
y[1] (analytic) = 1.599870435419922 " "
y[1] (numeric) = 1.5998704354199147 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 4.5800408584978780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3200000000000002 " "
y[1] (analytic) = 1.604885703242555 " "
y[1] (numeric) = 1.6048857032425476 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 4.5657282308150720000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3210000000000002 " "
y[1] (analytic) = 1.6099009710651881 " "
y[1] (numeric) = 1.6099009710651806 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 4.6894291656063414000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3220000000000002 " "
y[1] (analytic) = 1.614916238887821 " "
y[1] (numeric) = 1.6149162388878135 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 4.6748657209926570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3230000000000002 " "
y[1] (analytic) = 1.619931506710454 " "
y[1] (numeric) = 1.6199315067104465 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 4.6603924525066120000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3240000000000002 " "
y[1] (analytic) = 1.624946774533087 " "
y[1] (numeric) = 1.6249467745330795 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 4.6460085251840616000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3250000000000002 " "
y[1] (analytic) = 1.62996204235572 " "
y[1] (numeric) = 1.6299620423557124 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 4.6317131143373410000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3260000000000002 " "
y[1] (analytic) = 1.634977310178353 " "
y[1] (numeric) = 1.6349773101783454 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 4.6175054053976560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3270000000000002 " "
y[1] (analytic) = 1.639992578000986 " "
y[1] (numeric) = 1.6399925780009783 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 4.7387782582827170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3280000000000002 " "
y[1] (analytic) = 1.645007845823619 " "
y[1] (numeric) = 1.6450078458236113 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 4.7243307635928310000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3290000000000002 " "
y[1] (analytic) = 1.650023113646252 " "
y[1] (numeric) = 1.6500231136462442 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 4.7099710956183850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3300000000000002 " "
y[1] (analytic) = 1.655038381468885 " "
y[1] (numeric) = 1.6550383814688772 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 4.6956984559346920000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3310000000000002 " "
y[1] (analytic) = 1.6600536492915179 " "
y[1] (numeric) = 1.6600536492915101 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 4.6815120557657053000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3320000000000002 " "
y[1] (analytic) = 1.6650689171141508 " "
y[1] (numeric) = 1.665068917114143 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 4.66741111583870050000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3330000000000002 " "
y[1] (analytic) = 1.6700841849367838 " "
y[1] (numeric) = 1.670084184936776 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 4.6533948662415875000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3340000000000002 " "
y[1] (analytic) = 1.675099452759417 " "
y[1] (numeric) = 1.675099452759409 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 4.7720186190337166000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3350000000000002 " "
y[1] (analytic) = 1.68011472058205 " "
y[1] (numeric) = 1.680114720582042 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 4.7577737873351084000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3360000000000002 " "
y[1] (analytic) = 1.6851299884046829 " "
y[1] (numeric) = 1.6851299884046749 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 4.7436137463013730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3370000000000002 " "
y[1] (analytic) = 1.6901452562273158 " "
y[1] (numeric) = 1.6901452562273078 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 4.729537741119469500000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3380000000000002 " "
y[1] (analytic) = 1.6951605240499488 " "
y[1] (numeric) = 1.6951605240499408 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 4.7155450259090580000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3390000000000002 " "
y[1] (analytic) = 1.7001757918725817 " "
y[1] (numeric) = 1.7001757918725737 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 4.7016348635907420000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3400000000000002 " "
y[1] (analytic) = 1.705191059695215 " "
y[1] (numeric) = 1.7051910596952067 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 4.8180233736943356000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3410000000000002 " "
y[1] (analytic) = 1.7102063275178478 " "
y[1] (numeric) = 1.7102063275178396 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 4.8038942728917130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3420000000000002 " "
y[1] (analytic) = 1.7152215953404808 " "
y[1] (numeric) = 1.7152215953404726 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 4.7898477984095740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3430000000000002 " "
y[1] (analytic) = 1.7202368631631137 " "
y[1] (numeric) = 1.7202368631631055 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 4.7758832275687290000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3440000000000002 " "
y[1] (analytic) = 1.7252521309857467 " "
y[1] (numeric) = 1.7252521309857385 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 4.7619998460932390000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3450000000000002 " "
y[1] (analytic) = 1.7302673988083797 " "
y[1] (numeric) = 1.7302673988083714 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 4.7481969479886210000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3460000000000002 " "
y[1] (analytic) = 1.7352826666310126 " "
y[1] (numeric) = 1.7352826666310044 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 4.734473835422180000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3470000000000002 " "
y[1] (analytic) = 1.7402979344536458 " "
y[1] (numeric) = 1.7402979344536373 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 4.8484198137028440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3480000000000002 " "
y[1] (analytic) = 1.7453132022762787 " "
y[1] (numeric) = 1.7453132022762703 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 4.834487572858870400000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3490000000000002 " "
y[1] (analytic) = 1.7503284700989117 " "
y[1] (numeric) = 1.7503284700989032 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 4.8206351729366387000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3500000000000002 " "
y[1] (analytic) = 1.7553437379215446 " "
y[1] (numeric) = 1.7553437379215362 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 4.8068619295853920000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3510000000000002 " "
y[1] (analytic) = 1.7603590057441776 " "
y[1] (numeric) = 1.7603590057441691 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 4.7931671662532394000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3520000000000002 " "
y[1] (analytic) = 1.7653742735668105 " "
y[1] (numeric) = 1.765374273566802 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 4.7795502140763840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3530000000000002 " "
y[1] (analytic) = 1.7703895413894437 " "
y[1] (numeric) = 1.770389541389435 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 4.8914317383957495000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3540000000000002 " "
y[1] (analytic) = 1.7754048092120767 " "
y[1] (numeric) = 1.775404809212068 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 4.8776141346149715000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3550000000000002 " "
y[1] (analytic) = 1.7804200770347096 " "
y[1] (numeric) = 1.780420077034701 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 4.8638743764892950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3560000000000002 " "
y[1] (analytic) = 1.7854353448573426 " "
y[1] (numeric) = 1.785435344857334 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 4.850211808016010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3570000000000002 " "
y[1] (analytic) = 1.7904506126799755 " "
y[1] (numeric) = 1.7904506126799669 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 4.8366257805425760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3580000000000002 " "
y[1] (analytic) = 1.7954658805026085 " "
y[1] (numeric) = 1.7954658805025998 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 4.8231156526639657000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3590000000000002 " "
y[1] (analytic) = 1.8004811483252416 " "
y[1] (numeric) = 1.8004811483252328 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 4.9330059385863860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3600000000000002 " "
y[1] (analytic) = 1.8054964161478746 " "
y[1] (numeric) = 1.8054964161478657 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 4.9193031443125346000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3610000000000002 " "
y[1] (analytic) = 1.8105116839705075 " "
y[1] (numeric) = 1.8105116839704987 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 4.9056762657964337000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3620000000000002 " "
y[1] (analytic) = 1.8155269517931405 " "
y[1] (numeric) = 1.8155269517931316 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 4.8921246739019686000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3630000000000002 " "
y[1] (analytic) = 1.8205422196157734 " "
y[1] (numeric) = 1.8205422196157646 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 4.8786477464256540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3640000000000002 " "
y[1] (analytic) = 1.8255574874384064 " "
y[1] (numeric) = 1.8255574874383975 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 4.8652448680014090000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3650000000000002 " "
y[1] (analytic) = 1.8305727552610394 " "
y[1] (numeric) = 1.8305727552610305 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 4.8519154300068840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3660000000000002 " "
y[1] (analytic) = 1.8355880230836725 " "
y[1] (numeric) = 1.8355880230836634 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 4.9596253012331293000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3670000000000002 " "
y[1] (analytic) = 1.8406032909063055 " "
y[1] (numeric) = 1.8406032909062964 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 4.9461113358346740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3680000000000002 " "
y[1] (analytic) = 1.8456185587289384 " "
y[1] (numeric) = 1.8456185587289293 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 4.932670815900341000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3690000000000002 " "
y[1] (analytic) = 1.8506338265515714 " "
y[1] (numeric) = 1.8506338265515623 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 4.9193031443125346000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3700000000000002 " "
y[1] (analytic) = 1.8556490943742043 " "
y[1] (numeric) = 1.8556490943741952 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 4.9060077304089870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3710000000000002 " "
y[1] (analytic) = 1.8606643621968373 " "
y[1] (numeric) = 1.8606643621968282 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 4.8927839898957554000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3720000000000002 " "
y[1] (analytic) = 1.8656796300194705 " "
y[1] (numeric) = 1.8656796300194611 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 4.998646743414350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3730000000000002 " "
y[1] (analytic) = 1.8706948978421034 " "
y[1] (numeric) = 1.870694897842094 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 4.9852455457108263000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3740000000000002 " "
y[1] (analytic) = 1.8757101656647364 " "
y[1] (numeric) = 1.875710165664727 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 4.9719160121661450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3750000000000002 " "
y[1] (analytic) = 1.8807254334873693 " "
y[1] (numeric) = 1.88072543348736 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 4.9586575694670354000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3760000000000002 " "
y[1] (analytic) = 1.8857407013100023 " "
y[1] (numeric) = 1.885740701309993 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 4.9454696503993040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3770000000000002 " "
y[1] (analytic) = 1.8907559691326352 " "
y[1] (numeric) = 1.890755969132626 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 4.9323516937669450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3780000000000002 " "
y[1] (analytic) = 1.8957712369552682 " "
y[1] (numeric) = 1.8957712369552588 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 4.9193031443125357000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3790000000000002 " "
y[1] (analytic) = 1.9007865047779013 " "
y[1] (numeric) = 1.9007865047778918 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 5.0231406777017170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3800000000000002 " "
y[1] (analytic) = 1.9058017726005343 " "
y[1] (numeric) = 1.9058017726005247 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 5.0099218864446070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3810000000000002 " "
y[1] (analytic) = 1.9108170404231672 " "
y[1] (numeric) = 1.9108170404231577 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 4.9967724851678510000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38200000000000023 " "
y[1] (analytic) = 1.9158323082458002 " "
y[1] (numeric) = 1.9158323082457906 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 4.9836919289239550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38300000000000023 " "
y[1] (analytic) = 1.9208475760684331 " "
y[1] (numeric) = 1.9208475760684236 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 4.9706796784567910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38400000000000023 " "
y[1] (analytic) = 1.925862843891066 " "
y[1] (numeric) = 1.9258628438910566 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 4.9577352001274766000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38500000000000023 " "
y[1] (analytic) = 1.9308781117136993 " "
y[1] (numeric) = 1.9308781117136895 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 5.0598546627214640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38600000000000023 " "
y[1] (analytic) = 1.9358933795363322 " "
y[1] (numeric) = 1.9358933795363225 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 5.0467462309527570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38700000000000023 " "
y[1] (analytic) = 1.9409086473589652 " "
y[1] (numeric) = 1.9409086473589554 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 5.0337055430174770000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38800000000000023 " "
y[1] (analytic) = 1.9459239151815981 " "
y[1] (numeric) = 1.9459239151815884 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 5.0207320751231020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38900000000000023 " "
y[1] (analytic) = 1.950939183004231 " "
y[1] (numeric) = 1.9509391830042213 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 5.0078253088631460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39000000000000024 " "
y[1] (analytic) = 1.955954450826864 " "
y[1] (numeric) = 1.9559544508268543 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 4.9949847311481120000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39100000000000024 " "
y[1] (analytic) = 1.9609697186494972 " "
y[1] (numeric) = 1.9609697186494872 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.0954418758224460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39200000000000024 " "
y[1] (analytic) = 1.9659849864721302 " "
y[1] (numeric) = 1.9659849864721202 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.0824432996086130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39300000000000024 " "
y[1] (analytic) = 1.971000254294763 " "
y[1] (numeric) = 1.9710002542947531 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.0695108739098650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39400000000000024 " "
y[1] (analytic) = 1.976015522117396 " "
y[1] (numeric) = 1.976015522117386 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.0566440950420730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39500000000000024 " "
y[1] (analytic) = 1.981030789940029 " "
y[1] (numeric) = 1.981030789940019 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.0438424644217130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39600000000000024 " "
y[1] (analytic) = 1.986046057762662 " "
y[1] (numeric) = 1.986046057762652 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.0311054885014560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39700000000000024 " "
y[1] (analytic) = 1.991061325585295 " "
y[1] (numeric) = 1.991061325585285 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.0184326787067420000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39800000000000024 " "
y[1] (analytic) = 1.996076593407928 " "
y[1] (numeric) = 1.9960765934079179 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 5.1170640747371590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = sinh(0.1) * cosh(0.05) / tanh(0.02);"
Iterations = 298
"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 46 Minutes 21 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 45 Minutes 54 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 48 Minutes 55 Seconds
"Time to Timeout " Unknown
Percent Done = 6.102040816326536 "%"
(%o54) true
(%o54) diffeq.max