(%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 : array_x array_x ,
1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(0, 1),
1
temporary
array_y : temporary, array_y_higher : temporary, temporary : ---------,
2 1, 2 glob_h
array_y_higher : temporary, 0)), kkk : 2,
2, 1
array_tmp1 : array_x array_x + array_x array_x ,
2 2 1 1 2
array_tmp2 : array_tmp1 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp2 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary
array_y_higher : temporary, temporary : ---------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3, array_tmp1 : array_x array_x ,
2, 2 3 2 2
array_tmp2 : array_tmp1 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp2 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4, array_tmp2 : array_tmp1 ,
2, 3 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp2 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
array_tmp2 : array_tmp1 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp2 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp2 : array_tmp1 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
array_tmp2 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 : array_x array_x ,
1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(0, 1),
1
temporary
array_y : temporary, array_y_higher : temporary, temporary : ---------,
2 1, 2 glob_h
array_y_higher : temporary, 0)), kkk : 2,
2, 1
array_tmp1 : array_x array_x + array_x array_x ,
2 2 1 1 2
array_tmp2 : array_tmp1 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp2 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary
array_y_higher : temporary, temporary : ---------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3, array_tmp1 : array_x array_x ,
2, 2 3 2 2
array_tmp2 : array_tmp1 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp2 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4, array_tmp2 : array_tmp1 ,
2, 3 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp2 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
array_tmp2 : array_tmp1 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp2 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp2 : array_tmp1 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
array_tmp2 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)
x x x
(%i52) exact_soln_y(x) := block(----- + 1.0)
3.0
x x x
(%o52) exact_soln_y(x) := block(----- + 1.0)
3.0
(%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/multpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = x * x ;"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:10.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.00001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:20,"),
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, " (1.0 + x * x * x / 3.0) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_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, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 10.0, array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5,
1 + 0
glob_look_poles : true, glob_max_iter : 20, 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 ) = x * x ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-12-15T02:15:14-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mult"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = x * x ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 151 | "), logitem_str(html_log_file, "mult diffeq.max"), logitem_str(html_log_file, "\
mult 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/multpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = x * x ;"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:10.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.00001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:20,"),
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, " (1.0 + x * x * x / 3.0) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_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, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 10.0, array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5,
1 + 0
glob_look_poles : true, glob_max_iter : 20, 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 ) = x * x ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-12-15T02:15:14-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mult"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = x * x ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 151 | "), logitem_str(html_log_file, "mult diffeq.max"), logitem_str(html_log_file, "\
mult 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/multpostode.ode#################"
"diff ( y , x , 1 ) = x * x ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.1,"
"x_end:10.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.00001,"
"glob_look_poles:true,"
"glob_max_iter:20,"
"/* 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("
" (1.0 + x * x * x / 3.0) "
"));"
""
"/* 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 = 9.9 ""
estimated_steps = 9900. ""
step_error = 1.010101010101010200000000000000E-14 ""
est_needed_step_err = 1.010101010101010200000000000000E-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) = 1.0003333333333333 " "
y[1] (numeric) = 1.0003333333333333 " "
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) = 1.0003434336666666 " "
y[1] (numeric) = 1.0003434336666666 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10200000000000001 " "
y[1] (analytic) = 1.000353736 " "
y[1] (numeric) = 1.0003537359999999 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21966087529093080000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10300000000000001 " "
y[1] (analytic) = 1.0003642423333334 " "
y[1] (numeric) = 1.0003642423333332 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.219637563285107600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10400000000000001 " "
y[1] (analytic) = 1.0003749546666667 " "
y[1] (numeric) = 1.0003749546666665 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.219613794699792600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10500000000000001 " "
y[1] (analytic) = 1.000385875 " "
y[1] (numeric) = 1.0003858749999999 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.219589565126869600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10600000000000001 " "
y[1] (analytic) = 1.0003970053333333 " "
y[1] (numeric) = 1.0003970053333333 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10700000000000001 " "
y[1] (analytic) = 1.0004083476666668 " "
y[1] (numeric) = 1.0004083476666668 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10800000000000001 " "
y[1] (analytic) = 1.000419904 " "
y[1] (numeric) = 1.0004199040000001 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.219514066415769200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10900000000000001 " "
y[1] (analytic) = 1.0004316763333334 " "
y[1] (numeric) = 1.0004316763333334 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11000000000000001 " "
y[1] (analytic) = 1.0004436666666667 " "
y[1] (numeric) = 1.0004436666666667 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11100000000000002 " "
y[1] (analytic) = 1.000455877 " "
y[1] (numeric) = 1.000455877 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11200000000000002 " "
y[1] (analytic) = 1.0004683093333333 " "
y[1] (numeric) = 1.0004683093333333 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11300000000000002 " "
y[1] (analytic) = 1.0004809656666667 " "
y[1] (numeric) = 1.0004809656666667 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11400000000000002 " "
y[1] (analytic) = 1.000493848 " "
y[1] (numeric) = 1.000493848 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11500000000000002 " "
y[1] (analytic) = 1.0005069583333333 " "
y[1] (numeric) = 1.0005069583333335 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21932094600239600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11600000000000002 " "
y[1] (analytic) = 1.0005202986666666 " "
y[1] (numeric) = 1.0005202986666668 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21929135491740480000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11700000000000002 " "
y[1] (analytic) = 1.000533871 " "
y[1] (numeric) = 1.0005338710000002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.219261250027499400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11800000000000002 " "
y[1] (analytic) = 1.0005476773333333 " "
y[1] (numeric) = 1.0005476773333335 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.219230626938499800000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11900000000000002 " "
y[1] (analytic) = 1.0005617196666667 " "
y[1] (numeric) = 1.0005617196666667 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12000000000000002 " "
y[1] (analytic) = 1.000576 " "
y[1] (numeric) = 1.0005760000000001 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21916780859256420000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12100000000000002 " "
y[1] (analytic) = 1.0005905203333334 " "
y[1] (numeric) = 1.0005905203333334 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12200000000000003 " "
y[1] (analytic) = 1.0006052826666667 " "
y[1] (numeric) = 1.0006052826666667 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12300000000000003 " "
y[1] (analytic) = 1.000620289 " "
y[1] (numeric) = 1.000620289 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12400000000000003 " "
y[1] (analytic) = 1.0006355413333334 " "
y[1] (numeric) = 1.0006355413333334 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12500000000000003 " "
y[1] (analytic) = 1.0006510416666667 " "
y[1] (numeric) = 1.0006510416666667 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12600000000000003 " "
y[1] (analytic) = 1.000666792 " "
y[1] (numeric) = 1.000666792 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12700000000000003 " "
y[1] (analytic) = 1.0006827943333334 " "
y[1] (numeric) = 1.0006827943333334 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12800000000000003 " "
y[1] (analytic) = 1.0006990506666666 " "
y[1] (numeric) = 1.0006990506666666 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12900000000000003 " "
y[1] (analytic) = 1.000715563 " "
y[1] (numeric) = 1.000715563 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13000000000000003 " "
y[1] (analytic) = 1.0007323333333333 " "
y[1] (numeric) = 1.0007323333333333 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13100000000000003 " "
y[1] (analytic) = 1.0007493636666667 " "
y[1] (numeric) = 1.0007493636666667 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13200000000000003 " "
y[1] (analytic) = 1.000766656 " "
y[1] (numeric) = 1.000766656 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13300000000000003 " "
y[1] (analytic) = 1.0007842123333333 " "
y[1] (numeric) = 1.0007842123333333 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13400000000000004 " "
y[1] (analytic) = 1.0008020346666666 " "
y[1] (numeric) = 1.0008020346666666 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13500000000000004 " "
y[1] (analytic) = 1.000820125 " "
y[1] (numeric) = 1.000820125 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13600000000000004 " "
y[1] (analytic) = 1.0008384853333334 " "
y[1] (numeric) = 1.0008384853333332 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21858579759828500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13700000000000004 " "
y[1] (analytic) = 1.0008571176666667 " "
y[1] (numeric) = 1.0008571176666665 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.218544495568874600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13800000000000004 " "
y[1] (analytic) = 1.000876024 " "
y[1] (numeric) = 1.0008760239999999 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21850258773939100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.13900000000000004 " "
y[1] (analytic) = 1.0008952063333334 " "
y[1] (numeric) = 1.0008952063333332 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.218460069745629400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14000000000000004 " "
y[1] (analytic) = 1.0009146666666666 " "
y[1] (numeric) = 1.0009146666666666 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14100000000000004 " "
y[1] (analytic) = 1.000934407 " "
y[1] (numeric) = 1.000934407 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14200000000000004 " "
y[1] (analytic) = 1.0009544293333332 " "
y[1] (numeric) = 1.0009544293333332 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14300000000000004 " "
y[1] (analytic) = 1.0009747356666667 " "
y[1] (numeric) = 1.0009747356666665 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21828380890298600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14400000000000004 " "
y[1] (analytic) = 1.000995328 " "
y[1] (numeric) = 1.000995328 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14500000000000005 " "
y[1] (analytic) = 1.0010162083333334 " "
y[1] (numeric) = 1.0010162083333332 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21819190415238100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14600000000000005 " "
y[1] (analytic) = 1.0010373786666666 " "
y[1] (numeric) = 1.0010373786666664 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21814499295504800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14700000000000005 " "
y[1] (analytic) = 1.001058841 " "
y[1] (numeric) = 1.0010588409999999 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.218097436742295000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14800000000000005 " "
y[1] (analytic) = 1.0010805973333334 " "
y[1] (numeric) = 1.0010805973333332 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21804923116591300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.14900000000000005 " "
y[1] (analytic) = 1.0011026496666666 " "
y[1] (numeric) = 1.0011026496666666 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15000000000000005 " "
y[1] (analytic) = 1.001125 " "
y[1] (numeric) = 1.001125 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15100000000000005 " "
y[1] (analytic) = 1.0011476503333334 " "
y[1] (numeric) = 1.0011476503333334 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15200000000000005 " "
y[1] (analytic) = 1.0011706026666667 " "
y[1] (numeric) = 1.0011706026666667 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15300000000000005 " "
y[1] (analytic) = 1.001193859 " "
y[1] (numeric) = 1.001193859 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15400000000000005 " "
y[1] (analytic) = 1.0012174213333334 " "
y[1] (numeric) = 1.0012174213333334 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15500000000000005 " "
y[1] (analytic) = 1.0012412916666666 " "
y[1] (numeric) = 1.0012412916666666 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15600000000000006 " "
y[1] (analytic) = 1.001265472 " "
y[1] (numeric) = 1.001265472 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15700000000000006 " "
y[1] (analytic) = 1.0012899643333333 " "
y[1] (numeric) = 1.0012899643333333 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15800000000000006 " "
y[1] (analytic) = 1.0013147706666667 " "
y[1] (numeric) = 1.0013147706666665 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21753050518965100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.15900000000000006 " "
y[1] (analytic) = 1.001339893 " "
y[1] (numeric) = 1.001339893 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16000000000000006 " "
y[1] (analytic) = 1.0013653333333334 " "
y[1] (numeric) = 1.0013653333333332 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.217418533812147700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16100000000000006 " "
y[1] (analytic) = 1.0013910936666666 " "
y[1] (numeric) = 1.0013910936666666 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16200000000000006 " "
y[1] (analytic) = 1.001417176 " "
y[1] (numeric) = 1.001417176 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16300000000000006 " "
y[1] (analytic) = 1.0014435823333334 " "
y[1] (numeric) = 1.0014435823333332 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.217245273145333500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16400000000000006 " "
y[1] (analytic) = 1.0014703146666666 " "
y[1] (numeric) = 1.0014703146666666 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16500000000000006 " "
y[1] (analytic) = 1.001497375 " "
y[1] (numeric) = 1.001497375 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16600000000000006 " "
y[1] (analytic) = 1.0015247653333332 " "
y[1] (numeric) = 1.0015247653333335 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.217065544566230700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16700000000000007 " "
y[1] (analytic) = 1.0015524876666666 " "
y[1] (numeric) = 1.0015524876666668 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.217004177607628800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16800000000000007 " "
y[1] (analytic) = 1.001580544 " "
y[1] (numeric) = 1.001580544 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16900000000000007 " "
y[1] (analytic) = 1.0016089363333334 " "
y[1] (numeric) = 1.0016089363333334 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17000000000000007 " "
y[1] (analytic) = 1.0016376666666666 " "
y[1] (numeric) = 1.0016376666666666 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17100000000000007 " "
y[1] (analytic) = 1.001666737 " "
y[1] (numeric) = 1.001666737 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17200000000000007 " "
y[1] (analytic) = 1.0016961493333334 " "
y[1] (numeric) = 1.0016961493333334 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17300000000000007 " "
y[1] (analytic) = 1.0017259056666667 " "
y[1] (numeric) = 1.0017259056666667 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17400000000000007 " "
y[1] (analytic) = 1.001756008 " "
y[1] (numeric) = 1.001756008 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17500000000000007 " "
y[1] (analytic) = 1.0017864583333334 " "
y[1] (numeric) = 1.0017864583333334 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17600000000000007 " "
y[1] (analytic) = 1.0018172586666667 " "
y[1] (numeric) = 1.0018172586666667 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17700000000000007 " "
y[1] (analytic) = 1.001848411 " "
y[1] (numeric) = 1.001848411 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17800000000000007 " "
y[1] (analytic) = 1.0018799173333333 " "
y[1] (numeric) = 1.0018799173333335 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.216279626764445200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17900000000000008 " "
y[1] (analytic) = 1.0019117796666668 " "
y[1] (numeric) = 1.0019117796666668 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18000000000000008 " "
y[1] (analytic) = 1.001944 " "
y[1] (numeric) = 1.0019440000000002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.216137877217003400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18100000000000008 " "
y[1] (analytic) = 1.0019765803333334 " "
y[1] (numeric) = 1.0019765803333336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.216065817138784300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18200000000000008 " "
y[1] (analytic) = 1.0020095226666668 " "
y[1] (numeric) = 1.002009522666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.215992961165676700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18300000000000008 " "
y[1] (analytic) = 1.002042829 " "
y[1] (numeric) = 1.0020428290000003 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21591930503233300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18400000000000008 " "
y[1] (analytic) = 1.0020765013333333 " "
y[1] (numeric) = 1.0020765013333337 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.431689688952596400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18500000000000008 " "
y[1] (analytic) = 1.0021105416666667 " "
y[1] (numeric) = 1.0021105416666671 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.431539150476081500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18600000000000008 " "
y[1] (analytic) = 1.002144952 " "
y[1] (numeric) = 1.0021449520000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.431386986121969600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18700000000000008 " "
y[1] (analytic) = 1.0021797343333334 " "
y[1] (numeric) = 1.0021797343333338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.43123318738308100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18800000000000008 " "
y[1] (analytic) = 1.0022148906666666 " "
y[1] (numeric) = 1.0022148906666672 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.64661661863740900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18900000000000008 " "
y[1] (analytic) = 1.002250423 " "
y[1] (numeric) = 1.0022504230000007 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.64638097912874500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.19000000000000009 " "
y[1] (analytic) = 1.0022863333333334 " "
y[1] (numeric) = 1.002286333333334 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.64614284981531100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1910000000000001 " "
y[1] (analytic) = 1.0023226236666667 " "
y[1] (numeric) = 1.0023226236666674 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.64590221797312200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1920000000000001 " "
y[1] (analytic) = 1.002359296 " "
y[1] (numeric) = 1.0023592960000007 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.6456590708876310000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1930000000000001 " "
y[1] (analytic) = 1.0023963523333332 " "
y[1] (numeric) = 1.0023963523333341 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.86055119447176100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1940000000000001 " "
y[1] (analytic) = 1.0024337946666666 " "
y[1] (numeric) = 1.0024337946666675 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.86022024023507700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1950000000000001 " "
y[1] (analytic) = 1.002471625 " "
y[1] (numeric) = 1.0024716250000008 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.64491441116943200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1960000000000001 " "
y[1] (analytic) = 1.0025098453333334 " "
y[1] (numeric) = 1.002509845333334 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.64466107615736400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1970000000000001 " "
y[1] (analytic) = 1.0025484576666668 " "
y[1] (numeric) = 1.0025484576666674 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.64440516247419200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1980000000000001 " "
y[1] (analytic) = 1.002587464 " "
y[1] (numeric) = 1.0025874640000008 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.6441466574640310000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1990000000000001 " "
y[1] (analytic) = 1.0026268663333333 " "
y[1] (numeric) = 1.0026268663333342 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85851406464148600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2000000000000001 " "
y[1] (analytic) = 1.0026666666666666 " "
y[1] (numeric) = 1.0026666666666675 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85816243051986700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2010000000000001 " "
y[1] (analytic) = 1.0027068670000001 " "
y[1] (numeric) = 1.0027068670000008 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.64335546806516300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2020000000000001 " "
y[1] (analytic) = 1.0027474693333334 " "
y[1] (numeric) = 1.002747469333334 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.64308647139210700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2030000000000001 " "
y[1] (analytic) = 1.0027884756666667 " "
y[1] (numeric) = 1.0027884756666674 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.64281482026645300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2040000000000001 " "
y[1] (analytic) = 1.002829888 " "
y[1] (numeric) = 1.0028298880000008 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85672066945939800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2050000000000001 " "
y[1] (analytic) = 1.0028717083333334 " "
y[1] (numeric) = 1.0028717083333343 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85635133905795100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2060000000000001 " "
y[1] (analytic) = 1.0029139386666666 " "
y[1] (numeric) = 1.0029139386666677 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10699730238185050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2070000000000001 " "
y[1] (analytic) = 1.002956581 " "
y[1] (numeric) = 1.002956581000001 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85560189270172500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2080000000000001 " "
y[1] (analytic) = 1.0029996373333334 " "
y[1] (numeric) = 1.0029996373333343 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85522174326520800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2090000000000001 " "
y[1] (analytic) = 1.0030431096666668 " "
y[1] (numeric) = 1.0030431096666677 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85483795402658600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2100000000000001 " "
y[1] (analytic) = 1.003087 " "
y[1] (numeric) = 1.003087000000001 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85445050828218400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2110000000000001 " "
y[1] (analytic) = 1.0031313103333332 " "
y[1] (numeric) = 1.0031313103333344 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10675742366793190000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2120000000000001 " "
y[1] (analytic) = 1.0031760426666667 " "
y[1] (numeric) = 1.0031760426666676 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85366458053711100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2130000000000001 " "
y[1] (analytic) = 1.003221199 " "
y[1] (numeric) = 1.0032211990000008 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.8532660652052800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2140000000000001 " "
y[1] (analytic) = 1.0032667813333334 " "
y[1] (numeric) = 1.0032667813333342 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85286382670562800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2150000000000001 " "
y[1] (analytic) = 1.0033127916666666 " "
y[1] (numeric) = 1.0033127916666675 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85245784841151700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2160000000000001 " "
y[1] (analytic) = 1.003359232 " "
y[1] (numeric) = 1.0033592320000009 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85204811371213100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2170000000000001 " "
y[1] (analytic) = 1.0034061043333333 " "
y[1] (numeric) = 1.0034061043333342 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.8516346060126290000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2180000000000001 " "
y[1] (analytic) = 1.0034534106666666 " "
y[1] (numeric) = 1.0034534106666675 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85121730873428600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2190000000000001 " "
y[1] (analytic) = 1.003501153 " "
y[1] (numeric) = 1.0035011530000009 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85079620531462600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2200000000000001 " "
y[1] (analytic) = 1.0035493333333334 " "
y[1] (numeric) = 1.0035493333333343 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85037127920758400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2210000000000001 " "
y[1] (analytic) = 1.0035979536666666 " "
y[1] (numeric) = 1.0035979536666677 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10624281423545440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22200000000000011 " "
y[1] (analytic) = 1.003647016 " "
y[1] (numeric) = 1.003647016000001 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.1061887366037430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22300000000000011 " "
y[1] (analytic) = 1.0036965223333334 " "
y[1] (numeric) = 1.0036965223333343 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.84907339955050800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22400000000000012 " "
y[1] (analytic) = 1.0037464746666667 " "
y[1] (numeric) = 1.0037464746666676 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.84863301756631000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22500000000000012 " "
y[1] (analytic) = 1.003796875 " "
y[1] (numeric) = 1.0037968750000008 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.84818873041545700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22600000000000012 " "
y[1] (analytic) = 1.0038477253333333 " "
y[1] (numeric) = 1.0038477253333342 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.84774052165332700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22700000000000012 " "
y[1] (analytic) = 1.0038990276666666 " "
y[1] (numeric) = 1.0038990276666675 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.84728837485272300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22800000000000012 " "
y[1] (analytic) = 1.003950784 " "
y[1] (numeric) = 1.0039507840000008 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.84683227360401400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.22900000000000012 " "
y[1] (analytic) = 1.0040029963333332 " "
y[1] (numeric) = 1.0040029963333341 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.84637220151528600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23000000000000012 " "
y[1] (analytic) = 1.0040556666666667 " "
y[1] (numeric) = 1.0040556666666673 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63443110665936400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23100000000000012 " "
y[1] (analytic) = 1.004108797 " "
y[1] (numeric) = 1.0041087970000007 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63408005950468600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23200000000000012 " "
y[1] (analytic) = 1.0041623893333333 " "
y[1] (numeric) = 1.004162389333334 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63372599741902700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23300000000000012 " "
y[1] (analytic) = 1.0042164456666667 " "
y[1] (numeric) = 1.0042164456666673 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63336890816271600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23400000000000012 " "
y[1] (analytic) = 1.004270968 " "
y[1] (numeric) = 1.0042709680000006 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63300877950993400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23500000000000013 " "
y[1] (analytic) = 1.0043259583333333 " "
y[1] (numeric) = 1.004325958333334 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63264559924882300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23600000000000013 " "
y[1] (analytic) = 1.0043814186666666 " "
y[1] (numeric) = 1.0043814186666673 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63227935518159800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23700000000000013 " "
y[1] (analytic) = 1.004437351 " "
y[1] (numeric) = 1.0044373510000006 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63191003512467000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23800000000000013 " "
y[1] (analytic) = 1.0044937573333332 " "
y[1] (numeric) = 1.004493757333334 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63153762690874200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.23900000000000013 " "
y[1] (analytic) = 1.0045506396666666 " "
y[1] (numeric) = 1.0045506396666672 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63116211837894700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24000000000000013 " "
y[1] (analytic) = 1.004608 " "
y[1] (numeric) = 1.0046080000000006 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63078349739494400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24100000000000013 " "
y[1] (analytic) = 1.0046658403333333 " "
y[1] (numeric) = 1.004665840333334 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63040175183104200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24200000000000013 " "
y[1] (analytic) = 1.0047241626666668 " "
y[1] (numeric) = 1.0047241626666672 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.420011246384210600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24300000000000013 " "
y[1] (analytic) = 1.004782969 " "
y[1] (numeric) = 1.0047829690000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.419752559023147300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24400000000000013 " "
y[1] (analytic) = 1.0048422613333334 " "
y[1] (numeric) = 1.0048422613333339 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.419491764416805000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24500000000000013 " "
y[1] (analytic) = 1.0049020416666667 " "
y[1] (numeric) = 1.0049020416666672 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41922885452122700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24600000000000014 " "
y[1] (analytic) = 1.004962312 " "
y[1] (numeric) = 1.0049623120000004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41896382130261060000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24700000000000014 " "
y[1] (analytic) = 1.0050230743333333 " "
y[1] (numeric) = 1.0050230743333337 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41869665673738300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24800000000000014 " "
y[1] (analytic) = 1.0050843306666666 " "
y[1] (numeric) = 1.005084330666667 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.418427352812284700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.24900000000000014 " "
y[1] (analytic) = 1.005146083 " "
y[1] (numeric) = 1.0051460830000003 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.209077950762220700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2500000000000001 " "
y[1] (analytic) = 1.0052083333333333 " "
y[1] (numeric) = 1.0052083333333337 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.417882294881452000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2510000000000001 " "
y[1] (analytic) = 1.0052710836666667 " "
y[1] (numeric) = 1.005271083666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208803262450728700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2520000000000001 " "
y[1] (analytic) = 1.005334336 " "
y[1] (numeric) = 1.0053343360000002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208664291806614300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2530000000000001 " "
y[1] (analytic) = 1.0053980923333334 " "
y[1] (numeric) = 1.0053980923333337 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.2085242315281200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2540000000000001 " "
y[1] (analytic) = 1.0054623546666668 " "
y[1] (numeric) = 1.005462354666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208383077640376200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2550000000000001 " "
y[1] (analytic) = 1.005527125 " "
y[1] (numeric) = 1.0055271250000004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41648165234789300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2560000000000001 " "
y[1] (analytic) = 1.0055924053333334 " "
y[1] (numeric) = 1.0055924053333338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.416194946329732000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2570000000000001 " "
y[1] (analytic) = 1.0056581976666668 " "
y[1] (numeric) = 1.0056581976666672 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41590602930936800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2580000000000001 " "
y[1] (analytic) = 1.005724504 " "
y[1] (numeric) = 1.0057245040000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41561489338100700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2590000000000001 " "
y[1] (analytic) = 1.0057913263333333 " "
y[1] (numeric) = 1.0057913263333338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41532153065003900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2600000000000001 " "
y[1] (analytic) = 1.0058586666666667 " "
y[1] (numeric) = 1.0058586666666671 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.415025933233124300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2610000000000001 " "
y[1] (analytic) = 1.005926527 " "
y[1] (numeric) = 1.0059265270000004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.414728093258273000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2620000000000001 " "
y[1] (analytic) = 1.0059949093333334 " "
y[1] (numeric) = 1.0059949093333338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41442800286492350000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2630000000000001 " "
y[1] (analytic) = 1.0060638156666666 " "
y[1] (numeric) = 1.006063815666667 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41412565420402900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2640000000000001 " "
y[1] (analytic) = 1.006133248 " "
y[1] (numeric) = 1.0061332480000003 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.206910519719067200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2650000000000001 " "
y[1] (analytic) = 1.0062032083333334 " "
y[1] (numeric) = 1.0062032083333337 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20675707537073100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2660000000000001 " "
y[1] (analytic) = 1.0062736986666667 " "
y[1] (numeric) = 1.006273698666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.206602490149995600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2670000000000001 " "
y[1] (analytic) = 1.006344721 " "
y[1] (numeric) = 1.0063447210000003 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.206446760155770800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.2680000000000001 " "
y[1] (analytic) = 1.0064162773333334 " "
y[1] (numeric) = 1.0064162773333336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.206289881492927400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.26900000000000013 " "
y[1] (analytic) = 1.0064883696666667 " "
y[1] (numeric) = 1.0064883696666669 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20613185027233900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27000000000000013 " "
y[1] (analytic) = 1.006561 " "
y[1] (numeric) = 1.0065610000000003 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.205972662610922700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27100000000000013 " "
y[1] (analytic) = 1.0066341703333332 " "
y[1] (numeric) = 1.0066341703333337 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41162462926336500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27200000000000013 " "
y[1] (analytic) = 1.0067078826666667 " "
y[1] (numeric) = 1.006707882666667 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41130160492749400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27300000000000013 " "
y[1] (analytic) = 1.006782139 " "
y[1] (numeric) = 1.0067821390000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41097624448483200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27400000000000013 " "
y[1] (analytic) = 1.0068569413333333 " "
y[1] (numeric) = 1.0068569413333337 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41064854021839650000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27500000000000013 " "
y[1] (analytic) = 1.0069322916666668 " "
y[1] (numeric) = 1.006932291666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.205159242211855000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27600000000000013 " "
y[1] (analytic) = 1.007008192 " "
y[1] (numeric) = 1.0070081920000002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.204993034704441600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27700000000000014 " "
y[1] (analytic) = 1.0070846443333334 " "
y[1] (numeric) = 1.0070846443333337 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.204825643747350000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27800000000000014 " "
y[1] (analytic) = 1.0071616506666667 " "
y[1] (numeric) = 1.007161650666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.204657065507350800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.27900000000000014 " "
y[1] (analytic) = 1.007239213 " "
y[1] (numeric) = 1.0072392130000003 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.204487296157633700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28000000000000014 " "
y[1] (analytic) = 1.0073173333333334 " "
y[1] (numeric) = 1.0073173333333336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20431633187785200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28100000000000014 " "
y[1] (analytic) = 1.0073960136666666 " "
y[1] (numeric) = 1.0073960136666669 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20414416885416400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28200000000000014 " "
y[1] (analytic) = 1.007475256 " "
y[1] (numeric) = 1.0074752560000002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.203970803279274900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28300000000000014 " "
y[1] (analytic) = 1.0075550623333334 " "
y[1] (numeric) = 1.0075550623333336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.2037962313524800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28400000000000014 " "
y[1] (analytic) = 1.0076354346666667 " "
y[1] (numeric) = 1.007635434666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20362044927970700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28500000000000014 " "
y[1] (analytic) = 1.007716375 " "
y[1] (numeric) = 1.0077163750000002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.203443453273559200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28600000000000014 " "
y[1] (analytic) = 1.0077978853333334 " "
y[1] (numeric) = 1.0077978853333336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.203265239553356700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28700000000000014 " "
y[1] (analytic) = 1.0078799676666668 " "
y[1] (numeric) = 1.007879967666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.203085804345180400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28800000000000014 " "
y[1] (analytic) = 1.007962624 " "
y[1] (numeric) = 1.0079626240000004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.40581028776383100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.28900000000000015 " "
y[1] (analytic) = 1.0080458563333334 " "
y[1] (numeric) = 1.0080458563333337 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.202723254403291500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29000000000000015 " "
y[1] (analytic) = 1.0081296666666666 " "
y[1] (numeric) = 1.008129666666667 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.405080264311859000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29100000000000015 " "
y[1] (analytic) = 1.008214057 " "
y[1] (numeric) = 1.0082140570000004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.404711546786761500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29200000000000015 " "
y[1] (analytic) = 1.0082990293333334 " "
y[1] (numeric) = 1.0082990293333338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.40434034875234700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29300000000000015 " "
y[1] (analytic) = 1.0083845856666667 " "
y[1] (numeric) = 1.008384585666667 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.40396666274370740000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29400000000000015 " "
y[1] (analytic) = 1.008470728 " "
y[1] (numeric) = 1.0084707280000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.403590481310059600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29500000000000015 " "
y[1] (analytic) = 1.0085574583333334 " "
y[1] (numeric) = 1.0085574583333339 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.4032117970148300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29600000000000015 " "
y[1] (analytic) = 1.0086447786666666 " "
y[1] (numeric) = 1.0086447786666672 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.60424590365361500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29700000000000015 " "
y[1] (analytic) = 1.008732691 " "
y[1] (numeric) = 1.0087326910000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.402446890164904400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29800000000000015 " "
y[1] (analytic) = 1.0088211973333334 " "
y[1] (numeric) = 1.0088211973333339 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.402060652808896000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.29900000000000015 " "
y[1] (analytic) = 1.0089102996666668 " "
y[1] (numeric) = 1.0089102996666672 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.40167188298885400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30000000000000016 " "
y[1] (analytic) = 1.0090000000000001 " "
y[1] (numeric) = 1.0090000000000006 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.401280573340561000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30100000000000016 " "
y[1] (analytic) = 1.0090903003333334 " "
y[1] (numeric) = 1.0090903003333338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.40088671651453200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30200000000000016 " "
y[1] (analytic) = 1.0091812026666667 " "
y[1] (numeric) = 1.009181202666667 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.40049030517610240000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30300000000000016 " "
y[1] (analytic) = 1.009272709 " "
y[1] (numeric) = 1.0092727090000004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.400091332005516000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30400000000000016 " "
y[1] (analytic) = 1.0093648213333333 " "
y[1] (numeric) = 1.0093648213333337 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.399689789698013600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30500000000000016 " "
y[1] (analytic) = 1.0094575416666667 " "
y[1] (numeric) = 1.0094575416666671 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.39928567096391500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30600000000000016 " "
y[1] (analytic) = 1.009550872 " "
y[1] (numeric) = 1.0095508720000004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.39887896852871660000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30700000000000016 " "
y[1] (analytic) = 1.0096448143333334 " "
y[1] (numeric) = 1.0096448143333336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.199234837566584600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30800000000000016 " "
y[1] (analytic) = 1.0097393706666666 " "
y[1] (numeric) = 1.009739370666667 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.398057783533376000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.30900000000000016 " "
y[1] (analytic) = 1.009834543 " "
y[1] (numeric) = 1.0098345430000004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.39764328650087200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31000000000000016 " "
y[1] (analytic) = 1.0099303333333334 " "
y[1] (numeric) = 1.0099303333333338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.397226176822717000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31100000000000017 " "
y[1] (analytic) = 1.0100267436666668 " "
y[1] (numeric) = 1.0100267436666672 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.39680644730158500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31200000000000017 " "
y[1] (analytic) = 1.010123776 " "
y[1] (numeric) = 1.0101237760000006 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.59457613613377600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31300000000000017 " "
y[1] (analytic) = 1.0102214323333334 " "
y[1] (numeric) = 1.0102214323333338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.395959100019673500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31400000000000017 " "
y[1] (analytic) = 1.0103197146666667 " "
y[1] (numeric) = 1.0103197146666671 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.395531467943098500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31500000000000017 " "
y[1] (analytic) = 1.010418625 " "
y[1] (numeric) = 1.0104186250000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.39510118739213250000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31600000000000017 " "
y[1] (analytic) = 1.0105181653333333 " "
y[1] (numeric) = 1.0105181653333337 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.3946682512488400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31700000000000017 " "
y[1] (analytic) = 1.0106183376666666 " "
y[1] (numeric) = 1.010618337666667 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.39423265241142950000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.31800000000000017 " "
y[1] (analytic) = 1.010719144 " "
y[1] (numeric) = 1.0107191440000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.39379438379434330000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3190000000000002 " "
y[1] (analytic) = 1.0108205863333333 " "
y[1] (numeric) = 1.010820586333334 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.59003015749252100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3200000000000002 " "
y[1] (analytic) = 1.0109226666666666 " "
y[1] (numeric) = 1.0109226666666673 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.58936471344092900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3210000000000002 " "
y[1] (analytic) = 1.011025387 " "
y[1] (numeric) = 1.0110253870000006 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.39246348865483640000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3220000000000002 " "
y[1] (analytic) = 1.0111287493333334 " "
y[1] (numeric) = 1.0111287493333339 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.392014470391269000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3230000000000002 " "
y[1] (analytic) = 1.0112327556666667 " "
y[1] (numeric) = 1.0112327556666671 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.39156274716686500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3240000000000002 " "
y[1] (analytic) = 1.011337408 " "
y[1] (numeric) = 1.0113374080000004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.39110831199534370000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3250000000000002 " "
y[1] (analytic) = 1.0114427083333333 " "
y[1] (numeric) = 1.0114427083333337 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.39065115790728100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3260000000000002 " "
y[1] (analytic) = 1.0115486586666667 " "
y[1] (numeric) = 1.011548658666667 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.39019127795020200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3270000000000002 " "
y[1] (analytic) = 1.011655261 " "
y[1] (numeric) = 1.0116552610000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.389728665188670000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3280000000000002 " "
y[1] (analytic) = 1.0117625173333333 " "
y[1] (numeric) = 1.0117625173333338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.389263312704377000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3290000000000002 " "
y[1] (analytic) = 1.0118704296666667 " "
y[1] (numeric) = 1.0118704296666672 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.388795213596228000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3300000000000002 " "
y[1] (analytic) = 1.011979 " "
y[1] (numeric) = 1.0119790000000004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.38832436098044200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3310000000000002 " "
y[1] (analytic) = 1.0120882303333334 " "
y[1] (numeric) = 1.0120882303333338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.38785074799062600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3320000000000002 " "
y[1] (analytic) = 1.0121981226666668 " "
y[1] (numeric) = 1.0121981226666672 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.38737436777788200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3330000000000002 " "
y[1] (analytic) = 1.012308679 " "
y[1] (numeric) = 1.0123086790000004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.386895213510884600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3340000000000002 " "
y[1] (analytic) = 1.0124199013333333 " "
y[1] (numeric) = 1.0124199013333337 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.386413278375973500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3350000000000002 " "
y[1] (analytic) = 1.0125317916666667 " "
y[1] (numeric) = 1.012531791666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.192964277788623800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3360000000000002 " "
y[1] (analytic) = 1.012644352 " "
y[1] (numeric) = 1.0126443520000004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.385441038336652700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3370000000000002 " "
y[1] (analytic) = 1.0127575843333334 " "
y[1] (numeric) = 1.0127575843333336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.192475359947033000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3380000000000002 " "
y[1] (analytic) = 1.0128714906666667 " "
y[1] (numeric) = 1.012871490666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.192228796753700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3390000000000002 " "
y[1] (analytic) = 1.012986073 " "
y[1] (numeric) = 1.0129860730000002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.191980826226337700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3400000000000002 " "
y[1] (analytic) = 1.0131013333333334 " "
y[1] (numeric) = 1.0131013333333336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.191731445012061500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3410000000000002 " "
y[1] (analytic) = 1.0132172736666667 " "
y[1] (numeric) = 1.013217273666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.191480649767136300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3420000000000002 " "
y[1] (analytic) = 1.013333896 " "
y[1] (numeric) = 1.0133338960000002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.19122843715701900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3430000000000002 " "
y[1] (analytic) = 1.0134512023333333 " "
y[1] (numeric) = 1.0134512023333335 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.190974803856405300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3440000000000002 " "
y[1] (analytic) = 1.0135691946666667 " "
y[1] (numeric) = 1.013569194666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.19071974654927500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3450000000000002 " "
y[1] (analytic) = 1.013687875 " "
y[1] (numeric) = 1.0136878750000002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.190463261928937400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3460000000000002 " "
y[1] (analytic) = 1.0138072453333333 " "
y[1] (numeric) = 1.0138072453333336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.190205346698074200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3470000000000002 " "
y[1] (analytic) = 1.0139273076666666 " "
y[1] (numeric) = 1.0139273076666668 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.189945997568787400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3480000000000002 " "
y[1] (analytic) = 1.014048064 " "
y[1] (numeric) = 1.0140480640000002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.189685211262642000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3490000000000002 " "
y[1] (analytic) = 1.0141695163333333 " "
y[1] (numeric) = 1.0141695163333335 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.18942298451071300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3500000000000002 " "
y[1] (analytic) = 1.0142916666666666 " "
y[1] (numeric) = 1.0142916666666668 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.1891593140536300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3510000000000002 " "
y[1] (analytic) = 1.014414517 " "
y[1] (numeric) = 1.014414517 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3520000000000002 " "
y[1] (analytic) = 1.0145380693333335 " "
y[1] (numeric) = 1.0145380693333335 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3530000000000002 " "
y[1] (analytic) = 1.0146623256666667 " "
y[1] (numeric) = 1.0146623256666667 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3540000000000002 " "
y[1] (analytic) = 1.014787288 " "
y[1] (numeric) = 1.014787288 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3550000000000002 " "
y[1] (analytic) = 1.0149129583333334 " "
y[1] (numeric) = 1.0149129583333334 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3560000000000002 " "
y[1] (analytic) = 1.0150393386666667 " "
y[1] (numeric) = 1.0150393386666667 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3570000000000002 " "
y[1] (analytic) = 1.015166431 " "
y[1] (numeric) = 1.0151664310000001 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.18727292534982700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3580000000000002 " "
y[1] (analytic) = 1.0152942373333333 " "
y[1] (numeric) = 1.0152942373333336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.186997589075563600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3590000000000002 " "
y[1] (analytic) = 1.0154227596666667 " "
y[1] (numeric) = 1.015422759666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.18672078019919500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3600000000000002 " "
y[1] (analytic) = 1.015552 " "
y[1] (numeric) = 1.0155520000000002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.186442495559374000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3610000000000002 " "
y[1] (analytic) = 1.0156819603333334 " "
y[1] (numeric) = 1.0156819603333336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.18616273200480220000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3620000000000002 " "
y[1] (analytic) = 1.0158126426666667 " "
y[1] (numeric) = 1.015812642666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.18588148639427800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3630000000000002 " "
y[1] (analytic) = 1.015944049 " "
y[1] (numeric) = 1.0159440490000002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.185598755596740000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3640000000000002 " "
y[1] (analytic) = 1.0160761813333334 " "
y[1] (numeric) = 1.0160761813333337 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.185314536491309300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3650000000000002 " "
y[1] (analytic) = 1.0162090416666667 " "
y[1] (numeric) = 1.016209041666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.185028825967340600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3660000000000002 " "
y[1] (analytic) = 1.016342632 " "
y[1] (numeric) = 1.0163426320000002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.18474162092446100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3670000000000002 " "
y[1] (analytic) = 1.0164769543333334 " "
y[1] (numeric) = 1.0164769543333336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.184452918272618300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3680000000000002 " "
y[1] (analytic) = 1.0166120106666667 " "
y[1] (numeric) = 1.016612010666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.18416271493212500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3690000000000002 " "
y[1] (analytic) = 1.0167478030000001 " "
y[1] (numeric) = 1.0167478030000003 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.183871007833702600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3700000000000002 " "
y[1] (analytic) = 1.0168843333333333 " "
y[1] (numeric) = 1.0168843333333337 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.36715558783705600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3710000000000002 " "
y[1] (analytic) = 1.0170216036666666 " "
y[1] (numeric) = 1.017021603666667 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.36656614027655200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3720000000000002 " "
y[1] (analytic) = 1.017159616 " "
y[1] (numeric) = 1.0171596160000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.36597366691033300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3730000000000002 " "
y[1] (analytic) = 1.0172983723333333 " "
y[1] (numeric) = 1.0172983723333338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.36537816168401370000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3740000000000002 " "
y[1] (analytic) = 1.0174378746666668 " "
y[1] (numeric) = 1.017437874666667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.182389809282238600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3750000000000002 " "
y[1] (analytic) = 1.017578125 " "
y[1] (numeric) = 1.0175781250000004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.36417803153996250000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3760000000000002 " "
y[1] (analytic) = 1.0177191253333333 " "
y[1] (numeric) = 1.0177191253333338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.36357339462015300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3770000000000002 " "
y[1] (analytic) = 1.0178608776666667 " "
y[1] (numeric) = 1.017860877666667 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.36296570183626600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3780000000000002 " "
y[1] (analytic) = 1.018003384 " "
y[1] (numeric) = 1.0180033840000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.36235494724114440000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3790000000000002 " "
y[1] (analytic) = 1.0181466463333333 " "
y[1] (numeric) = 1.0181466463333337 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.36174112490934100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3800000000000002 " "
y[1] (analytic) = 1.0182906666666667 " "
y[1] (numeric) = 1.0182906666666671 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.361124228937211500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.3810000000000002 " "
y[1] (analytic) = 1.018435447 " "
y[1] (numeric) = 1.0184354470000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.360504253443003000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38200000000000023 " "
y[1] (analytic) = 1.0185809893333333 " "
y[1] (numeric) = 1.018580989333334 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.53982178885040800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38300000000000023 " "
y[1] (analytic) = 1.0187272956666666 " "
y[1] (numeric) = 1.0187272956666673 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.53888256070696900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38400000000000023 " "
y[1] (analytic) = 1.018874368 " "
y[1] (numeric) = 1.0188743680000008 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.53793868701085800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38500000000000023 " "
y[1] (analytic) = 1.0190222083333333 " "
y[1] (numeric) = 1.019022208333334 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.5369901590721200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38600000000000023 " "
y[1] (analytic) = 1.0191708186666668 " "
y[1] (numeric) = 1.0191708186666673 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.357357978822859500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38700000000000023 " "
y[1] (analytic) = 1.019320201 " "
y[1] (numeric) = 1.0193202010000006 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.53507910587454400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38800000000000023 " "
y[1] (analytic) = 1.0194703573333335 " "
y[1] (numeric) = 1.019470357333334 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.35607770893587600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.38900000000000023 " "
y[1] (analytic) = 1.0196212896666668 " "
y[1] (numeric) = 1.0196212896666672 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.35543288817795900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39000000000000024 " "
y[1] (analytic) = 1.019773 " "
y[1] (numeric) = 1.0197730000000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.35478493596185230000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39100000000000024 " "
y[1] (analytic) = 1.0199254903333335 " "
y[1] (numeric) = 1.019925490333334 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.35413384662956870000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39200000000000024 " "
y[1] (analytic) = 1.0200787626666667 " "
y[1] (numeric) = 1.0200787626666672 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.353479614545985300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39300000000000024 " "
y[1] (analytic) = 1.020232819 " "
y[1] (numeric) = 1.0202328190000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.35282223409892700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39400000000000024 " "
y[1] (analytic) = 1.0203876613333334 " "
y[1] (numeric) = 1.0203876613333338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.352161699699253500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39500000000000024 " "
y[1] (analytic) = 1.0205432916666668 " "
y[1] (numeric) = 1.0205432916666672 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.35149800578094900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39600000000000024 " "
y[1] (analytic) = 1.020699712 " "
y[1] (numeric) = 1.0206997120000005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.35083114680121060000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39700000000000024 " "
y[1] (analytic) = 1.0208569243333334 " "
y[1] (numeric) = 1.0208569243333339 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.350161117240531300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39800000000000024 " "
y[1] (analytic) = 1.0210149306666667 " "
y[1] (numeric) = 1.0210149306666672 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.34948791160278900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.39900000000000024 " "
y[1] (analytic) = 1.0211737330000001 " "
y[1] (numeric) = 1.0211737330000006 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.348811524415332500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = x * x ;"
Iterations = 299
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds
"Expected Time Remaining "= 0 Years 0 Days 1 Hours 36 Minutes 28 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 1 Hours 35 Minutes 45 Seconds
"Expected Total Time "= 0 Years 0 Days 1 Hours 38 Minutes 46 Seconds
"Time to Timeout " Unknown
Percent Done = 3.030303030303033 "%"
(%o54) true
(%o54) diffeq.max