(%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_y array_y ,
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 : ats(2, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(1, 2),
2
temporary
array_y : temporary, array_y_higher : temporary, temporary : ---------,
3 1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp1 : ats(3, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1 : ats(4, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
4 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_tmp1 : ats(5, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 :
kkk
ats(kkk, array_y, array_y, 1), 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_y array_y ,
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 : ats(2, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(1, 2),
2
temporary
array_y : temporary, array_y_higher : temporary, temporary : ---------,
3 1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp1 : ats(3, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1 : ats(4, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
4 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_tmp1 : ats(5, array_y, array_y, 1), array_tmp2 : array_tmp1 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 :
kkk
ats(kkk, array_y, array_y, 1), 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)
1.0
(%i52) exact_soln_y(x) := block(-------)
1.0 - x
1.0
(%o52) exact_soln_y(x) := block(-------)
1.0 - x
(%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/nonlinear1postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.0,"), omniout_str(ALWAYS, "x_end:0.5,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.01,"), omniout_str(ALWAYS,
"glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (1.0/(1.0 - x)) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_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 : 0.0,
iiif, jjjf
x_end : 0.5, array_y_init : exact_soln_y(x_start), glob_h : 0.01,
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"),
if glob_iter >= glob_max_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = y * y;"),
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,
"2012-12-15T02:36:02-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "nonlinear1"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;"),
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, "nonlinear1 diffeq.max"),
logitem_str(html_log_file,
"nonlinear1 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/nonlinear1postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.0,"), omniout_str(ALWAYS, "x_end:0.5,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.01,"), omniout_str(ALWAYS,
"glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (1.0/(1.0 - x)) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_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 : 0.0,
iiif, jjjf
x_end : 0.5, array_y_init : exact_soln_y(x_start), glob_h : 0.01,
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"),
if glob_iter >= glob_max_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = y * y;"),
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,
"2012-12-15T02:36:02-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "nonlinear1"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;"),
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, "nonlinear1 diffeq.max"),
logitem_str(html_log_file,
"nonlinear1 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/nonlinear1postode.ode#################"
"diff ( y , x , 1 ) = y * y;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.0,"
"x_end:0.5,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.01,"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (1.0/(1.0 - x)) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 0.5 ""
estimated_steps = 500. ""
step_error = 2.0000000000000E-13 ""
est_needed_step_err = 2.0000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 4.53595102575651440000000000000000000000000000000000000000000000E-47 ""
max_value3 = 4.53595102575651440000000000000000000000000000000000000000000000E-47 ""
value3 = 4.53595102575651440000000000000000000000000000000000000000000000E-47 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = 0.0 " "
y[1] (analytic) = 1. " "
y[1] (numeric) = 1. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.000E-3 " "
y[1] (analytic) = 1.001001001001001 " "
y[1] (numeric) = 1.001001001001001 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.000E-3 " "
y[1] (analytic) = 1.002004008016032 " "
y[1] (numeric) = 1.0020040080160322 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.216005157151812700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.000E-3 " "
y[1] (analytic) = 1.0030090270812437 " "
y[1] (numeric) = 1.003009027081244 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.213784711102562100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.000E-3 " "
y[1] (analytic) = 1.0040160642570282 " "
y[1] (numeric) = 1.0040160642570284 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.211564265053311800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.000E-3 " "
y[1] (analytic) = 1.0050251256281406 " "
y[1] (numeric) = 1.005025125628141 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.418687638008123600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.000E-3 " "
y[1] (analytic) = 1.0060362173038229 " "
y[1] (numeric) = 1.0060362173038233 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.414246745909622400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.000E-3 " "
y[1] (analytic) = 1.0070493454179255 " "
y[1] (numeric) = 1.007049345417926 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.409805853811122000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.000E-3 " "
y[1] (analytic) = 1.0080645161290323 " "
y[1] (numeric) = 1.0080645161290327 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.40536496171262100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.000000000000001000E-3 " "
y[1] (analytic) = 1.0090817356205852 " "
y[1] (numeric) = 1.0090817356205857 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.40092406961412100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.000000000000000200E-2 " "
y[1] (analytic) = 1.0101010101010102 " "
y[1] (numeric) = 1.0101010101010106 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.3964831775156200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.100000000000000300E-2 " "
y[1] (analytic) = 1.0111223458038423 " "
y[1] (numeric) = 1.0111223458038427 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.39204228541711870000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.200000000000000400E-2 " "
y[1] (analytic) = 1.0121457489878543 " "
y[1] (numeric) = 1.0121457489878547 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.387601393318618600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.300000000000000600E-2 " "
y[1] (analytic) = 1.0131712259371835 " "
y[1] (numeric) = 1.013171225937184 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.383160501220117500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.400000000000000700E-2 " "
y[1] (analytic) = 1.0141987829614605 " "
y[1] (numeric) = 1.014198782961461 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.37871960912161740000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.500000000000000800E-2 " "
y[1] (analytic) = 1.015228426395939 " "
y[1] (numeric) = 1.0152284263959397 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.56141807553467500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.600000000000001000E-2 " "
y[1] (analytic) = 1.016260162601626 " "
y[1] (numeric) = 1.0162601626016265 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.36983782492461560000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.700000000000001000E-2 " "
y[1] (analytic) = 1.017293997965412 " "
y[1] (numeric) = 1.0172939979654125 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.365396932826115500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.80000000000000100E-2 " "
y[1] (analytic) = 1.0183299389002036 " "
y[1] (numeric) = 1.0183299389002043 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.54143406109142200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.90000000000000100E-2 " "
y[1] (analytic) = 1.019367991845056 " "
y[1] (numeric) = 1.0193679918450567 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.53477272294367100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.00000000000000120E-2 " "
y[1] (analytic) = 1.0204081632653061 " "
y[1] (numeric) = 1.0204081632653068 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.5281113847959200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.10000000000000130E-2 " "
y[1] (analytic) = 1.0214504596527068 " "
y[1] (numeric) = 1.0214504596527076 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.69526672886422600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.200000000000001400E-2 " "
y[1] (analytic) = 1.0224948875255624 " "
y[1] (numeric) = 1.0224948875255633 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.68638494466722500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.300000000000001500E-2 " "
y[1] (analytic) = 1.0235414534288638 " "
y[1] (numeric) = 1.0235414534288647 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.67750316047022400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.400000000000001600E-2 " "
y[1] (analytic) = 1.0245901639344261 " "
y[1] (numeric) = 1.024590163934427 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.66862137627322300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.500000000000001700E-2 " "
y[1] (analytic) = 1.0256410256410258 " "
y[1] (numeric) = 1.0256410256410264 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.49480469405716500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.600000000000002000E-2 " "
y[1] (analytic) = 1.026694045174538 " "
y[1] (numeric) = 1.0266940451745388 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.48814335590941500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.700000000000002000E-2 " "
y[1] (analytic) = 1.027749229188078 " "
y[1] (numeric) = 1.027749229188079 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.64197602368221900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.800000000000002000E-2 " "
y[1] (analytic) = 1.02880658436214 " "
y[1] (numeric) = 1.0288065843621408 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.63309423948521700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 2.90000000000000200E-2 " "
y[1] (analytic) = 1.0298661174047374 " "
y[1] (numeric) = 1.0298661174047383 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.62421245528821600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.00000000000000200E-2 " "
y[1] (analytic) = 1.0309278350515465 " "
y[1] (numeric) = 1.0309278350515474 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.61533067109121400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.10000000000000200E-2 " "
y[1] (analytic) = 1.0319917440660475 " "
y[1] (numeric) = 1.0319917440660484 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.60644888689421200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.20000000000000230E-2 " "
y[1] (analytic) = 1.0330578512396695 " "
y[1] (numeric) = 1.0330578512396704 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.59756710269721100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.30000000000000240E-2 " "
y[1] (analytic) = 1.0341261633919339 " "
y[1] (numeric) = 1.034126163391935 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07358566481252640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.40000000000000250E-2 " "
y[1] (analytic) = 1.0351966873706004 " "
y[1] (numeric) = 1.0351966873706016 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07247544178790120000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.500000000000002600E-2 " "
y[1] (analytic) = 1.0362694300518136 " "
y[1] (numeric) = 1.0362694300518147 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07136521876327590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.600000000000002600E-2 " "
y[1] (analytic) = 1.037344398340249 " "
y[1] (numeric) = 1.0373443983402502 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07025499573865080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.700000000000003000E-2 " "
y[1] (analytic) = 1.0384215991692627 " "
y[1] (numeric) = 1.038421599169264 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2829737272568312000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.80000000000000300E-2 " "
y[1] (analytic) = 1.0395010395010396 " "
y[1] (numeric) = 1.039501039501041 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28164145962728040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 3.90000000000000300E-2 " "
y[1] (analytic) = 1.040582726326743 " "
y[1] (numeric) = 1.0405827263267444 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28030919199773020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.00000000000000300E-2 " "
y[1] (analytic) = 1.0416666666666667 " "
y[1] (numeric) = 1.041666666666668 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.27897692436818030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.10000000000000300E-2 " "
y[1] (analytic) = 1.0427528675703859 " "
y[1] (numeric) = 1.0427528675703872 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.277644656738630100000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.20000000000000300E-2 " "
y[1] (analytic) = 1.0438413361169103 " "
y[1] (numeric) = 1.0438413361169117 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.27631238910908000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.30000000000000300E-2 " "
y[1] (analytic) = 1.044932079414838 " "
y[1] (numeric) = 1.0449320794148396 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.48747680839278470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.40000000000000340E-2 " "
y[1] (analytic) = 1.0460251046025104 " "
y[1] (numeric) = 1.046025104602512 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.48592249615830950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.50000000000000340E-2 " "
y[1] (analytic) = 1.0471204188481675 " "
y[1] (numeric) = 1.047120418848169 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.48436818392383430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.600000000000003500E-2 " "
y[1] (analytic) = 1.0482180293501049 " "
y[1] (numeric) = 1.0482180293501064 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.4828138716893590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.700000000000003600E-2 " "
y[1] (analytic) = 1.0493179433368311 " "
y[1] (numeric) = 1.0493179433368327 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.48125955945488360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.800000000000003700E-2 " "
y[1] (analytic) = 1.050420168067227 " "
y[1] (numeric) = 1.0504201680672285 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.47970524722040860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 4.90000000000000400E-2 " "
y[1] (analytic) = 1.0515247108307046 " "
y[1] (numeric) = 1.0515247108307062 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.47815093498593310000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.00000000000000300E-2 " "
y[1] (analytic) = 1.0526315789473684 " "
y[1] (numeric) = 1.0526315789473701 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.6875389974302380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.10000000000000300E-2 " "
y[1] (analytic) = 1.053740779768177 " "
y[1] (numeric) = 1.0537407797681788 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.68576264059083770000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.20000000000000400E-2 " "
y[1] (analytic) = 1.0548523206751055 " "
y[1] (numeric) = 1.0548523206751073 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.68398628375143740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.30000000000000400E-2 " "
y[1] (analytic) = 1.0559662090813096 " "
y[1] (numeric) = 1.0559662090813113 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.6822099269120370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.40000000000000400E-2 " "
y[1] (analytic) = 1.0570824524312896 " "
y[1] (numeric) = 1.0570824524312916 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.89048776633171660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.50000000000000400E-2 " "
y[1] (analytic) = 1.0582010582010584 " "
y[1] (numeric) = 1.0582010582010601 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.67865721323323640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.60000000000000400E-2 " "
y[1] (analytic) = 1.0593220338983051 " "
y[1] (numeric) = 1.0593220338983071 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.88649096344306570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.700000000000004000E-2 " "
y[1] (analytic) = 1.0604453870625663 " "
y[1] (numeric) = 1.0604453870625683 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.88449256199874040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.800000000000004000E-2 " "
y[1] (analytic) = 1.0615711252653928 " "
y[1] (numeric) = 1.0615711252653948 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.88249416055441540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 5.900000000000004000E-2 " "
y[1] (analytic) = 1.0626992561105209 " "
y[1] (numeric) = 1.0626992561105228 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.88049575911009000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.000000000000004000E-2 " "
y[1] (analytic) = 1.0638297872340425 " "
y[1] (numeric) = 1.0638297872340448 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.08721928629529430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.10000000000000400E-2 " "
y[1] (analytic) = 1.0649627263045793 " "
y[1] (numeric) = 1.0649627263045816 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.0849988402460440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.20000000000000400E-2 " "
y[1] (analytic) = 1.0660980810234542 " "
y[1] (numeric) = 1.0660980810234564 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.08277839419679370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.30000000000000400E-2 " "
y[1] (analytic) = 1.0672358591248667 " "
y[1] (numeric) = 1.067235859124869 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.0805579481475430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.40000000000000500E-2 " "
y[1] (analytic) = 1.0683760683760684 " "
y[1] (numeric) = 1.0683760683760708 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.2861712523081220000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.50000000000000500E-2 " "
y[1] (analytic) = 1.0695187165775402 " "
y[1] (numeric) = 1.0695187165775426 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.2837287616539470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.60000000000000500E-2 " "
y[1] (analytic) = 1.0706638115631693 " "
y[1] (numeric) = 1.0706638115631717 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.28128627099977140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.70000000000000500E-2 " "
y[1] (analytic) = 1.0718113612004287 " "
y[1] (numeric) = 1.0718113612004314 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.48601139674065020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.80000000000000500E-2 " "
y[1] (analytic) = 1.072961373390558 " "
y[1] (numeric) = 1.0729613733905607 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.483346861481550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 6.90000000000000500E-2 " "
y[1] (analytic) = 1.0741138560687433 " "
y[1] (numeric) = 1.0741138560687462 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.6874058534076540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.00000000000000500E-2 " "
y[1] (analytic) = 1.0752688172043012 " "
y[1] (numeric) = 1.0752688172043041 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.6845192735436280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.10000000000000500E-2 " "
y[1] (analytic) = 1.0764262648008611 " "
y[1] (numeric) = 1.0764262648008642 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.88791213165495800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.20000000000000500E-2 " "
y[1] (analytic) = 1.0775862068965518 " "
y[1] (numeric) = 1.077586206896555 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.88480350718600600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.30000000000000500E-2 " "
y[1] (analytic) = 1.0787486515641855 " "
y[1] (numeric) = 1.0787486515641889 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.08753023148256030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.40000000000000500E-2 " "
y[1] (analytic) = 1.0799136069114472 " "
y[1] (numeric) = 1.0799136069114506 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.08419956240868430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.50000000000000600E-2 " "
y[1] (analytic) = 1.0810810810810811 " "
y[1] (numeric) = 1.0810810810810847 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.28626015289046340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.60000000000000600E-2 " "
y[1] (analytic) = 1.0822510822510822 " "
y[1] (numeric) = 1.082251082251086 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.48787665416239200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.70000000000000600E-2 " "
y[1] (analytic) = 1.0834236186348862 " "
y[1] (numeric) = 1.08342361863489 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.4841018958786660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.80000000000000600E-2 " "
y[1] (analytic) = 1.0845986984815619 " "
y[1] (numeric) = 1.0845986984815656 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.48032713759494000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 7.90000000000000600E-2 " "
y[1] (analytic) = 1.0857763300760044 " "
y[1] (numeric) = 1.0857763300760082 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.47655237931121500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.00000000000000600E-2 " "
y[1] (analytic) = 1.0869565217391306 " "
y[1] (numeric) = 1.0869565217391344 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.4727776210274890000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.10000000000000600E-2 " "
y[1] (analytic) = 1.0881392818280742 " "
y[1] (numeric) = 1.088139281828078 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.46900286274376360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.20000000000000600E-2 " "
y[1] (analytic) = 1.0893246187363834 " "
y[1] (numeric) = 1.0893246187363874 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.66906505178121730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.30000000000000600E-2 " "
y[1] (analytic) = 1.0905125408942205 " "
y[1] (numeric) = 1.0905125408942242 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.4614533461763125000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.40000000000000600E-2 " "
y[1] (analytic) = 1.091703056768559 " "
y[1] (numeric) = 1.091703056768563 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.6610714460039160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.50000000000000600E-2 " "
y[1] (analytic) = 1.092896174863388 " "
y[1] (numeric) = 1.092896174863392 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.6570746431152650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.60000000000000700E-2 " "
y[1] (analytic) = 1.0940919037199126 " "
y[1] (numeric) = 1.0940919037199166 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.65307784022661450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.70000000000000700E-2 " "
y[1] (analytic) = 1.095290251916758 " "
y[1] (numeric) = 1.0952902519167622 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.85180776163451750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.80000000000000700E-2 " "
y[1] (analytic) = 1.0964912280701755 " "
y[1] (numeric) = 1.0964912280701797 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.84758891414094250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 8.90000000000000700E-2 " "
y[1] (analytic) = 1.0976948408342482 " "
y[1] (numeric) = 1.0976948408342524 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.84337006664736640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.00000000000000700E-2 " "
y[1] (analytic) = 1.098901098901099 " "
y[1] (numeric) = 1.0989010989011032 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.8391512191537910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.10000000000000700E-2 " "
y[1] (analytic) = 1.1001100110011002 " "
y[1] (numeric) = 1.1001100110011044 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.83493237166021570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.20000000000000700E-2 " "
y[1] (analytic) = 1.1013215859030838 " "
y[1] (numeric) = 1.101321585903088 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.83071352416663960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.30000000000000700E-2 " "
y[1] (analytic) = 1.1025358324145536 " "
y[1] (numeric) = 1.102535832414558 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.02788913334006740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.40000000000000700E-2 " "
y[1] (analytic) = 1.1037527593818985 " "
y[1] (numeric) = 1.103752759381903 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.0234482412415670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.50000000000000700E-2 " "
y[1] (analytic) = 1.1049723756906078 " "
y[1] (numeric) = 1.1049723756906122 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.01900734914306670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.60000000000000700E-2 " "
y[1] (analytic) = 1.106194690265487 " "
y[1] (numeric) = 1.1061946902654913 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.01456645704456550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.70000000000000800E-2 " "
y[1] (analytic) = 1.1074197120708749 " "
y[1] (numeric) = 1.1074197120708795 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 4.21063184319336870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.80000000000000800E-2 " "
y[1] (analytic) = 1.108647450110865 " "
y[1] (numeric) = 1.1086474501108694 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.0056846728475637000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 9.90000000000000800E-2 " "
y[1] (analytic) = 1.109877913429523 " "
y[1] (numeric) = 1.1098779134295276 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 4.20130596978651700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10000000000000007 " "
y[1] (analytic) = 1.1111111111111112 " "
y[1] (numeric) = 1.111111111111116 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.396483177515620000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10100000000000008 " "
y[1] (analytic) = 1.1123470522803116 " "
y[1] (numeric) = 1.1123470522803165 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.39159819620726870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10200000000000008 " "
y[1] (analytic) = 1.11358574610245 " "
y[1] (numeric) = 1.113585746102455 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.3867132148989180000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10300000000000008 " "
y[1] (analytic) = 1.1148272017837237 " "
y[1] (numeric) = 1.1148272017837286 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.3818282335905673000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10400000000000008 " "
y[1] (analytic) = 1.1160714285714286 " "
y[1] (numeric) = 1.1160714285714337 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.5758952182950446000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10500000000000008 " "
y[1] (analytic) = 1.11731843575419 " "
y[1] (numeric) = 1.1173184357541952 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.5707881923817684000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10600000000000008 " "
y[1] (analytic) = 1.1185682326621924 " "
y[1] (numeric) = 1.1185682326621977 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.7641890432714720000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10700000000000008 " "
y[1] (analytic) = 1.1198208286674134 " "
y[1] (numeric) = 1.1198208286674187 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.7588599727532704000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10800000000000008 " "
y[1] (analytic) = 1.1210762331838566 " "
y[1] (numeric) = 1.1210762331838622 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.9515946898281970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10900000000000008 " "
y[1] (analytic) = 1.1223344556677892 " "
y[1] (numeric) = 1.1223344556677948 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.9460435747050710000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11000000000000008 " "
y[1] (analytic) = 1.1235955056179776 " "
y[1] (numeric) = 1.1235955056179834 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 5.1381121579652240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11100000000000008 " "
y[1] (analytic) = 1.124859392575928 " "
y[1] (numeric) = 1.124859392575934 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.3297366520155250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11200000000000009 " "
y[1] (analytic) = 1.1261261261261262 " "
y[1] (numeric) = 1.1261261261261322 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.323741447682551000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11300000000000009 " "
y[1] (analytic) = 1.1273957158962797 " "
y[1] (numeric) = 1.1273957158962857 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.3177462433495740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11400000000000009 " "
y[1] (analytic) = 1.1286681715575622 " "
y[1] (numeric) = 1.1286681715575684 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 5.5084825589801760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11500000000000009 " "
y[1] (analytic) = 1.1299435028248588 " "
y[1] (numeric) = 1.1299435028248652 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 5.6987747854009290000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11600000000000009 " "
y[1] (analytic) = 1.1312217194570138 " "
y[1] (numeric) = 1.1312217194570202 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 5.6923354918581020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11700000000000009 " "
y[1] (analytic) = 1.1325028312570782 " "
y[1] (numeric) = 1.1325028312570848 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 5.8819615844640790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11800000000000009 " "
y[1] (analytic) = 1.1337868480725626 " "
y[1] (numeric) = 1.1337868480725692 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 5.8753002463163270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11900000000000009 " "
y[1] (analytic) = 1.135073779795687 " "
y[1] (numeric) = 1.1350737797956938 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.0642602051075290000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12000000000000009 " "
y[1] (analytic) = 1.1363636363636365 " "
y[1] (numeric) = 1.1363636363636436 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.2527760746888800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1210000000000001 " "
y[1] (analytic) = 1.137656427758817 " "
y[1] (numeric) = 1.1376564277588241 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.245670647331280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1220000000000001 " "
y[1] (analytic) = 1.1389521640091118 " "
y[1] (numeric) = 1.138952164009119 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.2385652199736790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1230000000000001 " "
y[1] (analytic) = 1.1402508551881416 " "
y[1] (numeric) = 1.1402508551881487 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.2314597926160780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1240000000000001 " "
y[1] (analytic) = 1.1415525114155252 " "
y[1] (numeric) = 1.1415525114155325 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 6.4188654391728040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12500000000000008 " "
y[1] (analytic) = 1.142857142857143 " "
y[1] (numeric) = 1.1428571428571503 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 6.4115379672102780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12600000000000008 " "
y[1] (analytic) = 1.1441647597254005 " "
y[1] (numeric) = 1.144164759725408 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 6.598277479952230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12700000000000009 " "
y[1] (analytic) = 1.1454753722794961 " "
y[1] (numeric) = 1.1454753722795037 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 6.5907279633847790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.12800000000000009 " "
y[1] (analytic) = 1.1467889908256883 " "
y[1] (numeric) = 1.1467889908256959 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 6.5831784468173270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1290000000000001 " "
y[1] (analytic) = 1.1481056257175661 " "
y[1] (numeric) = 1.148105625717574 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 6.7690297811395780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1300000000000001 " "
y[1] (analytic) = 1.149425287356322 " "
y[1] (numeric) = 1.1494252873563298 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 6.7612582199672020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1310000000000001 " "
y[1] (analytic) = 1.1507479861910244 " "
y[1] (numeric) = 1.1507479861910321 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 6.7534866587948260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1320000000000001 " "
y[1] (analytic) = 1.1520737327188941 " "
y[1] (numeric) = 1.1520737327189021 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 6.9384498146973770000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1330000000000001 " "
y[1] (analytic) = 1.1534025374855825 " "
y[1] (numeric) = 1.1534025374855907 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 7.1229688813900780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1340000000000001 " "
y[1] (analytic) = 1.1547344110854505 " "
y[1] (numeric) = 1.1547344110854587 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 7.1147532310078520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1350000000000001 " "
y[1] (analytic) = 1.1560693641618498 " "
y[1] (numeric) = 1.1560693641618582 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 7.2986061638857780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1360000000000001 " "
y[1] (analytic) = 1.1574074074074077 " "
y[1] (numeric) = 1.157407407407416 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 7.2901684688986270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1370000000000001 " "
y[1] (analytic) = 1.1587485515643108 " "
y[1] (numeric) = 1.1587485515643194 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 7.4733552679617780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1380000000000001 " "
y[1] (analytic) = 1.1600928074245942 " "
y[1] (numeric) = 1.160092807424603 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 7.6560979778150780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1390000000000001 " "
y[1] (analytic) = 1.16144018583043 " "
y[1] (numeric) = 1.161440185830439 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 7.8383965984585290000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1400000000000001 " "
y[1] (analytic) = 1.1627906976744187 " "
y[1] (numeric) = 1.162790697674428 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 8.0202511298921310000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1410000000000001 " "
y[1] (analytic) = 1.1641443538998837 " "
y[1] (numeric) = 1.164144353899893 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 8.0109252564852780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1420000000000001 " "
y[1] (analytic) = 1.1655011655011658 " "
y[1] (numeric) = 1.165501165501175 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 8.0015993830784260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1430000000000001 " "
y[1] (analytic) = 1.166861143523921 " "
y[1] (numeric) = 1.1668611435239304 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 8.1825657360923280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1440000000000001 " "
y[1] (analytic) = 1.1682242990654208 " "
y[1] (numeric) = 1.1682242990654306 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 8.3630879998963770000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1450000000000001 " "
y[1] (analytic) = 1.169590643274854 " "
y[1] (numeric) = 1.169590643274864 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 8.5431661744905780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1460000000000001 " "
y[1] (analytic) = 1.1709601873536302 " "
y[1] (numeric) = 1.1709601873536402 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 8.5331741672689520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1470000000000001 " "
y[1] (analytic) = 1.172332942555686 " "
y[1] (numeric) = 1.172332942555696 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 8.5231821600473250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1480000000000001 " "
y[1] (analytic) = 1.1737089201877937 " "
y[1] (numeric) = 1.173708920187804 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 8.7023721562218250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1490000000000001 " "
y[1] (analytic) = 1.175088131609871 " "
y[1] (numeric) = 1.1750881316098813 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 8.8811180631864760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1500000000000001 " "
y[1] (analytic) = 1.1764705882352944 " "
y[1] (numeric) = 1.1764705882353048 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 8.8706819667549990000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1510000000000001 " "
y[1] (analytic) = 1.1778563015312133 " "
y[1] (numeric) = 1.177856301531224 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 9.0487617399048750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1520000000000001 " "
y[1] (analytic) = 1.1792452830188682 " "
y[1] (numeric) = 1.1792452830188789 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 9.0381035988684720000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1530000000000001 " "
y[1] (analytic) = 1.180637544273908 " "
y[1] (numeric) = 1.180637544273919 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 9.2155172382035730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1540000000000001 " "
y[1] (analytic) = 1.182033096926714 " "
y[1] (numeric) = 1.1820330969267252 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.3924867883288220000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1550000000000001 " "
y[1] (analytic) = 1.1834319526627222 " "
y[1] (numeric) = 1.1834319526627333 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.381384558082570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1560000000000001 " "
y[1] (analytic) = 1.184834123222749 " "
y[1] (numeric) = 1.1848341232227604 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 9.5576879743930440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1570000000000001 " "
y[1] (analytic) = 1.1862396204033216 " "
y[1] (numeric) = 1.1862396204033332 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 9.7335473014936710000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1580000000000001 " "
y[1] (analytic) = 1.1876484560570073 " "
y[1] (numeric) = 1.187648456057019 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 9.9089625393844460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1590000000000001 " "
y[1] (analytic) = 1.189060642092747 " "
y[1] (numeric) = 1.1890606420927587 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 9.8971941753234190000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16000000000000011 " "
y[1] (analytic) = 1.1904761904761907 " "
y[1] (numeric) = 1.1904761904762027 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.0071943279399419000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16100000000000012 " "
y[1] (analytic) = 1.191895113230036 " "
y[1] (numeric) = 1.1918951132300482 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.0246248294265568000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16200000000000012 " "
y[1] (analytic) = 1.1933174224343677 " "
y[1] (numeric) = 1.19331742243438 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.0420109219921868000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16300000000000012 " "
y[1] (analytic) = 1.1947431302270013 " "
y[1] (numeric) = 1.194743130227014 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.0593526056368317000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16400000000000012 " "
y[1] (analytic) = 1.196172248803828 " "
y[1] (numeric) = 1.1961722488038407 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.058086951388758900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16500000000000012 " "
y[1] (analytic) = 1.1976047904191618 " "
y[1] (numeric) = 1.1976047904191747 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.0753620216519265000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16600000000000012 " "
y[1] (analytic) = 1.1990407673860914 " "
y[1] (numeric) = 1.1990407673861043 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.0740741629433612000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16700000000000012 " "
y[1] (analytic) = 1.2004801920768309 " "
y[1] (numeric) = 1.200480192076844 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.0912826198250514000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16800000000000012 " "
y[1] (analytic) = 1.201923076923077 " "
y[1] (numeric) = 1.2019230769230904 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.108446667785756200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.16900000000000012 " "
y[1] (analytic) = 1.2033694344163661 " "
y[1] (numeric) = 1.2033694344163794 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.107114400156206000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17000000000000012 " "
y[1] (analytic) = 1.204819277108434 " "
y[1] (numeric) = 1.2048192771084476 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.1242118347354331000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17100000000000012 " "
y[1] (analytic) = 1.2062726176115803 " "
y[1] (numeric) = 1.2062726176115943 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.159672358141961000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17200000000000013 " "
y[1] (analytic) = 1.207729468599034 " "
y[1] (numeric) = 1.207729468599048 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.158273477130933000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17300000000000013 " "
y[1] (analytic) = 1.2091898428053207 " "
y[1] (numeric) = 1.209189842805335 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.1752376849472053000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17400000000000013 " "
y[1] (analytic) = 1.2106537530266346 " "
y[1] (numeric) = 1.210653753026649 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.1921574838424930000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17500000000000013 " "
y[1] (analytic) = 1.2121212121212124 " "
y[1] (numeric) = 1.212121212121227 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.2090328738167953000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17600000000000013 " "
y[1] (analytic) = 1.2135922330097089 " "
y[1] (numeric) = 1.2135922330097237 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.2258638548701127000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17700000000000013 " "
y[1] (analytic) = 1.2150668286755775 " "
y[1] (numeric) = 1.2150668286755923 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.2243761560171149000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17800000000000013 " "
y[1] (analytic) = 1.2165450121654504 " "
y[1] (numeric) = 1.2165450121654655 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.2411405236889547000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.17900000000000013 " "
y[1] (analytic) = 1.2180267965895253 " "
y[1] (numeric) = 1.2180267965895406 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 1.2578604824398096000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18000000000000013 " "
y[1] (analytic) = 1.2195121951219514 " "
y[1] (numeric) = 1.219512195121967 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.2745360322696794000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18100000000000013 " "
y[1] (analytic) = 1.2210012210012213 " "
y[1] (numeric) = 1.2210012210012369 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.272981720035204200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18200000000000013 " "
y[1] (analytic) = 1.2224938875305627 " "
y[1] (numeric) = 1.2224938875305784 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.2895906564835966000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18300000000000013 " "
y[1] (analytic) = 1.2239902080783356 " "
y[1] (numeric) = 1.2239902080783516 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.3061551840110040000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18400000000000014 " "
y[1] (analytic) = 1.2254901960784317 " "
y[1] (numeric) = 1.2254901960784477 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.3045564628555437000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18500000000000014 " "
y[1] (analytic) = 1.226993865030675 " "
y[1] (numeric) = 1.2269938650306913 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.3210543770014735000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18600000000000014 " "
y[1] (analytic) = 1.2285012285012287 " "
y[1] (numeric) = 1.228501228501245 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 1.3375078822264186000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18700000000000014 " "
y[1] (analytic) = 1.2300123001230014 " "
y[1] (numeric) = 1.230012300123018 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 1.3539169785303780000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18800000000000014 " "
y[1] (analytic) = 1.2315270935960594 " "
y[1] (numeric) = 1.2315270935960763 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.370281665913353000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.18900000000000014 " "
y[1] (analytic) = 1.2330456226880397 " "
y[1] (numeric) = 1.2330456226880568 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.3866019443753427000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.19000000000000014 " "
y[1] (analytic) = 1.234567901234568 " "
y[1] (numeric) = 1.2345679012345854 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.4028778139163475000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.19100000000000014 " "
y[1] (analytic) = 1.236093943139679 " "
y[1] (numeric) = 1.2360939431396962 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.4011458659979323000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.19200000000000014 " "
y[1] (analytic) = 1.2376237623762378 " "
y[1] (numeric) = 1.2376237623762554 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.4173551221574596000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.19300000000000014 " "
y[1] (analytic) = 1.2391573729863696 " "
y[1] (numeric) = 1.2391573729863872 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.4156009697785518000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.19400000000000014 " "
y[1] (analytic) = 1.240694789081886 " "
y[1] (numeric) = 1.240694789081904 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 1.4496404077135594000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.19500000000000015 " "
y[1] (analytic) = 1.2422360248447208 " "
y[1] (numeric) = 1.2422360248447388 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 1.4478418464136664000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.19600000000000015 " "
y[1] (analytic) = 1.2437810945273635 " "
y[1] (numeric) = 1.2437810945273817 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 1.463895671349746000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.19700000000000015 " "
y[1] (analytic) = 1.2453300124533004 " "
y[1] (numeric) = 1.2453300124533189 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.4799050873648410000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.19800000000000015 " "
y[1] (analytic) = 1.2468827930174566 " "
y[1] (numeric) = 1.2468827930174753 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.4958700944589506000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.19900000000000015 " "
y[1] (analytic) = 1.248439450686642 " "
y[1] (numeric) = 1.2484394506866607 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.4940049197775800000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.20000000000000015 " "
y[1] (analytic) = 1.2500000000000002 " "
y[1] (numeric) = 1.2500000000000193 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.5276668818842150000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.20100000000000015 " "
y[1] (analytic) = 1.251564455569462 " "
y[1] (numeric) = 1.2515644555694814 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.5434986622153699000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.20200000000000015 " "
y[1] (analytic) = 1.2531328320802009 " "
y[1] (numeric) = 1.2531328320802202 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.5415668741525218000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.20300000000000015 " "
y[1] (analytic) = 1.254705144291092 " "
y[1] (numeric) = 1.2547051442911115 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.5573320411021993000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.20400000000000015 " "
y[1] (analytic) = 1.2562814070351762 " "
y[1] (numeric) = 1.256281407035196 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.5730527991308912000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.20500000000000015 " "
y[1] (analytic) = 1.2578616352201262 " "
y[1] (numeric) = 1.2578616352201462 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.5887291482385987000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = y * y;"
Iterations = 205
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds
"Expected Time Remaining "= 0 Years 0 Days 0 Hours 4 Minutes 19 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 4 Minutes 16 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 7 Minutes 18 Seconds
"Time to Timeout " Unknown
Percent Done = 41.20000000000003 "%"
(%o54) true
(%o54) diffeq.max