(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m,
n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new,
ratio, term], n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float 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) rm0 - convfloat(m - 1) rm1,
array_y_higher
1, m - 2
if omniabs(hdrc) > glob_small_float glob_small_float
glob_h
then (rcs : ------, ord_no :
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
-----------------------------------------------------,
hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found_sing : 0, if (1 # found_sing) 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_sing : 1,
1, 2 1, 2
array_type_pole : 2, if glob_display_flag
1
then (if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1"))),
if (1 # found_sing) 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 > - 1.0 glob_smallish_float)
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, 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 for equation 1"))),
if (1 # found_sing) 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_sing : 1, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE for equation 1")),
if (1 # found_sing) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole > - 1.0
1, 1 1, 2
glob_smallish_float))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, 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 for equation 1"))),
if (1 # found_sing) 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,
1, 2 1, 2 1
found_sing : 1, if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))),
if 1 # found_sing 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 for equation 1")),
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, hdrc_BBB, m,
n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new,
ratio, term], n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float 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) rm0 - convfloat(m - 1) rm1,
array_y_higher
1, m - 2
if omniabs(hdrc) > glob_small_float glob_small_float
glob_h
then (rcs : ------, ord_no :
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
-----------------------------------------------------,
hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found_sing : 0, if (1 # found_sing) 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_sing : 1,
1, 2 1, 2
array_type_pole : 2, if glob_display_flag
1
then (if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1"))),
if (1 # found_sing) 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 > - 1.0 glob_smallish_float)
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, 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 for equation 1"))),
if (1 # found_sing) 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_sing : 1, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE for equation 1")),
if (1 # found_sing) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole > - 1.0
1, 1 1, 2
glob_smallish_float))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, 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 for equation 1"))),
if (1 # found_sing) 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,
1, 2 1, 2 1
found_sing : 1, if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))),
if 1 # found_sing 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 for equation 1")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_1D0 + array_const_0D0 ,
1 1 1
array_tmp2 : sin(array_x ), array_tmp2_g : cos(array_x ),
1 1 1 1
array_tmp3 : array_tmp1 - array_tmp2 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp2_g array_x - array_tmp2 array_x
1 2 1 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
2 1 2 1
array_tmp3 : array_tmp1 - array_tmp2 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp2_g array_x - array_tmp2 array_x
2 2 2 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
3 2 3 2
array_tmp3 : array_tmp1 - array_tmp2 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp2_g array_x - array_tmp2 array_x
3 2 3 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
4 3 4 3
array_tmp3 : array_tmp1 - array_tmp2 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp2_g array_x - array_tmp2 array_x
4 2 4 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
5 4 5 4
array_tmp3 : array_tmp1 - array_tmp2 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
array_tmp2_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp2 : ----------------------------,
kkk kkk - 1
- array_tmp2 array_x
kkk - 1 2
array_tmp2_g : ----------------------------,
kkk kkk - 1
array_tmp3 : - array_tmp2 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp3 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_1D0 + array_const_0D0 ,
1 1 1
array_tmp2 : sin(array_x ), array_tmp2_g : cos(array_x ),
1 1 1 1
array_tmp3 : array_tmp1 - array_tmp2 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp2_g array_x - array_tmp2 array_x
1 2 1 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
2 1 2 1
array_tmp3 : array_tmp1 - array_tmp2 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp2_g array_x - array_tmp2 array_x
2 2 2 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
3 2 3 2
array_tmp3 : array_tmp1 - array_tmp2 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp2_g array_x - array_tmp2 array_x
3 2 3 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
4 3 4 3
array_tmp3 : array_tmp1 - array_tmp2 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp2_g array_x - array_tmp2 array_x
4 2 4 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
5 4 5 4
array_tmp3 : array_tmp1 - array_tmp2 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
array_tmp2_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp2 : ----------------------------,
kkk kkk - 1
- array_tmp2 array_x
kkk - 1 2
array_tmp2_g : ----------------------------,
kkk kkk - 1
array_tmp3 : - array_tmp2 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp3 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole_debug(typ, radius, order2) :=
(if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS,
"DBG Radius of convergence ", 4, radius, 4, " "),
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " "))
(%o27) display_pole_debug(typ, radius, order2) :=
(if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS,
"DBG Radius of convergence ", 4, radius, 4, " "),
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " "))
(%i28) 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
(%o28) 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
(%i29) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o29) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i30) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o30) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i31) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o31) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i32) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o32) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i33) log_revs(file, revs) := printf(file, revs)
(%o33) log_revs(file, revs) := printf(file, revs)
(%i34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i35) 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, " | "))
(%o35) 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, " | "))
(%i36) logstart(file) := printf(file, "")
(%o36) logstart(file) := printf(file, "
")
(%i37) logend(file) := printf(file, "
~%")
(%o37) logend(file) := printf(file, "~%")
(%i38) 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())
(%o38) 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())
(%i39) 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
(%o39) 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
(%i40) 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
(%o40) 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
(%i41) factorial_2(nnn) := nnn!
(%o41) factorial_2(nnn) := nnn!
(%i42) 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
(%o42) 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
(%i43) 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)
(%o43) 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)
(%i44) convfp(mmm) := mmm
(%o44) convfp(mmm) := mmm
(%i45) convfloat(mmm) := mmm
(%o45) convfloat(mmm) := mmm
(%i46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i47) Si(x) := 0.0
(%o47) Si(x) := 0.0
(%i48) Ci(x) := 0.0
(%o48) Ci(x) := 0.0
(%i49) ln(x) := log(x)
(%o49) ln(x) := log(x)
(%i50) arcsin(x) := asin(x)
(%o50) arcsin(x) := asin(x)
(%i51) arccos(x) := acos(x)
(%o51) arccos(x) := acos(x)
(%i52) arctan(x) := atan(x)
(%o52) arctan(x) := atan(x)
(%i53) omniabs(x) := abs(x)
(%o53) omniabs(x) := abs(x)
(%i54) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o54) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i55) 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)
(%o55) 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)
(%i56) exact_soln_y(x) := block(x + cos(x) + 2.0)
(%o56) exact_soln_y(x) := block(x + cos(x) + 2.0)
(%i57) 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, max_terms,
opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer,
best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_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_max_h, 0.1, 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_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-201, 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_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/sub_c_sinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0 - sin(x);"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (2.0 + cos(x) + x) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, 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_g, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 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_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2_g : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 5.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
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, if glob_max_h < glob_h
then glob_h : glob_max_h, 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_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0,
omniout_str(DEBUGL, " "), glob_reached_optimal_h : true,
glob_optimal_clock_start_sec : elapsed_time_seconds(),
while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = 1.0 - sin(x);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-28T19:42:40-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sub_c_sin"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.0 - sin(x);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 165 | "), logitem_str(html_log_file, "sub_c_sin diffeq.max"),
logitem_str(html_log_file,
"sub_c_sin maxima results"),
logitem_str(html_log_file, "All Tests - All Languages"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%o57) 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, max_terms,
opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer,
best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_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_max_h, 0.1, 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_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-201, 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_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/sub_c_sinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0 - sin(x);"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (2.0 + cos(x) + x) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, 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_g, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 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_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2_g : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 5.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
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, if glob_max_h < glob_h
then glob_h : glob_max_h, 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_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0,
omniout_str(DEBUGL, " "), glob_reached_optimal_h : true,
glob_optimal_clock_start_sec : elapsed_time_seconds(),
while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = 1.0 - sin(x);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-28T19:42:40-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sub_c_sin"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.0 - sin(x);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 165 | "), logitem_str(html_log_file, "sub_c_sin diffeq.max"),
logitem_str(html_log_file,
"sub_c_sin maxima results"),
logitem_str(html_log_file, "All Tests - All Languages"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i58) main()
"##############ECHO OF PROBLEM#################"
"##############temp/sub_c_sinpostode.ode#################"
"diff ( y , x , 1 ) = 1.0 - sin(x);"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.1,"
"x_end:5.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (2.0 + cos(x) + x) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 4.9 ""
estimated_steps = 4900. ""
step_error = 2.040816326530612300000000000000E-14 ""
est_needed_step_err = 2.040816326530612300000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 2.467204025104944900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
max_value3 = 2.467204025104944900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
value3 = 2.467204025104944900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
best_h = 1.000E-3 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (analytic) = 3.095004165278026 " "
y[1] (numeric) = 3.095004165278026 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.101 " "
y[1] (analytic) = 3.0959038343759766 " "
y[1] (numeric) = 3.0959038343759766 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10200000000000001 " "
y[1] (analytic) = 3.096802508570176 " "
y[1] (numeric) = 3.096802508570176 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10300000000000001 " "
y[1] (analytic) = 3.09770018796195 " "
y[1] (numeric) = 3.0977001879619497 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.43360939698376500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10400000000000001 " "
y[1] (analytic) = 3.0985968726536184 " "
y[1] (numeric) = 3.0985968726536184 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10500000000000001 " "
y[1] (analytic) = 3.0994925627484973 " "
y[1] (numeric) = 3.0994925627484973 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10600000000000001 " "
y[1] (analytic) = 3.1003872583508962 " "
y[1] (numeric) = 3.1003872583508962 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10700000000000001 " "
y[1] (analytic) = 3.1012809595661204 " "
y[1] (numeric) = 3.10128095956612 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.43195413650039680000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10800000000000001 " "
y[1] (analytic) = 3.102173666500467 " "
y[1] (numeric) = 3.102173666500467 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10900000000000001 " "
y[1] (analytic) = 3.10306537926123 " "
y[1] (numeric) = 3.10306537926123 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000001 " "
y[1] (analytic) = 3.1039560979566967 " "
y[1] (numeric) = 3.1039560979566967 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11100000000000002 " "
y[1] (analytic) = 3.1048458226961486 " "
y[1] (numeric) = 3.104845822696148 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.43031002249390200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11200000000000002 " "
y[1] (analytic) = 3.10573455358986 " "
y[1] (numeric) = 3.1057345535898597 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.42990072778997900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11300000000000002 " "
y[1] (analytic) = 3.1066222907491015 " "
y[1] (numeric) = 3.1066222907491006 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.85898424905062500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11400000000000002 " "
y[1] (analytic) = 3.1075090342861342 " "
y[1] (numeric) = 3.107509034286134 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.429084211663700000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11500000000000002 " "
y[1] (analytic) = 3.108394784314216 " "
y[1] (numeric) = 3.1083947843142155 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.428676988171047300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11600000000000002 " "
y[1] (analytic) = 3.109279540947596 " "
y[1] (numeric) = 3.1092795409475955 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.428270453015364200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11700000000000002 " "
y[1] (analytic) = 3.1101633043015178 " "
y[1] (numeric) = 3.1101633043015173 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.42786460516675800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11800000000000002 " "
y[1] (analytic) = 3.111046074492218 " "
y[1] (numeric) = 3.1110460744922177 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.427459443597428600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11900000000000002 " "
y[1] (analytic) = 3.111927851636927 " "
y[1] (numeric) = 3.1119278516369264 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.427054967281661800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000002 " "
y[1] (analytic) = 3.1128086358538662 " "
y[1] (numeric) = 3.1128086358538662 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12100000000000002 " "
y[1] (analytic) = 3.113688427262253 " "
y[1] (numeric) = 3.113688427262253 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12200000000000003 " "
y[1] (analytic) = 3.1145672259822947 " "
y[1] (numeric) = 3.1145672259822947 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12300000000000003 " "
y[1] (analytic) = 3.115445032135194 " "
y[1] (numeric) = 3.1154450321351934 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.42544389411262600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12400000000000003 " "
y[1] (analytic) = 3.1163218458431428 " "
y[1] (numeric) = 3.1163218458431428 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12500000000000003 " "
y[1] (analytic) = 3.117197667229329 " "
y[1] (numeric) = 3.117197667229329 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12600000000000003 " "
y[1] (analytic) = 3.1180724964179305 " "
y[1] (numeric) = 3.118072496417931 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.42424273444647700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12700000000000003 " "
y[1] (analytic) = 3.1189463335341188 " "
y[1] (numeric) = 3.1189463335341188 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12800000000000003 " "
y[1] (analytic) = 3.1198191787040557 " "
y[1] (numeric) = 3.1198191787040557 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12900000000000003 " "
y[1] (analytic) = 3.1206910320548964 " "
y[1] (numeric) = 3.120691032054897 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.42304766889287700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13000000000000003 " "
y[1] (analytic) = 3.121561893714788 " "
y[1] (numeric) = 3.121561893714788 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13100000000000003 " "
y[1] (analytic) = 3.1224317638128687 " "
y[1] (numeric) = 3.1224317638128687 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13200000000000003 " "
y[1] (analytic) = 3.123300642479268 " "
y[1] (numeric) = 3.123300642479268 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13300000000000003 " "
y[1] (analytic) = 3.1241685298451074 " "
y[1] (numeric) = 3.1241685298451074 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13400000000000004 " "
y[1] (analytic) = 3.125035426042499 " "
y[1] (numeric) = 3.1250354260424995 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.421069361803846700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13500000000000004 " "
y[1] (analytic) = 3.125901331204548 " "
y[1] (numeric) = 3.125901331204548 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13600000000000004 " "
y[1] (analytic) = 3.126766245465348 " "
y[1] (numeric) = 3.126766245465348 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13700000000000004 " "
y[1] (analytic) = 3.127630168959985 " "
y[1] (numeric) = 3.127630168959985 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13800000000000004 " "
y[1] (analytic) = 3.1284931018245357 " "
y[1] (numeric) = 3.1284931018245357 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13900000000000004 " "
y[1] (analytic) = 3.1293550441960676 " "
y[1] (numeric) = 3.129355044196067 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.419107782843954400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14000000000000004 " "
y[1] (analytic) = 3.130215996212637 " "
y[1] (numeric) = 3.130215996212637 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14100000000000004 " "
y[1] (analytic) = 3.131075958013293 " "
y[1] (numeric) = 3.131075958013293 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14200000000000004 " "
y[1] (analytic) = 3.131934929738074 " "
y[1] (numeric) = 3.131934929738074 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14300000000000004 " "
y[1] (analytic) = 3.1327929115280075 " "
y[1] (numeric) = 3.132792911528007 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.417550480965113800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14400000000000004 " "
y[1] (analytic) = 3.1336499035251117 " "
y[1] (numeric) = 3.1336499035251113 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.417162808616549400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14500000000000005 " "
y[1] (analytic) = 3.1345059058723947 " "
y[1] (numeric) = 3.1345059058723947 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14600000000000005 " "
y[1] (analytic) = 3.1353609187138547 " "
y[1] (numeric) = 3.1353609187138547 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14700000000000005 " "
y[1] (analytic) = 3.1362149421944783 " "
y[1] (numeric) = 3.1362149421944783 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14800000000000005 " "
y[1] (analytic) = 3.137067976460242 " "
y[1] (numeric) = 3.137067976460242 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14900000000000005 " "
y[1] (analytic) = 3.137920021658112 " "
y[1] (numeric) = 3.137920021658112 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000005 " "
y[1] (analytic) = 3.1387710779360423 " "
y[1] (numeric) = 3.1387710779360427 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.414850585860762400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15100000000000005 " "
y[1] (analytic) = 3.1396211454429777 " "
y[1] (numeric) = 3.1396211454429777 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15200000000000005 " "
y[1] (analytic) = 3.1404702243288494 " "
y[1] (numeric) = 3.1404702243288494 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15300000000000005 " "
y[1] (analytic) = 3.1413183147445793 " "
y[1] (numeric) = 3.1413183147445793 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15400000000000005 " "
y[1] (analytic) = 3.1421654168420767 " "
y[1] (numeric) = 3.1421654168420767 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15500000000000005 " "
y[1] (analytic) = 3.14301153077424 " "
y[1] (numeric) = 3.1430115307742397 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.412941713709421000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15600000000000006 " "
y[1] (analytic) = 3.1438566566949544 " "
y[1] (numeric) = 3.1438566566949544 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15700000000000006 " "
y[1] (analytic) = 3.144700794759095 " "
y[1] (numeric) = 3.144700794759095 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15800000000000006 " "
y[1] (analytic) = 3.1455439451225224 " "
y[1] (numeric) = 3.1455439451225224 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15900000000000006 " "
y[1] (analytic) = 3.146386107942088 " "
y[1] (numeric) = 3.1463861079420874 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.411426298664030500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000006 " "
y[1] (analytic) = 3.147227283375627 " "
y[1] (numeric) = 3.1472272833756265 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.411049059582837300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16100000000000006 " "
y[1] (analytic) = 3.148067471581965 " "
y[1] (numeric) = 3.1480674715819648 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.410672464484692700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16200000000000006 " "
y[1] (analytic) = 3.148906672720914 " "
y[1] (numeric) = 3.148906672720914 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16300000000000006 " "
y[1] (analytic) = 3.1497448869532727 " "
y[1] (numeric) = 3.1497448869532723 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.409921202474360400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16400000000000006 " "
y[1] (analytic) = 3.150582114440826 " "
y[1] (numeric) = 3.150582114440826 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16500000000000006 " "
y[1] (analytic) = 3.1514183553463475 " "
y[1] (numeric) = 3.1514183553463475 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16600000000000006 " "
y[1] (analytic) = 3.152253609833596 " "
y[1] (numeric) = 3.152253609833596 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16700000000000007 " "
y[1] (analytic) = 3.153087878067317 " "
y[1] (numeric) = 3.153087878067317 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16800000000000007 " "
y[1] (analytic) = 3.1539211602132418 " "
y[1] (numeric) = 3.1539211602132418 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16900000000000007 " "
y[1] (analytic) = 3.154753456438088 " "
y[1] (numeric) = 3.1547534564380886 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.407682774524849400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000007 " "
y[1] (analytic) = 3.1555847669095605 " "
y[1] (numeric) = 3.155584766909561 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.407311933138097300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17100000000000007 " "
y[1] (analytic) = 3.1564150917963487 " "
y[1] (numeric) = 3.1564150917963487 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17200000000000007 " "
y[1] (analytic) = 3.1572444312681265 " "
y[1] (numeric) = 3.157244431268127 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.406572153400525400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17300000000000007 " "
y[1] (analytic) = 3.1580727854955555 " "
y[1] (numeric) = 3.158072785495556 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.406203213205478600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17400000000000007 " "
y[1] (analytic) = 3.1589001546502806 " "
y[1] (numeric) = 3.1589001546502815 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.811669809799527400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17500000000000007 " "
y[1] (analytic) = 3.1597265389049336 " "
y[1] (numeric) = 3.1597265389049345 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.810934455131491300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17600000000000007 " "
y[1] (analytic) = 3.1605519384331298 " "
y[1] (numeric) = 3.1605519384331306 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.810200360575144000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17700000000000007 " "
y[1] (analytic) = 3.161376353409469 " "
y[1] (numeric) = 3.1613763534094703 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.214201286453506700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17800000000000007 " "
y[1] (analytic) = 3.1621997840095375 " "
y[1] (numeric) = 3.1621997840095384 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.808735944488466300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17900000000000008 " "
y[1] (analytic) = 3.163022230409904 " "
y[1] (numeric) = 3.1630222304099047 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.808005619312463600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000008 " "
y[1] (analytic) = 3.1638436927881215 " "
y[1] (numeric) = 3.1638436927881224 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.807276546956788400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18100000000000008 " "
y[1] (analytic) = 3.1646641713227286 " "
y[1] (numeric) = 3.1646641713227295 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.806548725607415600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18200000000000008 " "
y[1] (analytic) = 3.165483666193246 " "
y[1] (numeric) = 3.1654836661932473 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.208733230180742300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18300000000000008 " "
y[1] (analytic) = 3.16630217758018 " "
y[1] (numeric) = 3.1663021775801807 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.805096828689005000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18400000000000008 " "
y[1] (analytic) = 3.1671197056650175 " "
y[1] (numeric) = 3.1671197056650184 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.804372749509414500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18500000000000008 " "
y[1] (analytic) = 3.1679362506302318 " "
y[1] (numeric) = 3.1679362506302327 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.803649914115002300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18600000000000008 " "
y[1] (analytic) = 3.1687518126592766 " "
y[1] (numeric) = 3.168751812659278 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.204392481063777000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18700000000000008 " "
y[1] (analytic) = 3.1695663919365917 " "
y[1] (numeric) = 3.1695663919365926 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.80220796749883500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18800000000000008 " "
y[1] (analytic) = 3.170379988647596 " "
y[1] (numeric) = 3.170379988647597 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.202233279041417400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18900000000000008 " "
y[1] (analytic) = 3.1711926029786937 " "
y[1] (numeric) = 3.171192602978695 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.20115646176391800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000009 " "
y[1] (analytic) = 3.1720042351172704 " "
y[1] (numeric) = 3.1720042351172717 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.2000814967415495000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1910000000000001 " "
y[1] (analytic) = 3.172814885251694 " "
y[1] (numeric) = 3.172814885251695 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.799338920870158600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1920000000000001 " "
y[1] (analytic) = 3.1736245535713135 " "
y[1] (numeric) = 3.173624553571315 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.197937112791029000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1930000000000001 " "
y[1] (analytic) = 3.174433240266462 " "
y[1] (numeric) = 3.174433240266463 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.797911792360048300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1940000000000001 " "
y[1] (analytic) = 3.175240945528451 " "
y[1] (numeric) = 3.1752409455284525 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.1958001058986100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1950000000000001 " "
y[1] (analytic) = 3.1760476695495776 " "
y[1] (numeric) = 3.1760476695495785 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.796489574811971700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1960000000000001 " "
y[1] (analytic) = 3.1768534125231156 " "
y[1] (numeric) = 3.1768534125231165 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.79578030323633200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1970000000000001 " "
y[1] (analytic) = 3.1776581746433226 " "
y[1] (numeric) = 3.177658174643324 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.1926083811696600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1980000000000001 " "
y[1] (analytic) = 3.178461956105437 " "
y[1] (numeric) = 3.1784619561054384 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.19154813852990900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1990000000000001 " "
y[1] (analytic) = 3.179264757105677 " "
y[1] (numeric) = 3.1792647571056785 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.190489724306732400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2000000000000001 " "
y[1] (analytic) = 3.1800665778412416 " "
y[1] (numeric) = 3.180066577841243 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.18943313587662400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2010000000000001 " "
y[1] (analytic) = 3.18086741851031 " "
y[1] (numeric) = 3.1808674185103114 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.18837837062107500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2020000000000001 " "
y[1] (analytic) = 3.1816672793120415 " "
y[1] (numeric) = 3.181667279312043 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.18732542592655500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2030000000000001 " "
y[1] (analytic) = 3.182466160446576 " "
y[1] (numeric) = 3.1824661604465767 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.790849532789667000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2040000000000001 " "
y[1] (analytic) = 3.1832640621150308 " "
y[1] (numeric) = 3.1832640621150317 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.790149991860869600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2050000000000001 " "
y[1] (analytic) = 3.184060984519505 " "
y[1] (numeric) = 3.184060984519506 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.78945165943219830000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2060000000000001 " "
y[1] (analytic) = 3.1848569278630765 " "
y[1] (numeric) = 3.184856927863078 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.18313180066173700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2070000000000001 " "
y[1] (analytic) = 3.1856518923498025 " "
y[1] (numeric) = 3.185651892349803 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.394029306580931200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2080000000000001 " "
y[1] (analytic) = 3.186445878184717 " "
y[1] (numeric) = 3.1864458781847174 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.393681947935846700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2090000000000001 " "
y[1] (analytic) = 3.1872388855738345 " "
y[1] (numeric) = 3.1872388855738354 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.786670380184623000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2100000000000001 " "
y[1] (analytic) = 3.1880309147241483 " "
y[1] (numeric) = 3.1880309147241492 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.785978064384538300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2110000000000001 " "
y[1] (analytic) = 3.188821965843629 " "
y[1] (numeric) = 3.18882196584363 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.785286946758566700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2120000000000001 " "
y[1] (analytic) = 3.1896120391412253 " "
y[1] (numeric) = 3.189612039141226 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.78459702559706700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2130000000000001 " "
y[1] (analytic) = 3.190401134826864 " "
y[1] (numeric) = 3.190401134826865 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.783908299193620400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2140000000000001 " "
y[1] (analytic) = 3.1911892531114487 " "
y[1] (numeric) = 3.19118925311145 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.17483114876753400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2150000000000001 " "
y[1] (analytic) = 3.1919763942068626 " "
y[1] (numeric) = 3.1919763942068635 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.782534423851271700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2160000000000001 " "
y[1] (analytic) = 3.1927625583259633 " "
y[1] (numeric) = 3.1927625583259642 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.781849271515564600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2170000000000001 " "
y[1] (analytic) = 3.193547745682587 " "
y[1] (numeric) = 3.193547745682588 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.781165307144285400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2180000000000001 " "
y[1] (analytic) = 3.1943319564915464 " "
y[1] (numeric) = 3.1943319564915473 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.780482529046995300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2190000000000001 " "
y[1] (analytic) = 3.195115190968631 " "
y[1] (numeric) = 3.1951151909686315 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.389900467768214000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2200000000000001 " "
y[1] (analytic) = 3.1958974493306056 " "
y[1] (numeric) = 3.195897449330606 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.389560262464238400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2210000000000001 " "
y[1] (analytic) = 3.1966787317952123 " "
y[1] (numeric) = 3.196678731795213 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.389220647771094700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22200000000000011 " "
y[1] (analytic) = 3.1974590385811683 " "
y[1] (numeric) = 3.197459038581169 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.777763245699757500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22300000000000011 " "
y[1] (analytic) = 3.1982383699081676 " "
y[1] (numeric) = 3.198238369908168 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.388543186863254200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22400000000000012 " "
y[1] (analytic) = 3.199016725996878 " "
y[1] (numeric) = 3.1990167259968785 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.388205338975448700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22500000000000012 " "
y[1] (analytic) = 3.1997941070689433 " "
y[1] (numeric) = 3.199794107068944 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.775736156704498600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22600000000000012 " "
y[1] (analytic) = 3.200570513346983 " "
y[1] (numeric) = 3.200570513346984 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.775062808321996400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22700000000000012 " "
y[1] (analytic) = 3.201345945054591 " "
y[1] (numeric) = 3.2013459450545914 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.387195315570588200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22800000000000012 " "
y[1] (analytic) = 3.2021204024163343 " "
y[1] (numeric) = 3.202120402416335 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.773719623502919300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22900000000000012 " "
y[1] (analytic) = 3.202893885657757 " "
y[1] (numeric) = 3.202893885657758 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.773049783751190000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000012 " "
y[1] (analytic) = 3.2036663950053748 " "
y[1] (numeric) = 3.2036663950053756 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.772381110233031000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23100000000000012 " "
y[1] (analytic) = 3.2044379306866793 " "
y[1] (numeric) = 3.2044379306866797 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.385856800649275500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23200000000000012 " "
y[1] (analytic) = 3.205208492930134 " "
y[1] (numeric) = 3.2052084929301343 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.38552362765046100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23300000000000012 " "
y[1] (analytic) = 3.2059780819651764 " "
y[1] (numeric) = 3.205978081965177 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.385191035298183000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23400000000000012 " "
y[1] (analytic) = 3.206746698022218 " "
y[1] (numeric) = 3.2067466980222186 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.384859022772074700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23500000000000013 " "
y[1] (analytic) = 3.2075143413326432 " "
y[1] (numeric) = 3.2075143413326432 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23600000000000013 " "
y[1] (analytic) = 3.2082810121288077 " "
y[1] (numeric) = 3.2082810121288077 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23700000000000013 " "
y[1] (analytic) = 3.2090467106440412 " "
y[1] (numeric) = 3.2090467106440412 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23800000000000013 " "
y[1] (analytic) = 3.209811437112645 " "
y[1] (numeric) = 3.209811437112645 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23900000000000013 " "
y[1] (analytic) = 3.210575191769893 " "
y[1] (numeric) = 3.210575191769893 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000013 " "
y[1] (analytic) = 3.2113379748520297 " "
y[1] (numeric) = 3.2113379748520297 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24100000000000013 " "
y[1] (analytic) = 3.212099786596273 " "
y[1] (numeric) = 3.212099786596273 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24200000000000013 " "
y[1] (analytic) = 3.21286062724081 " "
y[1] (numeric) = 3.21286062724081 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24300000000000013 " "
y[1] (analytic) = 3.2136204970248015 " "
y[1] (numeric) = 3.213620497024801 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.381896867602146500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24400000000000013 " "
y[1] (analytic) = 3.214379396188376 " "
y[1] (numeric) = 3.214379396188376 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24500000000000013 " "
y[1] (analytic) = 3.2151373249726354 " "
y[1] (numeric) = 3.2151373249726354 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24600000000000014 " "
y[1] (analytic) = 3.215894283619651 " "
y[1] (numeric) = 3.215894283619651 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24700000000000014 " "
y[1] (analytic) = 3.2166502723724637 " "
y[1] (numeric) = 3.2166502723724637 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24800000000000014 " "
y[1] (analytic) = 3.217405291475085 " "
y[1] (numeric) = 3.217405291475085 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24900000000000014 " "
y[1] (analytic) = 3.218159341172495 " "
y[1] (numeric) = 3.218159341172495 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (analytic) = 3.2189124217106446 " "
y[1] (numeric) = 3.218912421710645 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.379625015128736500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2510000000000001 " "
y[1] (analytic) = 3.219664533336454 " "
y[1] (numeric) = 3.219664533336454 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2520000000000001 " "
y[1] (analytic) = 3.2204156762978102 " "
y[1] (numeric) = 3.2204156762978102 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2530000000000001 " "
y[1] (analytic) = 3.2211658508435708 " "
y[1] (numeric) = 3.221165850843571 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.378659871654118200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2540000000000001 " "
y[1] (analytic) = 3.2219150572235615 " "
y[1] (numeric) = 3.221915057223562 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.378339285681696400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2550000000000001 " "
y[1] (analytic) = 3.2226632956885757 " "
y[1] (numeric) = 3.222663295688576 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.378019262652059300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2560000000000001 " "
y[1] (analytic) = 3.223410566490375 " "
y[1] (numeric) = 3.223410566490375 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2570000000000001 " "
y[1] (analytic) = 3.224156869881688 " "
y[1] (numeric) = 3.2241568698816883 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.377380902270920500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2580000000000001 " "
y[1] (analytic) = 3.2249022061162114 " "
y[1] (numeric) = 3.2249022061162123 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.754125126695761700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2590000000000001 " "
y[1] (analytic) = 3.22564657544861 " "
y[1] (numeric) = 3.2256465754486103 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.37674478422454100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (analytic) = 3.2263899781345136 " "
y[1] (numeric) = 3.2263899781345136 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2610000000000001 " "
y[1] (analytic) = 3.2271324144305193 " "
y[1] (numeric) = 3.2271324144305193 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2620000000000001 " "
y[1] (analytic) = 3.227873884594191 " "
y[1] (numeric) = 3.2278738845941914 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.375794797837628600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2630000000000001 " "
y[1] (analytic) = 3.2286143888840586 " "
y[1] (numeric) = 3.228614388884059 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.375479250105052200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2640000000000001 " "
y[1] (analytic) = 3.229353927559618 " "
y[1] (numeric) = 3.2293539275596186 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.375164258275200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2650000000000001 " "
y[1] (analytic) = 3.2300925008813306 " "
y[1] (numeric) = 3.230092500881331 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.374849821572889700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2660000000000001 " "
y[1] (analytic) = 3.230830109110622 " "
y[1] (numeric) = 3.230830109110623 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.74907187844866800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2670000000000001 " "
y[1] (analytic) = 3.2315667525098855 " "
y[1] (numeric) = 3.231566752509886 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.374222610457136500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2680000000000001 " "
y[1] (analytic) = 3.232302431342476 " "
y[1] (numeric) = 3.2323024313424766 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.373909834500289800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.26900000000000013 " "
y[1] (analytic) = 3.233037145872716 " "
y[1] (numeric) = 3.2330371458727165 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.373597610584169600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (analytic) = 3.2337708963658907 " "
y[1] (numeric) = 3.233770896365891 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.373285937940531800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27100000000000013 " "
y[1] (analytic) = 3.234503683088249 " "
y[1] (numeric) = 3.2345036830882496 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.372974815802509000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27200000000000013 " "
y[1] (analytic) = 3.2352355063070046 " "
y[1] (numeric) = 3.235235506307005 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.372664243404607400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27300000000000013 " "
y[1] (analytic) = 3.235966366290334 " "
y[1] (numeric) = 3.2359663662903344 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.37235421998270100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27400000000000013 " "
y[1] (analytic) = 3.2366962633073775 " "
y[1] (numeric) = 3.236696263307378 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.372044744774029400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27500000000000013 " "
y[1] (analytic) = 3.237425197628238 " "
y[1] (numeric) = 3.237425197628238 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27600000000000013 " "
y[1] (analytic) = 3.238153169523981 " "
y[1] (numeric) = 3.238153169523981 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27700000000000014 " "
y[1] (analytic) = 3.238880179266635 " "
y[1] (numeric) = 3.238880179266635 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27800000000000014 " "
y[1] (analytic) = 3.239606227129189 " "
y[1] (numeric) = 3.2396062271291894 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.370812310864079600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27900000000000014 " "
y[1] (analytic) = 3.240331313385597 " "
y[1] (numeric) = 3.240331313385597 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (analytic) = 3.241055438310771 " "
y[1] (numeric) = 3.241055438310771 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28100000000000014 " "
y[1] (analytic) = 3.241778602180587 " "
y[1] (numeric) = 3.241778602180587 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28200000000000014 " "
y[1] (analytic) = 3.242500805271881 " "
y[1] (numeric) = 3.2425008052718813 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.369588587697593800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28300000000000014 " "
y[1] (analytic) = 3.2432220478624494 " "
y[1] (numeric) = 3.24322204786245 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.369284012307310200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28400000000000014 " "
y[1] (analytic) = 3.2439423302310506 " "
y[1] (numeric) = 3.2439423302310506 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28500000000000014 " "
y[1] (analytic) = 3.2446616526574013 " "
y[1] (numeric) = 3.2446616526574013 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28600000000000014 " "
y[1] (analytic) = 3.245380015422179 " "
y[1] (numeric) = 3.245380015422179 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28700000000000014 " "
y[1] (analytic) = 3.2460974188070217 " "
y[1] (numeric) = 3.2460974188070213 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.368071109872206200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28800000000000014 " "
y[1] (analytic) = 3.246813863094525 " "
y[1] (numeric) = 3.2468138630945247 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.367769230314924700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28900000000000015 " "
y[1] (analytic) = 3.2475293485682455 " "
y[1] (numeric) = 3.247529348568245 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.367467887690839200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (analytic) = 3.248243875512697 " "
y[1] (numeric) = 3.2482438755126966 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.367167081258541300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29100000000000015 " "
y[1] (analytic) = 3.248957444213353 " "
y[1] (numeric) = 3.2489574442133526 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.366866810277925200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29200000000000015 " "
y[1] (analytic) = 3.249670054956645 " "
y[1] (numeric) = 3.249670054956644 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.73313414802037400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29300000000000015 " "
y[1] (analytic) = 3.2503817080299617 " "
y[1] (numeric) = 3.250381708029961 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.732535743435638400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29400000000000015 " "
y[1] (analytic) = 3.2510924037216498 " "
y[1] (numeric) = 3.2510924037216493 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.365969202664608000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29500000000000015 " "
y[1] (analytic) = 3.251802142321014 " "
y[1] (numeric) = 3.2518021423210137 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.365671066115629000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29600000000000015 " "
y[1] (analytic) = 3.2525109241183157 " "
y[1] (numeric) = 3.252510924118315 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.36537346133724500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29700000000000015 " "
y[1] (analytic) = 3.253218749404773 " "
y[1] (numeric) = 3.2532187494047724 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.365076387597101100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29800000000000015 " "
y[1] (analytic) = 3.2539256184725605 " "
y[1] (numeric) = 3.25392561847256 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.364779844164122300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29900000000000015 " "
y[1] (analytic) = 3.25463153161481 " "
y[1] (numeric) = 3.254631531614809 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.728967660617019000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (analytic) = 3.255336489125606 " "
y[1] (numeric) = 3.2553364891256056 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.364188345301737000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30100000000000016 " "
y[1] (analytic) = 3.256040491299993 " "
y[1] (numeric) = 3.2560404912999927 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.36389338841654700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30200000000000016 " "
y[1] (analytic) = 3.2567435384339687 " "
y[1] (numeric) = 3.2567435384339682 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.363598958926948400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30300000000000016 " "
y[1] (analytic) = 3.2574456308244857 " "
y[1] (numeric) = 3.257445630824485 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.726610112216424400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30400000000000016 " "
y[1] (analytic) = 3.258146768769451 " "
y[1] (numeric) = 3.2581467687694503 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.726023358473736400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30500000000000016 " "
y[1] (analytic) = 3.258846952567727 " "
y[1] (numeric) = 3.2588469525677266 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.362718827590702300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30600000000000016 " "
y[1] (analytic) = 3.25954618251913 " "
y[1] (numeric) = 3.25954618251913 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30700000000000016 " "
y[1] (analytic) = 3.26024445892443 " "
y[1] (numeric) = 3.2602444589244297 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.362134697091302600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30800000000000016 " "
y[1] (analytic) = 3.260941782085351 " "
y[1] (numeric) = 3.26094178208535 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.723686833599773000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30900000000000016 " "
y[1] (analytic) = 3.2616381523045685 " "
y[1] (numeric) = 3.261638152304568 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.361552658857278500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (analytic) = 3.262333569885713 " "
y[1] (numeric) = 3.262333569885713 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31100000000000017 " "
y[1] (analytic) = 3.2630280351333676 " "
y[1] (numeric) = 3.2630280351333676 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31200000000000017 " "
y[1] (analytic) = 3.2637215483530664 " "
y[1] (numeric) = 3.2637215483530664 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31300000000000017 " "
y[1] (analytic) = 3.264414109851296 " "
y[1] (numeric) = 3.264414109851296 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31400000000000017 " "
y[1] (analytic) = 3.265105719935495 " "
y[1] (numeric) = 3.265105719935495 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31500000000000017 " "
y[1] (analytic) = 3.265796378914054 " "
y[1] (numeric) = 3.2657963789140534 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.359819040517558600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31600000000000017 " "
y[1] (analytic) = 3.2664860870963124 " "
y[1] (numeric) = 3.266486087096312 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.359531919037892400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31700000000000017 " "
y[1] (analytic) = 3.267174844792563 " "
y[1] (numeric) = 3.267174844792563 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31800000000000017 " "
y[1] (analytic) = 3.2678626523140477 " "
y[1] (numeric) = 3.267862652314048 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.358959225338289300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3190000000000002 " "
y[1] (analytic) = 3.26854950997296 " "
y[1] (numeric) = 3.26854950997296 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (analytic) = 3.2692354180824412 " "
y[1] (numeric) = 3.2692354180824412 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3210000000000002 " "
y[1] (analytic) = 3.269920376956583 " "
y[1] (numeric) = 3.269920376956583 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3220000000000002 " "
y[1] (analytic) = 3.2706043869104273 " "
y[1] (numeric) = 3.2706043869104273 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3230000000000002 " "
y[1] (analytic) = 3.2712874482599643 " "
y[1] (numeric) = 3.271287448259964 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.357536495566229700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3240000000000002 " "
y[1] (analytic) = 3.271969561322131 " "
y[1] (numeric) = 3.271969561322131 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3250000000000002 " "
y[1] (analytic) = 3.272650726414816 " "
y[1] (numeric) = 3.272650726414816 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3260000000000002 " "
y[1] (analytic) = 3.273330943856853 " "
y[1] (numeric) = 3.273330943856853 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3270000000000002 " "
y[1] (analytic) = 3.274010213968026 " "
y[1] (numeric) = 3.2740102139680256 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.356407527244200600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3280000000000002 " "
y[1] (analytic) = 3.2746885370690633 " "
y[1] (numeric) = 3.2746885370690633 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3290000000000002 " "
y[1] (analytic) = 3.2753659134816426 " "
y[1] (numeric) = 3.2753659134816426 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (analytic) = 3.276042343528387 " "
y[1] (numeric) = 3.2760423435283874 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.355566147450238400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3310000000000002 " "
y[1] (analytic) = 3.276717827532867 " "
y[1] (numeric) = 3.2767178275328672 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.35528670219501300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3320000000000002 " "
y[1] (analytic) = 3.2773923658195985 " "
y[1] (numeric) = 3.2773923658195985 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3330000000000002 " "
y[1] (analytic) = 3.2780659587140426 " "
y[1] (numeric) = 3.2780659587140426 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3340000000000002 " "
y[1] (analytic) = 3.2787386065426065 " "
y[1] (numeric) = 3.278738606542607 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.354451400803645700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3350000000000002 " "
y[1] (analytic) = 3.2794103096326435 " "
y[1] (numeric) = 3.2794103096326435 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3360000000000002 " "
y[1] (analytic) = 3.2800810683124486 " "
y[1] (numeric) = 3.280081068312449 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.353897054985106500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3370000000000002 " "
y[1] (analytic) = 3.2807508829112644 " "
y[1] (numeric) = 3.280750882911265 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.35362063655375100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3380000000000002 " "
y[1] (analytic) = 3.281419753759276 " "
y[1] (numeric) = 3.2814197537592764 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.353344720197112700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3390000000000002 " "
y[1] (analytic) = 3.2820876811876127 " "
y[1] (numeric) = 3.2820876811876127 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (analytic) = 3.2827546655283464 " "
y[1] (numeric) = 3.2827546655283464 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3410000000000002 " "
y[1] (analytic) = 3.283420707114493 " "
y[1] (numeric) = 3.283420707114493 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3420000000000002 " "
y[1] (analytic) = 3.2840858062800113 " "
y[1] (numeric) = 3.2840858062800113 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3430000000000002 " "
y[1] (analytic) = 3.2847499633598023 " "
y[1] (numeric) = 3.284749963359802 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.351972645722557800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3440000000000002 " "
y[1] (analytic) = 3.2854131786897076 " "
y[1] (numeric) = 3.2854131786897076 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3450000000000002 " "
y[1] (analytic) = 3.286075452606513 " "
y[1] (numeric) = 3.286075452606513 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3460000000000002 " "
y[1] (analytic) = 3.2867367854479443 " "
y[1] (numeric) = 3.2867367854479443 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3470000000000002 " "
y[1] (analytic) = 3.287397177552669 " "
y[1] (numeric) = 3.2873971775526685 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.35088395427980700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3480000000000002 " "
y[1] (analytic) = 3.2880566292602937 " "
y[1] (numeric) = 3.2880566292602933 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.350613021375998400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3490000000000002 " "
y[1] (analytic) = 3.2887151409113677 " "
y[1] (numeric) = 3.2887151409113673 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.35034258311285900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3500000000000002 " "
y[1] (analytic) = 3.289372712847379 " "
y[1] (numeric) = 3.2893727128473786 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.35007263882129600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3510000000000002 " "
y[1] (analytic) = 3.2900293454107556 " "
y[1] (numeric) = 3.2900293454107556 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3520000000000002 " "
y[1] (analytic) = 3.290685038944866 " "
y[1] (numeric) = 3.2906850389448654 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.349534229482067200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3530000000000002 " "
y[1] (analytic) = 3.2913397937940148 " "
y[1] (numeric) = 3.2913397937940143 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.349265763101746300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3540000000000002 " "
y[1] (analytic) = 3.291993610303448 " "
y[1] (numeric) = 3.291993610303448 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3550000000000002 " "
y[1] (analytic) = 3.29264648881935 " "
y[1] (numeric) = 3.2926464888193494 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.34873030359630390000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3560000000000002 " "
y[1] (analytic) = 3.29329842968884 " "
y[1] (numeric) = 3.29329842968884 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3570000000000002 " "
y[1] (analytic) = 3.293949433259979 " "
y[1] (numeric) = 3.293949433259979 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3580000000000002 " "
y[1] (analytic) = 3.294599499881763 " "
y[1] (numeric) = 3.294599499881763 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3590000000000002 " "
y[1] (analytic) = 3.2952486299041244 " "
y[1] (numeric) = 3.295248629904125 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.347665259064180200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3600000000000002 " "
y[1] (analytic) = 3.295896823677935 " "
y[1] (numeric) = 3.295896823677935 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3610000000000002 " "
y[1] (analytic) = 3.2965440815549996 " "
y[1] (numeric) = 3.2965440815549996 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3620000000000002 " "
y[1] (analytic) = 3.2971904038880604 " "
y[1] (numeric) = 3.2971904038880604 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3630000000000002 " "
y[1] (analytic) = 3.2978357910307956 " "
y[1] (numeric) = 3.297835791030795 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.34660801201158300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3640000000000002 " "
y[1] (analytic) = 3.298480243337817 " "
y[1] (numeric) = 3.298480243337817 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3650000000000002 " "
y[1] (analytic) = 3.2991237611646733 " "
y[1] (numeric) = 3.2991237611646733 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3660000000000002 " "
y[1] (analytic) = 3.299766344867846 " "
y[1] (numeric) = 3.2997663448678463 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.345820168572718000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3670000000000002 " "
y[1] (analytic) = 3.300407994804752 " "
y[1] (numeric) = 3.300407994804752 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3680000000000002 " "
y[1] (analytic) = 3.301048711333741 " "
y[1] (numeric) = 3.301048711333741 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3690000000000002 " "
y[1] (analytic) = 3.3016884948140963 " "
y[1] (numeric) = 3.3016884948140963 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (analytic) = 3.3023273456060345 " "
y[1] (numeric) = 3.3023273456060345 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3710000000000002 " "
y[1] (analytic) = 3.3029652640707052 " "
y[1] (numeric) = 3.302965264070705 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.34451674282141700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3720000000000002 " "
y[1] (analytic) = 3.3036022505701887 " "
y[1] (numeric) = 3.3036022505701887 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3730000000000002 " "
y[1] (analytic) = 3.3042383054675 " "
y[1] (numeric) = 3.3042383054674995 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.343998733733070500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3740000000000002 " "
y[1] (analytic) = 3.304873429126583 " "
y[1] (numeric) = 3.3048734291265824 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.343740446869177700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3750000000000002 " "
y[1] (analytic) = 3.305507621912314 " "
y[1] (numeric) = 3.305507621912314 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3760000000000002 " "
y[1] (analytic) = 3.306140884190502 " "
y[1] (numeric) = 3.3061408841905013 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.343225305290631800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3770000000000002 " "
y[1] (analytic) = 3.306773216327882 " "
y[1] (numeric) = 3.306773216327882 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3780000000000002 " "
y[1] (analytic) = 3.3074046186921238 " "
y[1] (numeric) = 3.3074046186921238 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3790000000000002 " "
y[1] (analytic) = 3.308035091651824 " "
y[1] (numeric) = 3.308035091651824 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000002 " "
y[1] (analytic) = 3.3086646355765104 " "
y[1] (numeric) = 3.3086646355765104 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3810000000000002 " "
y[1] (analytic) = 3.3092932508366384 " "
y[1] (numeric) = 3.3092932508366384 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38200000000000023 " "
y[1] (analytic) = 3.3099209378035925 " "
y[1] (numeric) = 3.309920937803593 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.341691291710287000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38300000000000023 " "
y[1] (analytic) = 3.310547696849687 " "
y[1] (numeric) = 3.310547696849687 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38400000000000023 " "
y[1] (analytic) = 3.311173528348162 " "
y[1] (numeric) = 3.3111735283481614 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.341183740592431200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38500000000000023 " "
y[1] (analytic) = 3.311798432673185 " "
y[1] (numeric) = 3.311798432673185 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38600000000000023 " "
y[1] (analytic) = 3.3124224101998525 " "
y[1] (numeric) = 3.312422410199853 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.340678074398333800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38700000000000023 " "
y[1] (analytic) = 3.3130454613041875 " "
y[1] (numeric) = 3.313045461304188 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.340425946570760200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38800000000000023 " "
y[1] (analytic) = 3.3136675863631386 " "
y[1] (numeric) = 3.3136675863631386 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38900000000000023 " "
y[1] (analytic) = 3.31428878575458 " "
y[1] (numeric) = 3.3142887857545804 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.339923098309475400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39000000000000024 " "
y[1] (analytic) = 3.314909059857313 " "
y[1] (numeric) = 3.3149090598573134 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.33967237662072700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39100000000000024 " "
y[1] (analytic) = 3.3155284090510637 " "
y[1] (numeric) = 3.3155284090510637 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39200000000000024 " "
y[1] (analytic) = 3.3161468337164814 " "
y[1] (numeric) = 3.316146833716482 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.339172334996884800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39300000000000024 " "
y[1] (analytic) = 3.316764334235143 " "
y[1] (numeric) = 3.316764334235143 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39400000000000024 " "
y[1] (analytic) = 3.317380910989547 " "
y[1] (numeric) = 3.3173809109895473 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.3386741582159600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39500000000000024 " "
y[1] (analytic) = 3.317996564363117 " "
y[1] (numeric) = 3.3179965643631175 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.338425767584556500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39600000000000024 " "
y[1] (analytic) = 3.3186112947402004 " "
y[1] (numeric) = 3.3186112947402004 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39700000000000024 " "
y[1] (analytic) = 3.319225102506065 " "
y[1] (numeric) = 3.3192251025060653 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.337930378734387700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39800000000000024 " "
y[1] (analytic) = 3.319837988046904 " "
y[1] (numeric) = 3.3198379880469044 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.337683379276363400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39900000000000024 " "
y[1] (analytic) = 3.320449951749832 " "
y[1] (numeric) = 3.3204499517498323 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.337436842305163000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (analytic) = 3.3210609940028855 " "
y[1] (numeric) = 3.3210609940028855 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40100000000000025 " "
y[1] (analytic) = 3.321671115195021 " "
y[1] (numeric) = 3.3216711151950213 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.336945153355405000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40200000000000025 " "
y[1] (analytic) = 3.3222803157161183 " "
y[1] (numeric) = 3.3222803157161187 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.336700000145349000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40300000000000025 " "
y[1] (analytic) = 3.322888595956977 " "
y[1] (numeric) = 3.322888595956977 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40400000000000025 " "
y[1] (analytic) = 3.3234959563093156 " "
y[1] (numeric) = 3.323495956309316 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.336211073183359600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40500000000000025 " "
y[1] (analytic) = 3.324102397165775 " "
y[1] (numeric) = 3.3241023971657753 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.335967298205692800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40600000000000025 " "
y[1] (analytic) = 3.3247079189199136 " "
y[1] (numeric) = 3.324707918919914 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.335723981414681200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40700000000000025 " "
y[1] (analytic) = 3.32531252196621 " "
y[1] (numeric) = 3.3253125219662105 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.335481122199843600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40800000000000025 " "
y[1] (analytic) = 3.325916206700061 " "
y[1] (numeric) = 3.3259162067000614 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.335238719951647000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40900000000000025 " "
y[1] (analytic) = 3.3265189735177816 " "
y[1] (numeric) = 3.326518973517782 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.334996774061504600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (analytic) = 3.327120822816605 " "
y[1] (numeric) = 3.327120822816606 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.669510567843549300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41100000000000025 " "
y[1] (analytic) = 3.3277217549946823 " "
y[1] (numeric) = 3.327721754994683 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.669028497851511600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41200000000000025 " "
y[1] (analytic) = 3.3283217704510815 " "
y[1] (numeric) = 3.328321770451082 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.334273668467685400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41300000000000026 " "
y[1] (analytic) = 3.3289208695857857 " "
y[1] (numeric) = 3.3289208695857866 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.668067083885476400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41400000000000026 " "
y[1] (analytic) = 3.329519052799697 " "
y[1] (numeric) = 3.329519052799698 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.66758773749404300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41500000000000026 " "
y[1] (analytic) = 3.330116320494632 " "
y[1] (numeric) = 3.3301163204946325 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.333554648277573400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41600000000000026 " "
y[1] (analytic) = 3.3307126730733225 " "
y[1] (numeric) = 3.330712673073323 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.333315879932362000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41700000000000026 " "
y[1] (analytic) = 3.3313081109394163 " "
y[1] (numeric) = 3.3313081109394167 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.333077563110279800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41800000000000026 " "
y[1] (analytic) = 3.331902634497475 " "
y[1] (numeric) = 3.331902634497476 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.665679394422287300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41900000000000026 " "
y[1] (analytic) = 3.332496244152976 " "
y[1] (numeric) = 3.3324962441529764 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.33260228163569080000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (analytic) = 3.3330889403123085 " "
y[1] (numeric) = 3.333088940312309 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.332365315785577800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42100000000000026 " "
y[1] (analytic) = 3.333680723382777 " "
y[1] (numeric) = 3.3336807233827774 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.332128799063376200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42200000000000026 " "
y[1] (analytic) = 3.334271593772598 " "
y[1] (numeric) = 3.3342715937725984 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.331892730872571200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42300000000000026 " "
y[1] (analytic) = 3.334861551890901 " "
y[1] (numeric) = 3.334861551890902 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.66331422123511800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42400000000000027 " "
y[1] (analytic) = 3.3354505981477285 " "
y[1] (numeric) = 3.3354505981477294 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.662843875407287500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42500000000000027 " "
y[1] (analytic) = 3.3360387329540337 " "
y[1] (numeric) = 3.3360387329540346 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.662374423074071500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42600000000000027 " "
y[1] (analytic) = 3.336625956721682 " "
y[1] (numeric) = 3.336625956721683 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.661905863049698000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42700000000000027 " "
y[1] (analytic) = 3.337212269863449 " "
y[1] (numeric) = 3.3372122698634503 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.992157291225293400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42800000000000027 " "
y[1] (analytic) = 3.3377976727930228 " "
y[1] (numeric) = 3.3377976727930236 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.660971415193390000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42900000000000027 " "
y[1] (analytic) = 3.3383821659249993 " "
y[1] (numeric) = 3.338382165925 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.660505524998899000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000027 " "
y[1] (analytic) = 3.3389657496748852 " "
y[1] (numeric) = 3.3389657496748866 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.99006078358219400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43100000000000027 " "
y[1] (analytic) = 3.339548424459098 " "
y[1] (numeric) = 3.3395484244590987 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.65957640618426500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4320000000000003 " "
y[1] (analytic) = 3.3401301906949614 " "
y[1] (numeric) = 3.3401301906949623 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.659113175212272600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4330000000000003 " "
y[1] (analytic) = 3.3407110488007095 " "
y[1] (numeric) = 3.340711048800711 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.987976242448331700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4340000000000003 " "
y[1] (analytic) = 3.341290999195485 " "
y[1] (numeric) = 3.3412909991954862 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.987284046408920400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4350000000000003 " "
y[1] (analytic) = 3.3418700422993366 " "
y[1] (numeric) = 3.341870042299338 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.98659317294557600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4360000000000003 " "
y[1] (analytic) = 3.342448178533222 " "
y[1] (numeric) = 3.342448178533223 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.65726908020422200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4370000000000003 " "
y[1] (analytic) = 3.343025408319004 " "
y[1] (numeric) = 3.343025408319005 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.98521538674185800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4380000000000003 " "
y[1] (analytic) = 3.343601732079453 " "
y[1] (numeric) = 3.3436017320794544 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.984528470505438500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4390000000000003 " "
y[1] (analytic) = 3.344177150238246 " "
y[1] (numeric) = 3.344177150238247 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.655895246568650300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (analytic) = 3.344751663219964 " "
y[1] (numeric) = 3.3447516632199648 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.65543905536198600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4410000000000003 " "
y[1] (analytic) = 3.345325271450094 " "
y[1] (numeric) = 3.3453252714500947 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.654983738891039700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4420000000000003 " "
y[1] (analytic) = 3.3458979753550273 " "
y[1] (numeric) = 3.3458979753550286 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.98179394399742100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4430000000000003 " "
y[1] (analytic) = 3.3464697753620616 " "
y[1] (numeric) = 3.3464697753620625 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.654075725527900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4440000000000003 " "
y[1] (analytic) = 3.347040671899395 " "
y[1] (numeric) = 3.3470406718993964 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.98043453948871800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4450000000000003 " "
y[1] (analytic) = 3.3476106653961324 " "
y[1] (numeric) = 3.3476106653961337 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.979756795859464000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4460000000000003 " "
y[1] (analytic) = 3.348179756282279 " "
y[1] (numeric) = 3.348179756282281 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.305440474237456000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4470000000000003 " "
y[1] (analytic) = 3.3487479449887454 " "
y[1] (numeric) = 3.3487479449887467 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.97840521722116500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4480000000000003 " "
y[1] (analytic) = 3.349315231947341 " "
y[1] (numeric) = 3.349315231947343 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.303641838357062000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4490000000000003 " "
y[1] (analytic) = 3.3498816175907806 " "
y[1] (numeric) = 3.349881617590782 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.97705883859964200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (analytic) = 3.350447102352677 " "
y[1] (numeric) = 3.3504471023526787 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.301850126667860000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4510000000000003 " "
y[1] (analytic) = 3.3510116866675466 " "
y[1] (numeric) = 3.351011686667548 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.975717646258277000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4520000000000003 " "
y[1] (analytic) = 3.3515753709708043 " "
y[1] (numeric) = 3.3515753709708056 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.97504899066103500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4530000000000003 " "
y[1] (analytic) = 3.352138155698766 " "
y[1] (numeric) = 3.3521381556987673 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.97438162650092700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4540000000000003 " "
y[1] (analytic) = 3.3527000412886467 " "
y[1] (numeric) = 3.352700041288648 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.97371555207222300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4550000000000003 " "
y[1] (analytic) = 3.3532610281785615 " "
y[1] (numeric) = 3.3532610281785624 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.648700510447794500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4560000000000003 " "
y[1] (analytic) = 3.3538211168075227 " "
y[1] (numeric) = 3.3538211168075236 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.648258177065733000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4570000000000003 " "
y[1] (analytic) = 3.354380307615442 " "
y[1] (numeric) = 3.354380307615443 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.64781670010313330000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4580000000000003 " "
y[1] (analytic) = 3.354938601043128 " "
y[1] (numeric) = 3.3549386010431292 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.97106411764422460000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4590000000000003 " "
y[1] (analytic) = 3.355495997532288 " "
y[1] (numeric) = 3.355495997532289 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.646936310915920500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (analytic) = 3.3560524975255253 " "
y[1] (numeric) = 3.356052497525526 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.646497396435229500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4610000000000003 " "
y[1] (analytic) = 3.35660810146634 " "
y[1] (numeric) = 3.3566081014663407 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.646059333861832000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4620000000000003 " "
y[1] (analytic) = 3.3571628097991275 " "
y[1] (numeric) = 3.3571628097991284 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.645622122071787400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4630000000000003 " "
y[1] (analytic) = 3.3577166229691793 " "
y[1] (numeric) = 3.3577166229691806 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.967778639914178500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4640000000000003 " "
y[1] (analytic) = 3.358269541422684 " "
y[1] (numeric) = 3.3582695414226844 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.322375123177070600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4650000000000003 " "
y[1] (analytic) = 3.358821565606721 " "
y[1] (numeric) = 3.3588215656067213 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.322157790093397000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4660000000000003 " "
y[1] (analytic) = 3.3593726959692667 " "
y[1] (numeric) = 3.359372695969267 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.321940880161649700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4670000000000003 " "
y[1] (analytic) = 3.359922932959191 " "
y[1] (numeric) = 3.3599229329591918 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.64344878564782500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4680000000000003 " "
y[1] (analytic) = 3.360472277026257 " "
y[1] (numeric) = 3.3604722770262576 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.321508327523074300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4690000000000003 " "
y[1] (analytic) = 3.3610207286211202 " "
y[1] (numeric) = 3.3610207286211207 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.321292683702825800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (analytic) = 3.361568288195329 " "
y[1] (numeric) = 3.3615682881953295 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.321077460807656700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4710000000000003 " "
y[1] (analytic) = 3.3621149562013244 " "
y[1] (numeric) = 3.3621149562013244 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4720000000000003 " "
y[1] (analytic) = 3.3626607330924374 " "
y[1] (numeric) = 3.3626607330924374 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4730000000000003 " "
y[1] (analytic) = 3.3632056193228914 " "
y[1] (numeric) = 3.3632056193228914 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4740000000000003 " "
y[1] (analytic) = 3.3637496153478006 " "
y[1] (numeric) = 3.3637496153478006 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4750000000000003 " "
y[1] (analytic) = 3.364292721623168 " "
y[1] (numeric) = 3.3642927216231686 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.320007640820871000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4760000000000003 " "
y[1] (analytic) = 3.3648349386058887 " "
y[1] (numeric) = 3.364834938605889 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.319794931854983400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4770000000000003 " "
y[1] (analytic) = 3.365376266753745 " "
y[1] (numeric) = 3.365376266753745 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4780000000000003 " "
y[1] (analytic) = 3.3659167065254074 " "
y[1] (numeric) = 3.365916706525408 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.319370764550172600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4790000000000003 " "
y[1] (analytic) = 3.3664562583804383 " "
y[1] (numeric) = 3.3664562583804383 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000003 " "
y[1] (analytic) = 3.3669949227792846 " "
y[1] (numeric) = 3.3669949227792846 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4810000000000003 " "
y[1] (analytic) = 3.3675327001832818 " "
y[1] (numeric) = 3.3675327001832818 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4820000000000003 " "
y[1] (analytic) = 3.3680695910546525 " "
y[1] (numeric) = 3.3680695910546525 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4830000000000003 " "
y[1] (analytic) = 3.368605595856506 " "
y[1] (numeric) = 3.3686055958565064 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.31831761603764700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4840000000000003 " "
y[1] (analytic) = 3.369140715052838 " "
y[1] (numeric) = 3.369140715052838 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4850000000000003 " "
y[1] (analytic) = 3.3696749491085285 " "
y[1] (numeric) = 3.3696749491085285 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4860000000000003 " "
y[1] (analytic) = 3.3702082984893433 " "
y[1] (numeric) = 3.3702082984893433 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4870000000000003 " "
y[1] (analytic) = 3.3707407636619333 " "
y[1] (numeric) = 3.3707407636619338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.317482538667878200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4880000000000003 " "
y[1] (analytic) = 3.3712723450938338 " "
y[1] (numeric) = 3.3712723450938338 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4890000000000003 " "
y[1] (analytic) = 3.3718030432534625 " "
y[1] (numeric) = 3.3718030432534625 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000003 " "
y[1] (analytic) = 3.3723328586101218 " "
y[1] (numeric) = 3.3723328586101213 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.31686054867398300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4910000000000003 " "
y[1] (analytic) = 3.372861791633996 " "
y[1] (numeric) = 3.372861791633995 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.633308076551348400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4920000000000003 " "
y[1] (analytic) = 3.3733898427961515 " "
y[1] (numeric) = 3.373389842796151 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.316447936779117600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4930000000000003 " "
y[1] (analytic) = 3.373917012568538 " "
y[1] (numeric) = 3.3739170125685374 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.316242243646594000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4940000000000003 " "
y[1] (analytic) = 3.374443301423985 " "
y[1] (numeric) = 3.3744433014239847 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.316036958341131000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.49500000000000033 " "
y[1] (analytic) = 3.374968709836204 " "
y[1] (numeric) = 3.374968709836204 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.49600000000000033 " "
y[1] (analytic) = 3.375493238279787 " "
y[1] (numeric) = 3.3754932382797866 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.315627609067226400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.49700000000000033 " "
y[1] (analytic) = 3.3760168872302048 " "
y[1] (numeric) = 3.3760168872302043 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.315423544028560800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.49800000000000033 " "
y[1] (analytic) = 3.3765396571638084 " "
y[1] (numeric) = 3.376539657163808 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.315219884676504000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.49900000000000033 " "
y[1] (analytic) = 3.377061548557829 " "
y[1] (numeric) = 3.377061548557828 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.630033260955581500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000003 " "
y[1] (analytic) = 3.377582561890373 " "
y[1] (numeric) = 3.3775825618903723 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.629627561799784400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5010000000000003 " "
y[1] (analytic) = 3.3781026976404287 " "
y[1] (numeric) = 3.378102697640428 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.62922267082202400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5020000000000003 " "
y[1] (analytic) = 3.3786219562878594 " "
y[1] (numeric) = 3.378621956287859 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.314409293480084400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5030000000000003 " "
y[1] (analytic) = 3.379140338313407 " "
y[1] (numeric) = 3.379140338313407 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5040000000000003 " "
y[1] (analytic) = 3.3796578441986904 " "
y[1] (numeric) = 3.3796578441986895 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.62801283634293600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5050000000000003 " "
y[1] (analytic) = 3.3801744744262017 " "
y[1] (numeric) = 3.380174474426201 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.6276111674705700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5060000000000003 " "
y[1] (analytic) = 3.3806902294793115 " "
y[1] (numeric) = 3.3806902294793106 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.62721030148012400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5070000000000003 " "
y[1] (analytic) = 3.3812051098422646 " "
y[1] (numeric) = 3.3812051098422637 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.62681023731671600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5080000000000003 " "
y[1] (analytic) = 3.381719116000181 " "
y[1] (numeric) = 3.38171911600018 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.626410973926900400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5090000000000003 " "
y[1] (analytic) = 3.382232248439054 " "
y[1] (numeric) = 3.382232248439053 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.626012510258666000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000003 " "
y[1] (analytic) = 3.3827445076457514 " "
y[1] (numeric) = 3.3827445076457505 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.6256148452614303000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5110000000000003 " "
y[1] (analytic) = 3.3832558941080135 " "
y[1] (numeric) = 3.383255894108013 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.312608988943018100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5120000000000003 " "
y[1] (analytic) = 3.383766408314455 " "
y[1] (numeric) = 3.3837664083144543 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.62482190708474670000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5130000000000003 " "
y[1] (analytic) = 3.3842760507545604 " "
y[1] (numeric) = 3.3842760507545595 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.624426631811244700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5140000000000003 " "
y[1] (analytic) = 3.3847848219186876 " "
y[1] (numeric) = 3.3847848219186867 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.624032151020624000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5150000000000003 " "
y[1] (analytic) = 3.3852927222980655 " "
y[1] (numeric) = 3.3852927222980647 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.623638463669386600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5160000000000003 " "
y[1] (analytic) = 3.385799752384794 " "
y[1] (numeric) = 3.3857997523847927 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.934868353073163000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5170000000000003 " "
y[1] (analytic) = 3.386305912671842 " "
y[1] (numeric) = 3.386305912671841 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.934280197677150000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5180000000000003 " "
y[1] (analytic) = 3.3868112036530498 " "
y[1] (numeric) = 3.386811203653049 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.622462151838067500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5190000000000003 " "
y[1] (analytic) = 3.3873156258231267 " "
y[1] (numeric) = 3.387315625823126 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.622071627837443000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000004 " "
y[1] (analytic) = 3.38781917967765 " "
y[1] (numeric) = 3.387819179677649 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.62168189207971600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5210000000000004 " "
y[1] (analytic) = 3.388321865713066 " "
y[1] (numeric) = 3.388321865713065 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.621292943529760500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5220000000000004 " "
y[1] (analytic) = 3.388823684426688 " "
y[1] (numeric) = 3.3888236844266877 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.310452390576916000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5230000000000004 " "
y[1] (analytic) = 3.389324636316699 " "
y[1] (numeric) = 3.389324636316698 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.93077610587934400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5240000000000004 " "
y[1] (analytic) = 3.389824721882145 " "
y[1] (numeric) = 3.389824721882144 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.93019621619393900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5250000000000004 " "
y[1] (analytic) = 3.3903239416229414 " "
y[1] (numeric) = 3.39032394162294 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.92961750113009600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5260000000000004 " "
y[1] (analytic) = 3.390822296039868 " "
y[1] (numeric) = 3.390822296039867 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.929039959145424500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = 1.0 - sin(x);"
Iterations = 427
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Expected Time Remaining "= 0 Years 0 Days 0 Hours 31 Minutes 30 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 31 Minutes 24 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 34 Minutes 25 Seconds
"Time to Timeout " Unknown
Percent Done = 8.734693877551027 "%"
(%o58) true
(%o58) diffeq.max