(%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_2D0 array_x ,
1 1 1
array_tmp2 : array_const_3D0 + array_tmp1 , array_tmp3 : sinh(array_tmp2 ),
1 1 1 1 1
array_tmp3_g : cosh(array_tmp2 ), array_tmp4 :
1 1 1
array_tmp3 + array_const_0D0 , if not array_y_set_initial
1 1 1, 2
then (if 1 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(0, 1), array_y : temporary,
1 2
temporary 1.0
array_y_higher : temporary, temporary : -------------,
1, 2 glob_h
array_y_higher : temporary, 0)), kkk : 2,
2, 1
array_tmp1 : array_const_2D0 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp3_g array_tmp2
1 2
array_tmp3 : -------------------------,
2 1
array_tmp3 array_tmp2
1 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
2 1 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp4 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_tmp3_g array_tmp2
2 2
array_tmp3 : -------------------------,
3 2
array_tmp3 array_tmp2
2 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
3 2 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp4 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_tmp3_g array_tmp2
3 2
array_tmp3 : -------------------------,
4 3
array_tmp3 array_tmp2
3 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
4 3 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp4 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_tmp3_g array_tmp2
4 2
array_tmp3 : -------------------------,
5 4
array_tmp3 array_tmp2
4 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
5 4 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp4 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
while kkk <= glob_max_terms do (array_tmp3 :
kkk
array_tmp3_g array_tmp2
kkk - 1 2
-------------------------------, array_tmp3_g :
kkk - 1 kkk
- array_tmp3 array_tmp2
kkk - 1 2
-------------------------------, array_tmp4 : array_tmp3 , order_d : 1,
kkk - 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_tmp4 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_2D0 array_x ,
1 1 1
array_tmp2 : array_const_3D0 + array_tmp1 , array_tmp3 : sinh(array_tmp2 ),
1 1 1 1 1
array_tmp3_g : cosh(array_tmp2 ), array_tmp4 :
1 1 1
array_tmp3 + array_const_0D0 , if not array_y_set_initial
1 1 1, 2
then (if 1 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(0, 1), array_y : temporary,
1 2
temporary 1.0
array_y_higher : temporary, temporary : -------------,
1, 2 glob_h
array_y_higher : temporary, 0)), kkk : 2,
2, 1
array_tmp1 : array_const_2D0 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp3_g array_tmp2
1 2
array_tmp3 : -------------------------,
2 1
array_tmp3 array_tmp2
1 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
2 1 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp4 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_tmp3_g array_tmp2
2 2
array_tmp3 : -------------------------,
3 2
array_tmp3 array_tmp2
2 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
3 2 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp4 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_tmp3_g array_tmp2
3 2
array_tmp3 : -------------------------,
4 3
array_tmp3 array_tmp2
3 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
4 3 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp4 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_tmp3_g array_tmp2
4 2
array_tmp3 : -------------------------,
5 4
array_tmp3 array_tmp2
4 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
5 4 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp4 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
while kkk <= glob_max_terms do (array_tmp3 :
kkk
array_tmp3_g array_tmp2
kkk - 1 2
-------------------------------, array_tmp3_g :
kkk - 1 kkk
- array_tmp3 array_tmp2
kkk - 1 2
-------------------------------, array_tmp4 : array_tmp3 , order_d : 1,
kkk - 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_tmp4 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)
cosh(3.0 + 2.0 x)
(%i56) exact_soln_y(x) := block(-----------------)
2.0
cosh(3.0 + 2.0 x)
(%o56) exact_soln_y(x) := block(-----------------)
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/lin_sinhpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.0,"), omniout_str(ALWAYS, "x_end:10.0,"),
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:10,"),
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, " (cosh(2.0*x+3.0)/2.0) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32,
max_terms : 30, glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3_g, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3_g : 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_tmp4 : 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, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_g : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 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_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term),
term
array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.0,
iiif, jjjf
x_end : 10.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 10, 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 ) = sinh (2.0 * x + 3.0) ;"),
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,
"2013-01-28T15:55:24-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_sinh"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"),
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, "lin_sinh diffeq.max"),
logitem_str(html_log_file,
"lin_sinh 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/lin_sinhpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.0,"), omniout_str(ALWAYS, "x_end:10.0,"),
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:10,"),
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, " (cosh(2.0*x+3.0)/2.0) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32,
max_terms : 30, glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3_g, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3_g : 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_tmp4 : 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, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_g : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 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_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term),
term
array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.0,
iiif, jjjf
x_end : 10.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 10, 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 ) = sinh (2.0 * x + 3.0) ;"),
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,
"2013-01-28T15:55:24-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_sinh"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"),
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, "lin_sinh diffeq.max"),
logitem_str(html_log_file,
"lin_sinh 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/lin_sinhpostode.ode#################"
"diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.0,"
"x_end:10.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_iter:10,"
"/* 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("
" (cosh(2.0*x+3.0)/2.0) "
"));"
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 10. ""
estimated_steps = 10000. ""
step_error = 1.00000000000000E-14 ""
est_needed_step_err = 1.00000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 8.3761314624468130000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 ""
max_value3 = 8.3761314624468130000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 ""
value3 = 8.3761314624468130000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 ""
best_h = 1.000E-3 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.0 " "
y[1] (analytic) = 5.033830997888883 " "
y[1] (numeric) = 5.033830997888883 " "
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] = 1.000E-3 " "
y[1] (analytic) = 5.043858947160228 " "
y[1] (numeric) = 5.043858947160229 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.760910503257002400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.000E-3 " "
y[1] (analytic) = 5.0539070718740895 " "
y[1] (numeric) = 5.053907071874089 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.75740947957472220000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.000E-3 " "
y[1] (analytic) = 5.063975412222974 " "
y[1] (numeric) = 5.063975412222975 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.753915347922738700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.000E-3 " "
y[1] (analytic) = 5.074064008480262 " "
y[1] (numeric) = 5.074064008480262 " "
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] = 5.000E-3 " "
y[1] (analytic) = 5.084172901000347 " "
y[1] (numeric) = 5.084172901000348 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.746947708102865300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.000E-3 " "
y[1] (analytic) = 5.094302130218817 " "
y[1] (numeric) = 5.094302130218817 " "
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] = 7.000E-3 " "
y[1] (analytic) = 5.1044517366525985 " "
y[1] (numeric) = 5.104451736652600 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.740007478810203200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.000E-3 " "
y[1] (analytic) = 5.1146217609001345 " "
y[1] (numeric) = 5.1146217609001345 " "
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] = 9.000000000000001000E-3 " "
y[1] (analytic) = 5.124812243641531 " "
y[1] (numeric) = 5.124812243641532 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.733094555419289500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.000000000000000200E-2 " "
y[1] (analytic) = 5.135023225638738 " "
y[1] (numeric) = 5.135023225638738 " "
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] = 1.100000000000000300E-2 " "
y[1] (analytic) = 5.1452547477356925 " "
y[1] (numeric) = 5.145254747735693 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.726208833665606200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.200000000000000400E-2 " "
y[1] (analytic) = 5.1555068508585 " "
y[1] (numeric) = 5.1555068508585 " "
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] = 1.300000000000000600E-2 " "
y[1] (analytic) = 5.1657795760155825 " "
y[1] (numeric) = 5.165779576015583 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.719350209644806600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.400000000000000700E-2 " "
y[1] (analytic) = 5.176072964297859 " "
y[1] (numeric) = 5.176072964297859 " "
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] = 1.500000000000000800E-2 " "
y[1] (analytic) = 5.186387056878892 " "
y[1] (numeric) = 5.186387056878893 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.712518579811937200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.600000000000001000E-2 " "
y[1] (analytic) = 5.196721895015070 " "
y[1] (numeric) = 5.196721895015070 " "
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] = 1.700000000000001000E-2 " "
y[1] (analytic) = 5.207077520045754 " "
y[1] (numeric) = 5.207077520045755 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.705713840980652200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.80000000000000100E-2 " "
y[1] (analytic) = 5.217453973393464 " "
y[1] (numeric) = 5.2174539733934635 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.702321523542733900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.90000000000000100E-2 " "
y[1] (analytic) = 5.227851296564022 " "
y[1] (numeric) = 5.2278512965640225 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.698935890322427500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.00000000000000120E-2 " "
y[1] (analytic) = 5.238269531146739 " "
y[1] (numeric) = 5.238269531146738 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.695556928521945000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.10000000000000130E-2 " "
y[1] (analytic) = 5.248708718814562 " "
y[1] (numeric) = 5.248708718814562 " "
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] = 2.200000000000001400E-2 " "
y[1] (analytic) = 5.259168901324261 " "
y[1] (numeric) = 5.25916890132426 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.68881896810060900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.300000000000001500E-2 " "
y[1] (analytic) = 5.269650120516576 " "
y[1] (numeric) = 5.269650120516576 " "
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] = 2.400000000000001600E-2 " "
y[1] (analytic) = 5.280152418316401 " "
y[1] (numeric) = 5.2801524183163995 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.36421508068255600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.500000000000001700E-2 " "
y[1] (analytic) = 5.290675836732937 " "
y[1] (numeric) = 5.2906758367329365 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.678761744451512700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.600000000000002000E-2 " "
y[1] (analytic) = 5.301220417859877 " "
y[1] (numeric) = 5.301220417859875 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.350845087323066600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.700000000000002000E-2 " "
y[1] (analytic) = 5.311786203875554 " "
y[1] (numeric) = 5.3117862038755534 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.672089925328880400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.800000000000002000E-2 " "
y[1] (analytic) = 5.322373237043132 " "
y[1] (numeric) = 5.32237323704313 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.33752775366635800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.90000000000000200E-2 " "
y[1] (analytic) = 5.332981559710750 " "
y[1] (numeric) = 5.332981559710750 " "
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] = 3.00000000000000200E-2 " "
y[1] (analytic) = 5.343611214311723 " "
y[1] (numeric) = 5.343611214311721 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.324262877962861000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.10000000000000200E-2 " "
y[1] (analytic) = 5.354262243364674 " "
y[1] (numeric) = 5.354262243364674 " "
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] = 3.20000000000000230E-2 " "
y[1] (analytic) = 5.36493468947374 " "
y[1] (numeric) = 5.364934689473738 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.31105025916820200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.30000000000000240E-2 " "
y[1] (analytic) = 5.375628595328715 " "
y[1] (numeric) = 5.375628595328714 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.652231741738872700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.40000000000000250E-2 " "
y[1] (analytic) = 5.386344003705240 " "
y[1] (numeric) = 5.386344003705239 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.29788969694156700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.500000000000002600E-2 " "
y[1] (analytic) = 5.397080957464961 " "
y[1] (numeric) = 5.3970809574649605 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.64566443731336500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.600000000000002600E-2 " "
y[1] (analytic) = 5.40783949955571 " "
y[1] (numeric) = 5.407839499555708 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.28478099164405700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.700000000000003000E-2 " "
y[1] (analytic) = 5.418619673011665 " "
y[1] (numeric) = 5.418619673011664 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.63912301157404600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.80000000000000300E-2 " "
y[1] (analytic) = 5.429421520953539 " "
y[1] (numeric) = 5.429421520953537 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.27172394433703700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.90000000000000300E-2 " "
y[1] (analytic) = 5.4402450865887335 " "
y[1] (numeric) = 5.440245086588733 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.632607365226354500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.00000000000000300E-2 " "
y[1] (analytic) = 5.4510904132115305 " "
y[1] (numeric) = 5.451090413211529 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.2587183567804800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.10000000000000300E-2 " "
y[1] (analytic) = 5.461957544203247 " "
y[1] (numeric) = 5.461957544203246 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.626117399324616000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.20000000000000300E-2 " "
y[1] (analytic) = 5.472846523032424 " "
y[1] (numeric) = 5.472846523032422 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.245764031431302000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.30000000000000300E-2 " "
y[1] (analytic) = 5.483757393254990 " "
y[1] (numeric) = 5.483757393254988 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.619653015271213200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.40000000000000340E-2 " "
y[1] (analytic) = 5.494690198514440 " "
y[1] (numeric) = 5.494690198514439 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.23286077144169350000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.50000000000000340E-2 " "
y[1] (analytic) = 5.50564498254201 " "
y[1] (numeric) = 5.50564498254201 " "
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] = 4.600000000000003500E-2 " "
y[1] (analytic) = 5.5166217891568525 " "
y[1] (numeric) = 5.516621789156852 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.6100041903287200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.700000000000003600E-2 " "
y[1] (analytic) = 5.527620662266205 " "
y[1] (numeric) = 5.527620662266205 " "
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] = 4.800000000000003700E-2 " "
y[1] (analytic) = 5.53864164586558 " "
y[1] (numeric) = 5.538641645865578 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.207206663616239400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.90000000000000400E-2 " "
y[1] (analytic) = 5.54968478403892 " "
y[1] (numeric) = 5.549684784038920 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.60041237342804820000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.00000000000000300E-2 " "
y[1] (analytic) = 5.560750120958798 " "
y[1] (numeric) = 5.560750120958796 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.19445542554601700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.10000000000000300E-2 " "
y[1] (analytic) = 5.571837700886572 " "
y[1] (numeric) = 5.571837700886571 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.59404933772353300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.20000000000000400E-2 " "
y[1] (analytic) = 5.582947568172582 " "
y[1] (numeric) = 5.582947568172579 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.77263170854483830000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.30000000000000400E-2 " "
y[1] (analytic) = 5.5940797672563045 " "
y[1] (numeric) = 5.594079767256304 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.5877113960706800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.40000000000000400E-2 " "
y[1] (analytic) = 5.6052343426665585 " "
y[1] (numeric) = 5.605234342666556 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.753655416006720700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.50000000000000400E-2 " "
y[1] (analytic) = 5.616411339021654 " "
y[1] (numeric) = 5.616411339021653 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.58139845194251900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.60000000000000400E-2 " "
y[1] (analytic) = 5.627610801029596 " "
y[1] (numeric) = 5.627610801029594 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.15650264775818900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.700000000000004000E-2 " "
y[1] (analytic) = 5.638832773488244 " "
y[1] (numeric) = 5.638832773488243 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.57511040915421290000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.800000000000004000E-2 " "
y[1] (analytic) = 5.650077301285507 " "
y[1] (numeric) = 5.650077301285505 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.715927087394255500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.900000000000004000E-2 " "
y[1] (analytic) = 5.661344429399506 " "
y[1] (numeric) = 5.661344429399504 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.13769434372440650000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.000000000000004000E-2 " "
y[1] (analytic) = 5.672634202898773 " "
y[1] (numeric) = 5.67263420289877 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.69717447625791100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.10000000000000400E-2 " "
y[1] (analytic) = 5.683946666942412 " "
y[1] (numeric) = 5.683946666942411 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.562608644563350000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.20000000000000400E-2 " "
y[1] (analytic) = 5.695281866780301 " "
y[1] (numeric) = 5.695281866780299 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.678495852228487500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.30000000000000400E-2 " "
y[1] (analytic) = 5.706639847753248 " "
y[1] (numeric) = 5.706639847753247 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.556394732094068500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.40000000000000500E-2 " "
y[1] (analytic) = 5.718020655293198 " "
y[1] (numeric) = 5.718020655293195 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.65989093032359600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.50000000000000500E-2 " "
y[1] (analytic) = 5.72942433492339 " "
y[1] (numeric) = 5.729424334923388 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.10041067925893600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.60000000000000500E-2 " "
y[1] (analytic) = 5.740850932258564 " "
y[1] (numeric) = 5.740850932258561 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.64135942657562640000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.70000000000000500E-2 " "
y[1] (analytic) = 5.752300493005118 " "
y[1] (numeric) = 5.752300493005117 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.54404037268248280000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.80000000000000500E-2 " "
y[1] (analytic) = 5.763773062961317 " "
y[1] (numeric) = 5.763773062961314 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.62290105802914500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.90000000000000500E-2 " "
y[1] (analytic) = 5.77526868801745 " "
y[1] (numeric) = 5.775268688017448 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.0757994742060096000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.00000000000000500E-2 " "
y[1] (analytic) = 5.786787414156038 " "
y[1] (numeric) = 5.786787414156035 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.60451554273828400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.10000000000000500E-2 " "
y[1] (analytic) = 5.798329287451995 " "
y[1] (numeric) = 5.7983292874519945 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.531783339077012500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.20000000000000500E-2 " "
y[1] (analytic) = 5.809894354072838 " "
y[1] (numeric) = 5.809894354072835 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.586202599764124000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.30000000000000500E-2 " "
y[1] (analytic) = 5.821482660278840 " "
y[1] (numeric) = 5.821482660278837 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.051382170251394400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.40000000000000500E-2 " "
y[1] (analytic) = 5.833094252423246 " "
y[1] (numeric) = 5.833094252423243 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.56796194917208200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.50000000000000600E-2 " "
y[1] (analytic) = 5.844729176952438 " "
y[1] (numeric) = 5.844729176952437 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.519622882104590000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.60000000000000600E-2 " "
y[1] (analytic) = 5.856387480406133 " "
y[1] (numeric) = 5.856387480406130 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.549793312029268000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.70000000000000600E-2 " "
y[1] (analytic) = 5.868069209417556 " "
y[1] (numeric) = 5.868069209417555 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.027157274405366500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.80000000000000600E-2 " "
y[1] (analytic) = 5.879774410713643 " "
y[1] (numeric) = 5.87977441071364 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.53169641040186500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.90000000000000600E-2 " "
y[1] (analytic) = 5.89150313111521 " "
y[1] (numeric) = 5.891503131115209 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.01511651588310600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.00000000000000600E-2 " "
y[1] (analytic) = 5.90325541753716 " "
y[1] (numeric) = 5.9032554175371565 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 6.01822795646998000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.10000000000000600E-2 " "
y[1] (analytic) = 5.915031316988648 " "
y[1] (numeric) = 5.915031316988646 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.00312330434895600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.20000000000000600E-2 " "
y[1] (analytic) = 5.926830876573293 " "
y[1] (numeric) = 5.92683087657329 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.495716706937530000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.30000000000000600E-2 " "
y[1] (analytic) = 5.9386541434893445 " "
y[1] (numeric) = 5.938654143489343 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.991177456171114600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.40000000000000600E-2 " "
y[1] (analytic) = 5.950501165029891 " "
y[1] (numeric) = 5.950501165029888 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.97044447227270600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.50000000000000600E-2 " "
y[1] (analytic) = 5.962371988583029 " "
y[1] (numeric) = 5.962371988583026 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.4689181825664800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.60000000000000700E-2 " "
y[1] (analytic) = 5.974266661632073 " "
y[1] (numeric) = 5.974266661632070 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.94669418025267300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.70000000000000700E-2 " "
y[1] (analytic) = 5.986185231755727 " "
y[1] (numeric) = 5.986185231755725 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.451140677982123000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.80000000000000700E-2 " "
y[1] (analytic) = 5.998127746628293 " "
y[1] (numeric) = 5.998127746628288 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 7.40379712819049200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.90000000000000700E-2 " "
y[1] (analytic) = 6.010094254019840 " "
y[1] (numeric) = 6.010094254019837 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.43343339801735460000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.00000000000000700E-2 " "
y[1] (analytic) = 6.022084801796418 " "
y[1] (numeric) = 6.022084801796415 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.89947467651187600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.10000000000000700E-2 " "
y[1] (analytic) = 6.034099437920231 " "
y[1] (numeric) = 6.034099437920228 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.41579607116776200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.20000000000000700E-2 " "
y[1] (analytic) = 6.046138210449843 " "
y[1] (numeric) = 6.04613821044984 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.8760047407784500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.30000000000000700E-2 " "
y[1] (analytic) = 6.058201167540357 " "
y[1] (numeric) = 6.058201167540354 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.39822842690808600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.40000000000000700E-2 " "
y[1] (analytic) = 6.070288357443621 " "
y[1] (numeric) = 6.070288357443617 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 7.31578441912900800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.50000000000000700E-2 " "
y[1] (analytic) = 6.0823998285084055 " "
y[1] (numeric) = 6.082399828508403 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.38073019568955700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.60000000000000700E-2 " "
y[1] (analytic) = 6.0945356291806165 " "
y[1] (numeric) = 6.094535629180613 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.8293427013374400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.70000000000000800E-2 " "
y[1] (analytic) = 6.106695808003468 " "
y[1] (numeric) = 6.106695808003465 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.36330110893721200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.80000000000000800E-2 " "
y[1] (analytic) = 6.118880413617696 " "
y[1] (numeric) = 6.118880413617692 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 7.2576873517863290000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.90000000000000800E-2 " "
y[1] (analytic) = 6.131089494761735 " "
y[1] (numeric) = 6.131089494761732 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.34594089904721600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10000000000000007 " "
y[1] (analytic) = 6.14332310027193 " "
y[1] (numeric) = 6.1433231002719255 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 7.22881089927380300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10100000000000008 " "
y[1] (analytic) = 6.155581279082714 " "
y[1] (numeric) = 6.155581279082711 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.32864929938417900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10200000000000008 " "
y[1] (analytic) = 6.167864080226825 " "
y[1] (numeric) = 6.167864080226821 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.76003886043780800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10300000000000008 " "
y[1] (analytic) = 6.180171552835478 " "
y[1] (numeric) = 6.180171552835476 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.311426044278463500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10400000000000008 " "
y[1] (analytic) = 6.192503746138586 " "
y[1] (numeric) = 6.1925037461385815 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 7.17139993862708800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10500000000000008 " "
y[1] (analytic) = 6.204860709464931 " "
y[1] (numeric) = 6.204860709464929 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.294270869023502600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10600000000000008 " "
y[1] (analytic) = 6.2172424922423914 " "
y[1] (numeric) = 6.217242492242387 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 7.14286454813654300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10700000000000008 " "
y[1] (analytic) = 6.229649143998107 " "
y[1] (numeric) = 6.229649143998103 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.70291134649746200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10800000000000008 " "
y[1] (analytic) = 6.242080714358707 " "
y[1] (numeric) = 6.2420807143587025 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 7.11444196529725700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10900000000000008 " "
y[1] (analytic) = 6.254537253050485 " "
y[1] (numeric) = 6.254537253050482 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.26016370403872750000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000008 " "
y[1] (analytic) = 6.267018809899617 " "
y[1] (numeric) = 6.2670188098996125 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 7.08613175292473600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11100000000000008 " "
y[1] (analytic) = 6.279525434832342 " "
y[1] (numeric) = 6.279525434832339 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.657614919582462000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11200000000000009 " "
y[1] (analytic) = 6.292057177875182 " "
y[1] (numeric) = 6.2920571778751775 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 7.05793347542386500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11300000000000009 " "
y[1] (analytic) = 6.30461408915512 " "
y[1] (numeric) = 6.304614089155117 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.22632570593618900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11400000000000009 " "
y[1] (analytic) = 6.317196218899824 " "
y[1] (numeric) = 6.317196218899820 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 7.02984669878440700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11500000000000009 " "
y[1] (analytic) = 6.329803617437823 " "
y[1] (numeric) = 6.32980361743782 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.20950699285505770000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11600000000000009 " "
y[1] (analytic) = 6.342436335198735 " "
y[1] (numeric) = 6.34243633519873 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 7.00187099057648500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11700000000000009 " "
y[1] (analytic) = 6.3550944227134405 " "
y[1] (numeric) = 6.355094422713438 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.19275479145862400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11800000000000009 " "
y[1] (analytic) = 6.367777930614314 " "
y[1] (numeric) = 6.367777930614310 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.97400591994608700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11900000000000009 " "
y[1] (analytic) = 6.380486909635397 " "
y[1] (numeric) = 6.380486909635394 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.176068843706219000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000009 " "
y[1] (analytic) = 6.393221410612629 " "
y[1] (numeric) = 6.393221410612624 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.94625105761053100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1210000000000001 " "
y[1] (analytic) = 6.405981484484025 " "
y[1] (numeric) = 6.4059814844840215 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.545931856664830000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1220000000000001 " "
y[1] (analytic) = 6.418767182289903 " "
y[1] (numeric) = 6.418767182289898 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 8.30232717102476100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1230000000000001 " "
y[1] (analytic) = 6.431578555173066 " "
y[1] (numeric) = 6.431578555173062 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.5238595755671400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1240000000000001 " "
y[1] (analytic) = 6.444415654379027 " "
y[1] (numeric) = 6.444415654379022 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.89107024852285500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12500000000000008 " "
y[1] (analytic) = 6.457278531256196 " "
y[1] (numeric) = 6.4572785312561924 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.50187460801595300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12600000000000008 " "
y[1] (analytic) = 6.470167237256103 " "
y[1] (numeric) = 6.470167237256097 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 8.23637214122571500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12700000000000009 " "
y[1] (analytic) = 6.483081823933582 " "
y[1] (numeric) = 6.483081823933579 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.47997661495641400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12800000000000009 " "
y[1] (analytic) = 6.496022342947004 " "
y[1] (numeric) = 6.496022342947 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.8363251603071900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1290000000000001 " "
y[1] (analytic) = 6.508988846058457 " "
y[1] (numeric) = 6.508988846058454 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.09362394393085360000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1300000000000001 " "
y[1] (analytic) = 6.521981385133975 " "
y[1] (numeric) = 6.521981385133971 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.44729196390909600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1310000000000001 " "
y[1] (analytic) = 6.535000012143727 " "
y[1] (numeric) = 6.535000012143724 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.077330151719934500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1320000000000001 " "
y[1] (analytic) = 6.548044779162243 " "
y[1] (numeric) = 6.54804477916224 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.425609931847527000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1330000000000001 " "
y[1] (analytic) = 6.5611157383686045 " "
y[1] (numeric) = 6.561115738368602 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.06110083307706150000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1340000000000001 " "
y[1] (analytic) = 6.57421294204667 " "
y[1] (numeric) = 6.574212942046666 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.75501712166642600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1350000000000001 " "
y[1] (analytic) = 6.587336442585267 " "
y[1] (numeric) = 6.587336442585264 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.04493573741718900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1360000000000001 " "
y[1] (analytic) = 6.600486292478420 " "
y[1] (numeric) = 6.600486292478416 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.38250292686615200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1370000000000001 " "
y[1] (analytic) = 6.61366254432554 " "
y[1] (numeric) = 6.613662544325538 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.68588974338333560000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1380000000000001 " "
y[1] (analytic) = 6.626865250831659 " "
y[1] (numeric) = 6.6268652508316555 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.36107728817126900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1390000000000001 " "
y[1] (analytic) = 6.640094464807615 " "
y[1] (numeric) = 6.640094464807612 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.01279721730220300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1400000000000001 " "
y[1] (analytic) = 6.653350239170286 " "
y[1] (numeric) = 6.6533502391702815 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.67467056274258700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1410000000000001 " "
y[1] (analytic) = 6.666632626942781 " "
y[1] (numeric) = 6.6666326269427785 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.99682329626477700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1420000000000001 " "
y[1] (analytic) = 6.679941681254677 " "
y[1] (numeric) = 6.679941681254673 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.64810010387172100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1430000000000001 " "
y[1] (analytic) = 6.6932774553422005 " "
y[1] (numeric) = 6.693277455342198 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.980912605040289300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1440000000000001 " "
y[1] (analytic) = 6.706640002548474 " "
y[1] (numeric) = 6.706640002548470 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.6216348228220400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1450000000000001 " "
y[1] (analytic) = 6.720029376323695 " "
y[1] (numeric) = 6.7200293763236925 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.965064897615156500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1460000000000001 " "
y[1] (analytic) = 6.733445630225385 " "
y[1] (numeric) = 6.733445630225382 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.276219448261266000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1470000000000001 " "
y[1] (analytic) = 6.746888817918572 " "
y[1] (numeric) = 6.7468888179185695 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.94927992888193140000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1480000000000001 " "
y[1] (analytic) = 6.760358993176029 " "
y[1] (numeric) = 6.760358993176025 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.255214526901077000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1490000000000001 " "
y[1] (analytic) = 6.773856209878469 " "
y[1] (numeric) = 6.773856209878467 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.622371636424388000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1500000000000001 " "
y[1] (analytic) = 6.787380522014784 " "
y[1] (numeric) = 6.78738052201478 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.54286596146576500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1510000000000001 " "
y[1] (analytic) = 6.800931983682233 " "
y[1] (numeric) = 6.80093198368223 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.91789723157577400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1520000000000001 " "
y[1] (analytic) = 6.814510649086689 " "
y[1] (numeric) = 6.814510649086684 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.51681731408815800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1530000000000001 " "
y[1] (analytic) = 6.828116572542823 " "
y[1] (numeric) = 6.82811657254282 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.9022990172941500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1540000000000001 " "
y[1] (analytic) = 6.841749808474355 " "
y[1] (numeric) = 6.841749808474350 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.49087181323121600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1550000000000001 " "
y[1] (analytic) = 6.85541041141424 " "
y[1] (numeric) = 6.855410411414237 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.886762570281615500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1560000000000001 " "
y[1] (analytic) = 6.869098436004914 " "
y[1] (numeric) = 6.86909843600491 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.46502905712246700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1570000000000001 " "
y[1] (analytic) = 6.882813936998488 " "
y[1] (numeric) = 6.8828139369984855 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.87128764992061840000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1580000000000001 " "
y[1] (analytic) = 6.896556969256990 " "
y[1] (numeric) = 6.896556969256986 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.43928864547474600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1590000000000001 " "
y[1] (analytic) = 6.910327587752562 " "
y[1] (numeric) = 6.910327587752560 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.85587401648343500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000011 " "
y[1] (analytic) = 6.924125847567701 " "
y[1] (numeric) = 6.924125847567697 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.4136501794816700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16100000000000012 " "
y[1] (analytic) = 6.93795180389546 " "
y[1] (numeric) = 6.937951803895458 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.84052143112945200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16200000000000012 " "
y[1] (analytic) = 6.951805512039688 " "
y[1] (numeric) = 6.951805512039685 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.11049060945049400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16300000000000012 " "
y[1] (analytic) = 6.96568702741523 " "
y[1] (numeric) = 6.965687027415228 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.550153103934970000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16400000000000012 " "
y[1] (analytic) = 6.979596405548173 " "
y[1] (numeric) = 6.979596405548170 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.09014199728855600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16500000000000012 " "
y[1] (analytic) = 6.993533702076041 " "
y[1] (numeric) = 6.993533702076038 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.80999845372791200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16600000000000012 " "
y[1] (analytic) = 7.007498972748045 " "
y[1] (numeric) = 7.00749897274804 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.33734248948322900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16700000000000012 " "
y[1] (analytic) = 7.02149227342528 " "
y[1] (numeric) = 7.021492273425277 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.79482758841026400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16800000000000012 " "
y[1] (analytic) = 7.035513660080974 " "
y[1] (numeric) = 7.035513660080970 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.31210784750223200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16900000000000012 " "
y[1] (analytic) = 7.049563188800685 " "
y[1] (numeric) = 7.049563188800683 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.77971682463021200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000012 " "
y[1] (analytic) = 7.063640915782555 " "
y[1] (numeric) = 7.063640915782550 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.28697317919739700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17100000000000012 " "
y[1] (analytic) = 7.077746897337502 " "
y[1] (numeric) = 7.0777468973375 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.76466592794200800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17200000000000013 " "
y[1] (analytic) = 7.09188118988948 " "
y[1] (numeric) = 7.091881189889476 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.26193809455208000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17300000000000013 " "
y[1] (analytic) = 7.106043849975669 " "
y[1] (numeric) = 7.106043849975666 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.749674664770748500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17400000000000013 " "
y[1] (analytic) = 7.120234934246737 " "
y[1] (numeric) = 7.120234934246732 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.23700220499878300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17500000000000013 " "
y[1] (analytic) = 7.134454499467031 " "
y[1] (numeric) = 7.1344544994670285 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.73474280240966700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17600000000000013 " "
y[1] (analytic) = 7.14870260251484 " "
y[1] (numeric) = 7.1487026025148355 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.21216512341465500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17700000000000013 " "
y[1] (analytic) = 7.162979300382586 " "
y[1] (numeric) = 7.162979300382584 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.71987010901742900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17800000000000013 " "
y[1] (analytic) = 7.177284650177090 " "
y[1] (numeric) = 7.177284650177084 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 7.42491175694036900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17900000000000013 " "
y[1] (analytic) = 7.1916187091197585 " "
y[1] (numeric) = 7.191618709119755 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.940075138153906500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000013 " "
y[1] (analytic) = 7.205981534546856 " "
y[1] (numeric) = 7.205981534546852 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.16278584285865700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18100000000000013 " "
y[1] (analytic) = 7.220373183909698 " "
y[1] (numeric) = 7.220373183909694 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.92040174144679400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18200000000000013 " "
y[1] (analytic) = 7.234793714774904 " "
y[1] (numeric) = 7.2347937147748995 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.13824287682374600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18300000000000013 " "
y[1] (analytic) = 7.249243184824613 " "
y[1] (numeric) = 7.249243184824610 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.675604737165181000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18400000000000014 " "
y[1] (analytic) = 7.263721651856730 " "
y[1] (numeric) = 7.263721651856726 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.11379718462292600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18500000000000014 " "
y[1] (analytic) = 7.278229173785137 " "
y[1] (numeric) = 7.278229173785134 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.660966418449076400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18600000000000014 " "
y[1] (analytic) = 7.292765808639946 " "
y[1] (numeric) = 7.292765808639942 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.0894483862890200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18700000000000014 " "
y[1] (analytic) = 7.307331614567711 " "
y[1] (numeric) = 7.307331614567707 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.861848163176147000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18800000000000014 " "
y[1] (analytic) = 7.3219266498316795 " "
y[1] (numeric) = 7.321926649831675 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.06519610327251200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18900000000000014 " "
y[1] (analytic) = 7.336550972812007 " "
y[1] (numeric) = 7.336550972812004 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.631863622258857400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000014 " "
y[1] (analytic) = 7.351204642006011 " "
y[1] (numeric) = 7.351204642006007 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.04103995843705300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19100000000000014 " "
y[1] (analytic) = 7.365887716028382 " "
y[1] (numeric) = 7.365887716028379 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.82319825629393500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19200000000000014 " "
y[1] (analytic) = 7.380600253611440 " "
y[1] (numeric) = 7.380600253611436 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.01697957605498300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19300000000000014 " "
y[1] (analytic) = 7.395342313605352 " "
y[1] (numeric) = 7.395342313605349 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.602991107251898000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19400000000000014 " "
y[1] (analytic) = 7.410113954978380 " "
y[1] (numeric) = 7.410113954978376 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 5.99301458180285500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19500000000000015 " "
y[1] (analytic) = 7.424915236817107 " "
y[1] (numeric) = 7.424915236817104 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.58864064317938500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19600000000000015 " "
y[1] (analytic) = 7.439746218326683 " "
y[1] (numeric) = 7.439746218326679 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 5.96914460275696500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19700000000000015 " "
y[1] (analytic) = 7.454606958831050 " "
y[1] (numeric) = 7.454606958831047 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.57434707666760600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19800000000000015 " "
y[1] (analytic) = 7.469497517773194 " "
y[1] (numeric) = 7.469497517773190 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 5.94536926738887900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19900000000000015 " "
y[1] (analytic) = 7.484417954715365 " "
y[1] (numeric) = 7.484417954715362 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.560110185217079700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20000000000000015 " "
y[1] (analytic) = 7.499368329339338 " "
y[1] (numeric) = 7.499368329339333 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 5.92168820556097400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20100000000000015 " "
y[1] (analytic) = 7.5143487014466235 " "
y[1] (numeric) = 7.514348701446620 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.54592974716147150000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20200000000000015 " "
y[1] (analytic) = 7.5293591309587375 " "
y[1] (numeric) = 7.529359130958733 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 5.89810104852197900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20300000000000015 " "
y[1] (analytic) = 7.544399677917411 " "
y[1] (numeric) = 7.544399677917409 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.53180554166492100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20400000000000015 " "
y[1] (analytic) = 7.559470402484859 " "
y[1] (numeric) = 7.559470402484855 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.69968594312201500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20500000000000015 " "
y[1] (analytic) = 7.574571364943993 " "
y[1] (numeric) = 7.574571364943991 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.345158232479581400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20600000000000016 " "
y[1] (analytic) = 7.589702625698690 " "
y[1] (numeric) = 7.589702625698686 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.68096558456853500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20700000000000016 " "
y[1] (analytic) = 7.604864245274005 " "
y[1] (numeric) = 7.604864245274003 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.335816632761270300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20800000000000016 " "
y[1] (analytic) = 7.620056284316445 " "
y[1] (numeric) = 7.620056284316441 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.66231947146200860000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20900000000000016 " "
y[1] (analytic) = 7.635278803594178 " "
y[1] (numeric) = 7.6352788035941765 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.326512083048048700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21000000000000016 " "
y[1] (analytic) = 7.65053186399731 " "
y[1] (numeric) = 7.650531863997307 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.643747313202158400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21100000000000016 " "
y[1] (analytic) = 7.665815526538095 " "
y[1] (numeric) = 7.665815526538093 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.317244438312825400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21200000000000016 " "
y[1] (analytic) = 7.681129852351211 " "
y[1] (numeric) = 7.681129852351208 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.6252488202800100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21300000000000016 " "
y[1] (analytic) = 7.696474902693975 " "
y[1] (numeric) = 7.696474902693972 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.462020331109917000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21400000000000016 " "
y[1] (analytic) = 7.711850738946614 " "
y[1] (numeric) = 7.71185073894661 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 5.75852963034295100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21500000000000016 " "
y[1] (analytic) = 7.727257422612489 " "
y[1] (numeric) = 7.727257422612486 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.448228929585122600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21600000000000016 " "
y[1] (analytic) = 7.742695015318360 " "
y[1] (numeric) = 7.742695015318356 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.588471677848236500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21700000000000016 " "
y[1] (analytic) = 7.758163578814612 " "
y[1] (numeric) = 7.75816357881461 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.28966149186514620000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21800000000000017 " "
y[1] (analytic) = 7.773663174975527 " "
y[1] (numeric) = 7.773663174975524 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.570192454745359300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21900000000000017 " "
y[1] (analytic) = 7.789193865799505 " "
y[1] (numeric) = 7.789193865799502 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.42081004145976600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22000000000000017 " "
y[1] (analytic) = 7.8047557134093335 " "
y[1] (numeric) = 7.80475571340933 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.55198574978662230000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22100000000000017 " "
y[1] (analytic) = 7.820348780052420 " "
y[1] (numeric) = 7.820348780052417 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.27145475139325400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22200000000000017 " "
y[1] (analytic) = 7.835973128101056 " "
y[1] (numeric) = 7.8359731281010525 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.53385127886656470000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22300000000000017 " "
y[1] (analytic) = 7.85162882005265 " "
y[1] (numeric) = 7.851628820052648 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.262405521340397600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22400000000000017 " "
y[1] (analytic) = 7.867315918529995 " "
y[1] (numeric) = 7.867315918529992 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.386841569212391500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22500000000000017 " "
y[1] (analytic) = 7.883034486281502 " "
y[1] (numeric) = 7.8830344862815 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.253392196230482000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22600000000000017 " "
y[1] (analytic) = 7.898784586181467 " "
y[1] (numeric) = 7.898784586181463 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.497797908067777700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22700000000000017 " "
y[1] (analytic) = 7.9145662812303055 " "
y[1] (numeric) = 7.914566281230304 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.24441463534514580000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22800000000000017 " "
y[1] (analytic) = 7.930379634554825 " "
y[1] (numeric) = 7.930379634554821 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.479878445314723000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22900000000000018 " "
y[1] (analytic) = 7.946224709408454 " "
y[1] (numeric) = 7.946224709408451 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.353209047745056600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000018 " "
y[1] (analytic) = 7.962101569171518 " "
y[1] (numeric) = 7.962101569171514 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.462030090844686400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23100000000000018 " "
y[1] (analytic) = 7.978010277351472 " "
y[1] (numeric) = 7.978010277351470 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.339849369039600300000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23200000000000018 " "
y[1] (analytic) = 7.993950897583176 " "
y[1] (numeric) = 7.993950897583171 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 5.55531570733471500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23300000000000018 " "
y[1] (analytic) = 8.009923493629126 " "
y[1] (numeric) = 8.009923493629122 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.435390277605313300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23400000000000018 " "
y[1] (analytic) = 8.025928129379732 " "
y[1] (numeric) = 8.025928129379727 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.63981838897004700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23500000000000018 " "
y[1] (analytic) = 8.041964868853555 " "
y[1] (numeric) = 8.041964868853551 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.41771847643866700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23600000000000018 " "
y[1] (analytic) = 8.058033776197579 " "
y[1] (numeric) = 8.058033776197574 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.61336334173996300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23700000000000018 " "
y[1] (analytic) = 8.074134915687448 " "
y[1] (numeric) = 8.074134915687445 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.40011681238796300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23800000000000018 " "
y[1] (analytic) = 8.09026835172775 " "
y[1] (numeric) = 8.090268351727744 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.58701329364764600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23900000000000018 " "
y[1] (analytic) = 8.106434148852241 " "
y[1] (numeric) = 8.106434148852237 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.38258501033221400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000019 " "
y[1] (analytic) = 8.12263237172414 " "
y[1] (numeric) = 8.122632371724135 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.56076783279258800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2410000000000002 " "
y[1] (analytic) = 8.138863085136354 " "
y[1] (numeric) = 8.13886308513635 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.36512279619086450000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2420000000000002 " "
y[1] (analytic) = 8.155126354011761 " "
y[1] (numeric) = 8.155126354011758 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.356417699221557500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2430000000000002 " "
y[1] (analytic) = 8.171422243403457 " "
y[1] (numeric) = 8.171422243403454 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.34772989692033100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2440000000000002 " "
y[1] (analytic) = 8.187750818495024 " "
y[1] (numeric) = 8.187750818495019 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.50858903297728700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2450000000000002 " "
y[1] (analytic) = 8.204112144600778 " "
y[1] (numeric) = 8.204112144600774 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.3304060405105305000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2460000000000002 " "
y[1] (analytic) = 8.220506287166053 " "
y[1] (numeric) = 8.220506287166048 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.48265487798550300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2470000000000002 " "
y[1] (analytic) = 8.236933311767434 " "
y[1] (numeric) = 8.23693331176743 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.31315095598143240000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2480000000000002 " "
y[1] (analytic) = 8.253393284113049 " "
y[1] (numeric) = 8.253393284113043 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.45682367815753500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2490000000000002 " "
y[1] (analytic) = 8.2698862700428 " "
y[1] (numeric) = 8.269886270042797 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.29596437337960440000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25000000000000017 " "
y[1] (analytic) = 8.286412335528661 " "
y[1] (numeric) = 8.286412335528656 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.43109502933124900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25100000000000017 " "
y[1] (analytic) = 8.302971546674911 " "
y[1] (numeric) = 8.302971546674907 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.27884602377477200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25200000000000017 " "
y[1] (analytic) = 8.31956396971842 " "
y[1] (numeric) = 8.319563969718416 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.2703123525844400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25300000000000017 " "
y[1] (analytic) = 8.3361896710289 " "
y[1] (numeric) = 8.336189671028896 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.26179563925637600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25400000000000017 " "
y[1] (analytic) = 8.352848717109179 " "
y[1] (numeric) = 8.352848717109174 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.37994377569079100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25500000000000017 " "
y[1] (analytic) = 8.369541174595462 " "
y[1] (numeric) = 8.369541174595458 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.244812952930146500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25600000000000017 " "
y[1] (analytic) = 8.386267110257606 " "
y[1] (numeric) = 8.3862671102576 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.35452037019251900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2570000000000002 " "
y[1] (analytic) = 8.403026590999369 " "
y[1] (numeric) = 8.403026590999366 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.22789769891466940000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2580000000000002 " "
y[1] (analytic) = 8.419819683858703 " "
y[1] (numeric) = 8.419819683858698 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.3291979143174490000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2590000000000002 " "
y[1] (analytic) = 8.436646456007995 " "
y[1] (numeric) = 8.436646456007992 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.211049612337973700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000002 " "
y[1] (analytic) = 8.453506974754365 " "
y[1] (numeric) = 8.45350697475436 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.30397601151278300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2610000000000002 " "
y[1] (analytic) = 8.470401307539902 " "
y[1] (numeric) = 8.470401307539898 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.19426842933411370000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2620000000000002 " "
y[1] (analytic) = 8.487329521941966 " "
y[1] (numeric) = 8.48732952194196 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.27885426673220400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2630000000000002 " "
y[1] (analytic) = 8.50429168567343 " "
y[1] (numeric) = 8.504291685673428 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.088776943519883600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2640000000000002 " "
y[1] (analytic) = 8.521287866582979 " "
y[1] (numeric) = 8.521287866582975 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.169221524287188300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2650000000000002 " "
y[1] (analytic) = 8.538318132655354 " "
y[1] (numeric) = 8.538318132655352 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.08045286179541380000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2660000000000002 " "
y[1] (analytic) = 8.555382552011647 " "
y[1] (numeric) = 8.555382552011643 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.152606452373241000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2670000000000002 " "
y[1] (analytic) = 8.572481192909551 " "
y[1] (numeric) = 8.57248119290955 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.072161839059508400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2680000000000002 " "
y[1] (analytic) = 8.58961412374366 " "
y[1] (numeric) = 8.589614123743658 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.068028684187329700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2690000000000002 " "
y[1] (analytic) = 8.606781413045715 " "
y[1] (numeric) = 8.606781413045713 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.06390374537424680000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2700000000000002 " "
y[1] (analytic) = 8.6239831294849 " "
y[1] (numeric) = 8.623983129484897 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.11957401291055200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2710000000000002 " "
y[1] (analytic) = 8.641219341868098 " "
y[1] (numeric) = 8.641219341868096 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.055678451296237800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2720000000000002 " "
y[1] (analytic) = 8.65849011914019 " "
y[1] (numeric) = 8.658490119140184 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.15473419138109700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2730000000000002 " "
y[1] (analytic) = 8.675795530384297 " "
y[1] (numeric) = 8.675795530384296 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.047485827874929200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2740000000000002 " "
y[1] (analytic) = 8.6931356448221 " "
y[1] (numeric) = 8.693135644822096 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.08680345499567500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2750000000000002 " "
y[1] (analytic) = 8.710510531814068 " "
y[1] (numeric) = 8.710510531814066 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.03932574665092900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2760000000000002 " "
y[1] (analytic) = 8.727920260859781 " "
y[1] (numeric) = 8.727920260859777 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.07051573870649200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2770000000000002 " "
y[1] (analytic) = 8.74536490159817 " "
y[1] (numeric) = 8.745364901598169 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.03119807965432080000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2780000000000002 " "
y[1] (analytic) = 8.76284452380783 " "
y[1] (numeric) = 8.762844523807827 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.054292723268237400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2790000000000002 " "
y[1] (analytic) = 8.780359197407266 " "
y[1] (numeric) = 8.780359197407265 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.023102699402989000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2800000000000002 " "
y[1] (analytic) = 8.797908992455204 " "
y[1] (numeric) = 8.797908992455199 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.05720123130483200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2810000000000002 " "
y[1] (analytic) = 8.815493979150837 " "
y[1] (numeric) = 8.815493979150833 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.030078957801886400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2820000000000002 " "
y[1] (analytic) = 8.833114227834145 " "
y[1] (numeric) = 8.83311422783414 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.03305966700650800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2830000000000002 " "
y[1] (analytic) = 8.850769808986136 " "
y[1] (numeric) = 8.850769808986133 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.014016583273300500000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2840000000000002 " "
y[1] (analytic) = 8.86846079322917 " "
y[1] (numeric) = 8.868460793229165 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.00901401319759200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2850000000000002 " "
y[1] (analytic) = 8.886187251327197 " "
y[1] (numeric) = 8.886187251327193 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.9980180231627300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2860000000000002 " "
y[1] (analytic) = 8.903949254186081 " "
y[1] (numeric) = 8.903949254186076 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.98506389251416200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2870000000000002 " "
y[1] (analytic) = 8.92174687285385 " "
y[1] (numeric) = 8.921746872853847 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.98208302637493900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2880000000000002 " "
y[1] (analytic) = 8.939580178521009 " "
y[1] (numeric) = 8.939580178521005 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.974139286022123600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2890000000000002 " "
y[1] (analytic) = 8.957449242520799 " "
y[1] (numeric) = 8.957449242520797 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.983105671386812500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2900000000000002 " "
y[1] (analytic) = 8.975354136329507 " "
y[1] (numeric) = 8.975354136329502 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.9374487482675400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2910000000000002 " "
y[1] (analytic) = 8.993294931566721 " "
y[1] (numeric) = 8.99329493156672 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.975201361589051500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2920000000000002 " "
y[1] (analytic) = 9.011271699995659 " "
y[1] (numeric) = 9.011271699995655 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.94252198477403900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"
Iterations = 293
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds
"Expected Time Remaining "= 0 Years 0 Days 1 Hours 39 Minutes 26 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 1 Hours 38 Minutes 38 Seconds
"Expected Total Time "= 0 Years 0 Days 1 Hours 41 Minutes 39 Seconds
"Time to Timeout " Unknown
Percent Done = 2.940000000000002 "%"
(%o58) true
(%o58) diffeq.max