(%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_0D1 array_x ,
1 1 1
array_tmp2 : exp(array_tmp1 ), array_tmp3 : array_const_0D2 array_x ,
1 1 1 1 1
array_tmp2
1
array_tmp4 : exp(array_tmp3 ), array_tmp5 : -----------,
1 1 1 array_tmp4
1
array_tmp6 : array_tmp5 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_0D1 array_x ,
2 1 2
array_tmp2 array_tmp1
1 2
array_tmp2 : -----------------------,
2 1
array_tmp3 : array_const_0D2 array_x ,
2 1 2
array_tmp4 array_tmp3
1 2
array_tmp4 : -----------------------,
2 1
array_tmp2 - ats(2, array_tmp4, array_tmp5, 2)
2
array_tmp5 : -----------------------------------------------,
2 array_tmp4
1
array_tmp6 : array_tmp5 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp6 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp2 array_tmp1 array_tmp4 array_tmp3
2 2 2 2
array_tmp2 : -----------------------, array_tmp4 : -----------------------,
3 2 3 2
array_tmp2 - ats(3, array_tmp4, array_tmp5, 2)
3
array_tmp5 : -----------------------------------------------,
3 array_tmp4
1
array_tmp6 : array_tmp5 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp6 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
array_tmp2 array_tmp1 array_tmp4 array_tmp3
3 2 3 2
array_tmp2 : -----------------------, array_tmp4 : -----------------------,
4 3 4 3
array_tmp2 - ats(4, array_tmp4, array_tmp5, 2)
4
array_tmp5 : -----------------------------------------------,
4 array_tmp4
1
array_tmp6 : array_tmp5 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp6 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
array_tmp2 array_tmp1 array_tmp4 array_tmp3
4 2 4 2
array_tmp2 : -----------------------, array_tmp4 : -----------------------,
5 4 5 4
array_tmp2 - ats(5, array_tmp4, array_tmp5, 2)
5
array_tmp5 : -----------------------------------------------,
5 array_tmp4
1
array_tmp6 : array_tmp5 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp6 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp2 :
kkk
array_tmp2 array_tmp1 array_tmp4 array_tmp3
kkk - 1 2 kkk - 1 2
-----------------------------, array_tmp4 : -----------------------------,
kkk - 1 kkk kkk - 1
array_tmp2 - ats(kkk, array_tmp4, array_tmp5, 2)
kkk
array_tmp5 : ---------------------------------------------------,
kkk array_tmp4
1
array_tmp6 : array_tmp5 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp6 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_0D1 array_x ,
1 1 1
array_tmp2 : exp(array_tmp1 ), array_tmp3 : array_const_0D2 array_x ,
1 1 1 1 1
array_tmp2
1
array_tmp4 : exp(array_tmp3 ), array_tmp5 : -----------,
1 1 1 array_tmp4
1
array_tmp6 : array_tmp5 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_0D1 array_x ,
2 1 2
array_tmp2 array_tmp1
1 2
array_tmp2 : -----------------------,
2 1
array_tmp3 : array_const_0D2 array_x ,
2 1 2
array_tmp4 array_tmp3
1 2
array_tmp4 : -----------------------,
2 1
array_tmp2 - ats(2, array_tmp4, array_tmp5, 2)
2
array_tmp5 : -----------------------------------------------,
2 array_tmp4
1
array_tmp6 : array_tmp5 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp6 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp2 array_tmp1 array_tmp4 array_tmp3
2 2 2 2
array_tmp2 : -----------------------, array_tmp4 : -----------------------,
3 2 3 2
array_tmp2 - ats(3, array_tmp4, array_tmp5, 2)
3
array_tmp5 : -----------------------------------------------,
3 array_tmp4
1
array_tmp6 : array_tmp5 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp6 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
array_tmp2 array_tmp1 array_tmp4 array_tmp3
3 2 3 2
array_tmp2 : -----------------------, array_tmp4 : -----------------------,
4 3 4 3
array_tmp2 - ats(4, array_tmp4, array_tmp5, 2)
4
array_tmp5 : -----------------------------------------------,
4 array_tmp4
1
array_tmp6 : array_tmp5 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp6 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
array_tmp2 array_tmp1 array_tmp4 array_tmp3
4 2 4 2
array_tmp2 : -----------------------, array_tmp4 : -----------------------,
5 4 5 4
array_tmp2 - ats(5, array_tmp4, array_tmp5, 2)
5
array_tmp5 : -----------------------------------------------,
5 array_tmp4
1
array_tmp6 : array_tmp5 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp6 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp2 :
kkk
array_tmp2 array_tmp1 array_tmp4 array_tmp3
kkk - 1 2 kkk - 1 2
-----------------------------, array_tmp4 : -----------------------------,
kkk - 1 kkk kkk - 1
array_tmp2 - ats(kkk, array_tmp4, array_tmp5, 2)
kkk
array_tmp5 : ---------------------------------------------------,
kkk array_tmp4
1
array_tmp6 : array_tmp5 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp6 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)
10.0 exp(0.1 x)
(%i56) exact_soln_y(x) := block(- ---------------)
exp(0.2 x)
10.0 exp(0.1 x)
(%o56) exact_soln_y(x) := block(- ---------------)
exp(0.2 x)
(%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/div_exp_exppostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp(0.1 * x) / exp(0.2 * x);"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "glob_display_interval:0.1,"),
omniout_str(ALWAYS, "glob_max_minutes: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, " (- 10.0 * (exp(0.1* x)/exp(0.2*x))) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32,
max_terms : 30, glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 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 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 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, 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_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term),
term
array_const_0D2 : 0.2, 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),
iiif, jjjf
x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1,
glob_max_minutes : 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 ) = exp(0.1 * x) / exp(0.2 * x);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-28T13:03:41-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "div_exp_exp"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = exp(0.1 * x) / exp(0.2 * x);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 165 | "), logitem_str(html_log_file, "div_exp_exp diffeq.max"),
logitem_str(html_log_file,
"div_exp_exp 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/div_exp_exppostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp(0.1 * x) / exp(0.2 * x);"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "glob_display_interval:0.1,"),
omniout_str(ALWAYS, "glob_max_minutes: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, " (- 10.0 * (exp(0.1* x)/exp(0.2*x))) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32,
max_terms : 30, glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 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 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 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, 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_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term),
term
array_const_0D2 : 0.2, 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),
iiif, jjjf
x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1,
glob_max_minutes : 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 ) = exp(0.1 * x) / exp(0.2 * x);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-28T13:03:41-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "div_exp_exp"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = exp(0.1 * x) / exp(0.2 * x);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 165 | "), logitem_str(html_log_file, "div_exp_exp diffeq.max"),
logitem_str(html_log_file,
"div_exp_exp 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/div_exp_exppostode.ode#################"
"diff ( y , x , 1 ) = exp(0.1 * x) / exp(0.2 * x);"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:-5.0,"
"x_end:5.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"glob_display_interval:0.1,"
"glob_max_minutes: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("
" (- 10.0 * (exp(0.1* x)/exp(0.2*x))) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 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 = 9.7324084620180040000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-130 ""
max_value3 = 9.7324084620180040000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-130 ""
value3 = 9.7324084620180040000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-130 ""
best_h = 1.000E-3 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = -5. " "
y[1] (analytic) = -16.487212707001284 " "
y[1] (numeric) = -16.487212707001284 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 163.5744731589114 " "
Order of pole = 10.467265531724244 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.999 " "
y[1] (analytic) = -16.485564068163896 " "
y[1] (numeric) = -16.4855640681639 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.1550452651246100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.998000000000000 " "
y[1] (analytic) = -16.483915594182154 " "
y[1] (numeric) = -16.483915594182157 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.15526078042670800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.996999999999999 " "
y[1] (analytic) = -16.482267285039566 " "
y[1] (numeric) = -16.48226728503957 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.155476317281413700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.995999999999999 " "
y[1] (analytic) = -16.48061914071965 " "
y[1] (numeric) = -16.480619140719654 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.155691875690882700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.994999999999998 " "
y[1] (analytic) = -16.478971161205923 " "
y[1] (numeric) = -16.47897116120593 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.311814911314542600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.993999999999998 " "
y[1] (analytic) = -16.477323346481917 " "
y[1] (numeric) = -16.477323346481917 " "
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] = -4.992999999999998 " "
y[1] (analytic) = -16.475675696531138 " "
y[1] (numeric) = -16.47567569653114 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.15633868026942600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.991999999999997 " "
y[1] (analytic) = -16.474028211337117 " "
y[1] (numeric) = -16.47402821133712 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.156554324919505700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.990999999999997 " "
y[1] (analytic) = -16.472380890883375 " "
y[1] (numeric) = -16.472380890883382 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.313539982270258600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.989999999999997 " "
y[1] (analytic) = -16.47073373515345 " "
y[1] (numeric) = -16.470733735153452 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.15698567891845200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.988999999999996 " "
y[1] (analytic) = -16.469086744130855 " "
y[1] (numeric) = -16.46908674413086 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.157201388271631800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.987999999999996 " "
y[1] (analytic) = -16.46743991779913 " "
y[1] (numeric) = -16.467439917799133 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.157417119196825600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.986999999999996 " "
y[1] (analytic) = -16.465793256141804 " "
y[1] (numeric) = -16.465793256141808 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.157632871696190700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.985999999999995 " "
y[1] (analytic) = -16.464146759142412 " "
y[1] (numeric) = -16.464146759142416 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.15784864577188400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.984999999999995 " "
y[1] (analytic) = -16.462500426784487 " "
y[1] (numeric) = -16.46250042678449 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.158064441426064400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.983999999999995 " "
y[1] (analytic) = -16.460854259051565 " "
y[1] (numeric) = -16.460854259051573 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.31656051732177800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 122.15789964091266 " "
Order of pole = 0.972041204348093 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.982999999999994 " "
y[1] (analytic) = -16.459208255927187 " "
y[1] (numeric) = -16.459208255927194 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.316992194957033000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.981999999999994 " "
y[1] (analytic) = -16.45756241739489 " "
y[1] (numeric) = -16.4575624173949 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 6.47613587364331500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.980999999999994 " "
y[1] (analytic) = -16.455916743438223 " "
y[1] (numeric) = -16.45591674343823 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.31785567974162400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.979999999999993 " "
y[1] (analytic) = -16.454271234040718 " "
y[1] (numeric) = -16.45427123404073 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 6.47743123034939500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.978999999999993 " "
y[1] (analytic) = -16.452625889185928 " "
y[1] (numeric) = -16.45262588918594 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 6.47807900586066600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.977999999999993 " "
y[1] (analytic) = -16.450980708857397 " "
y[1] (numeric) = -16.450980708857408 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 6.47872684615272700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.976999999999992 " "
y[1] (analytic) = -16.449335693038673 " "
y[1] (numeric) = -16.449335693038684 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 6.47937475123205700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.975999999999992 " "
y[1] (analytic) = -16.447690841713307 " "
y[1] (numeric) = -16.447690841713317 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 6.48002272110513200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.974999999999992 " "
y[1] (analytic) = -16.446046154864845 " "
y[1] (numeric) = -16.44604615486486 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.64089434103791700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.973999999999991 " "
y[1] (analytic) = -16.444401632476847 " "
y[1] (numeric) = -16.44440163247686 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.64175847367793400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.972999999999991 " "
y[1] (analytic) = -16.44275727453287 " "
y[1] (numeric) = -16.44275727453288 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 6.48196701955164900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.971999999999990 " "
y[1] (analytic) = -16.44111308101646 " "
y[1] (numeric) = -16.44111308101647 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 6.48261524866452200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.97099999999999 " "
y[1] (analytic) = -16.439469051911182 " "
y[1] (numeric) = -16.439469051911196 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.64435139013806000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96999999999999 " "
y[1] (analytic) = -16.4378251872006 " "
y[1] (numeric) = -16.43782518720061 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 6.48391190137520200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96899999999999 " "
y[1] (analytic) = -16.43618148686826 " "
y[1] (numeric) = -16.436181486868275 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.64608043331464200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.967999999999990 " "
y[1] (analytic) = -16.43453795089774 " "
y[1] (numeric) = -16.434537950897756 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.64694508458981700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.966999999999989 " "
y[1] (analytic) = -16.432894579272606 " "
y[1] (numeric) = -16.432894579272617 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 6.48585736675083100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.965999999999989 " "
y[1] (analytic) = -16.43125137197641 " "
y[1] (numeric) = -16.431251371976423 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.64867464655716700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.964999999999988 " "
y[1] (analytic) = -16.429608328992728 " "
y[1] (numeric) = -16.429608328992742 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.64953955726663800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.963999999999988 " "
y[1] (analytic) = -16.427965450305134 " "
y[1] (numeric) = -16.427965450305148 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.65040455447150400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.962999999999988 " "
y[1] (analytic) = -16.42632273589719 " "
y[1] (numeric) = -16.426322735897205 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.65126963818041700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.961999999999987 " "
y[1] (analytic) = -16.42468018575248 " "
y[1] (numeric) = -16.424680185752493 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.65213480840202400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.960999999999987 " "
y[1] (analytic) = -16.42303779985457 " "
y[1] (numeric) = -16.42303779985458 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 6.48975004885873500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.959999999999987 " "
y[1] (analytic) = -16.42139557818703 " "
y[1] (numeric) = -16.421395578187045 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.65386540841793800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.958999999999986 " "
y[1] (analytic) = -16.419753520733455 " "
y[1] (numeric) = -16.41975352073347 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.65473083822954800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.957999999999986 " "
y[1] (analytic) = -16.418111627477412 " "
y[1] (numeric) = -16.418111627477426 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.65559635458847000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.956999999999986 " "
y[1] (analytic) = -16.416469898402482 " "
y[1] (numeric) = -16.4164698984025 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.08205774468791910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.955999999999985 " "
y[1] (analytic) = -16.414828333492256 " "
y[1] (numeric) = -16.414828333492274 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.08216595587285700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.954999999999985 " "
y[1] (analytic) = -16.413186932730312 " "
y[1] (numeric) = -16.41318693273033 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.08227417787945450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.953999999999985 " "
y[1] (analytic) = -16.41154569610024 " "
y[1] (numeric) = -16.411545696100255 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.65905928567035000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.952999999999984 " "
y[1] (analytic) = -16.40990462358562 " "
y[1] (numeric) = -16.40990462358564 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.0824906543619571000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.951999999999984 " "
y[1] (analytic) = -16.40826371517005 " "
y[1] (numeric) = -16.40826371517007 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.0825989088400270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.950999999999984 " "
y[1] (analytic) = -16.406622970837116 " "
y[1] (numeric) = -16.406622970837137 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.29924860897290330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.949999999999983 " "
y[1] (analytic) = -16.40498239057041 " "
y[1] (numeric) = -16.404982390570435 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.5159416303853040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.948999999999983 " "
y[1] (analytic) = -16.403341974353538 " "
y[1] (numeric) = -16.403341974353555 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.08292373723450190000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.947999999999983 " "
y[1] (analytic) = -16.401701722170074 " "
y[1] (numeric) = -16.401701722170095 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.29963844202762970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.946999999999982 " "
y[1] (analytic) = -16.400061634003627 " "
y[1] (numeric) = -16.400061634003652 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.51639648109861520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.945999999999982 " "
y[1] (analytic) = -16.398421709837805 " "
y[1] (numeric) = -16.398421709837827 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.2998983957105370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.944999999999982 " "
y[1] (analytic) = -16.396781949656198 " "
y[1] (numeric) = -16.39678194965622 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.30002839204981650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.943999999999981 " "
y[1] (analytic) = -16.39514235344241 " "
y[1] (numeric) = -16.39514235344243 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.30015840138938020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.942999999999981 " "
y[1] (analytic) = -16.39350292118004 " "
y[1] (numeric) = -16.393502921180065 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.51700316101894970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.941999999999980 " "
y[1] (analytic) = -16.391863652852706 " "
y[1] (numeric) = -16.39186365285273 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.517154868920320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.94099999999998 " "
y[1] (analytic) = -16.390224548444007 " "
y[1] (numeric) = -16.39022454844403 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.51730659199323940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93999999999998 " "
y[1] (analytic) = -16.38858560793755 " "
y[1] (numeric) = -16.38858560793758 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 1.73423809170197120000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93899999999998 " "
y[1] (analytic) = -16.38694683131696 " "
y[1] (numeric) = -16.38694683131698 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.30080864313696500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.937999999999980 " "
y[1] (analytic) = -16.385308218565825 " "
y[1] (numeric) = -16.38530821856585 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.51776185225646260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.936999999999979 " "
y[1] (analytic) = -16.38366976966778 " "
y[1] (numeric) = -16.383669769667804 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.51791363603075050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.935999999999979 " "
y[1] (analytic) = -16.38203148460643 " "
y[1] (numeric) = -16.382031484606458 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 1.73493192569619980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.934999999999978 " "
y[1] (analytic) = -16.380393363365393 " "
y[1] (numeric) = -16.380393363365425 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 1.95199360600918360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.933999999999978 " "
y[1] (analytic) = -16.378755405928295 " "
y[1] (numeric) = -16.378755405928324 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 1.7352789467822910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.932999999999978 " "
y[1] (analytic) = -16.377117612278752 " "
y[1] (numeric) = -16.377117612278777 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.51852092293444620000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.931999999999977 " "
y[1] (analytic) = -16.37547998240038 " "
y[1] (numeric) = -16.375479982400407 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 1.73562603727954040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.930999999999977 " "
y[1] (analytic) = -16.37384251627681 " "
y[1] (numeric) = -16.373842516276838 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 1.73579960856168780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.929999999999977 " "
y[1] (analytic) = -16.372205213891664 " "
y[1] (numeric) = -16.372205213891693 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 1.73597319720183160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.928999999999976 " "
y[1] (analytic) = -16.370568075228576 " "
y[1] (numeric) = -16.3705680752286 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.51912845280149340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.927999999999976 " "
y[1] (analytic) = -16.368931100271162 " "
y[1] (numeric) = -16.36893110027119 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 1.73632042656305050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.926999999999976 " "
y[1] (analytic) = -16.36729428900306 " "
y[1] (numeric) = -16.36729428900309 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 1.95355582569854860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.925999999999975 " "
y[1] (analytic) = -16.365657641407903 " "
y[1] (numeric) = -16.365657641407935 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 1.95375119104922280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.924999999999975 " "
y[1] (analytic) = -16.36402115746932 " "
y[1] (numeric) = -16.364021157469356 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 2.17105175104156640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.923999999999975 " "
y[1] (analytic) = -16.36238483717095 " "
y[1] (numeric) = -16.36238483717099 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.38839575377952060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.922999999999974 " "
y[1] (analytic) = -16.36074868049643 " "
y[1] (numeric) = -16.36074868049647 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.3886346052972750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.921999999999974 " "
y[1] (analytic) = -16.359112687429402 " "
y[1] (numeric) = -16.359112687429437 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 2.17170316427397790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.920999999999974 " "
y[1] (analytic) = -16.357476857953493 " "
y[1] (numeric) = -16.357476857953532 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.38911237999421160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 124.67726009233134 " "
Order of pole = 11.054936951068935 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.919999999999973 " "
y[1] (analytic) = -16.355841192052356 " "
y[1] (numeric) = -16.355841192052395 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.38935130317817130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.918999999999973 " "
y[1] (analytic) = -16.35420568970963 " "
y[1] (numeric) = -16.35420568970967 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.3895902502556440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.917999999999973 " "
y[1] (analytic) = -16.352570350908962 " "
y[1] (numeric) = -16.352570350909 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 2.3898292212290187000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.916999999999972 " "
y[1] (analytic) = -16.350935175633996 " "
y[1] (numeric) = -16.35093517563404 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 2.60734714483711270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.915999999999972 " "
y[1] (analytic) = -16.349300163868385 " "
y[1] (numeric) = -16.349300163868428 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 2.60760789258876640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.914999999999972 " "
y[1] (analytic) = -16.347665315595773 " "
y[1] (numeric) = -16.347665315595815 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 2.60786866641649960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.913999999999971 " "
y[1] (analytic) = -16.346030630799813 " "
y[1] (numeric) = -16.34603063079986 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 2.8254735885164960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.912999999999971 " "
y[1] (analytic) = -16.34439610946416 " "
y[1] (numeric) = -16.34439610946421 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 3.043122007695740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.911999999999970 " "
y[1] (analytic) = -16.34276175157247 " "
y[1] (numeric) = -16.34276175157252 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 3.04342633511262600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.91099999999997 " "
y[1] (analytic) = -16.341127557108397 " "
y[1] (numeric) = -16.34112755710845 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 3.26114002817547540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90999999999997 " "
y[1] (analytic) = -16.3394935260556 " "
y[1] (numeric) = -16.339493526055655 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 3.47889723571683960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90899999999997 " "
y[1] (analytic) = -16.33785965839774 " "
y[1] (numeric) = -16.337859658397793 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 3.26179232140825950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.907999999999970 " "
y[1] (analytic) = -16.336225954118472 " "
y[1] (numeric) = -16.33622595411853 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 3.47959308474656600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.906999999999969 " "
y[1] (analytic) = -16.334592413201474 " "
y[1] (numeric) = -16.334592413201523 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 3.0449484287718870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.905999999999969 " "
y[1] (analytic) = -16.33295903563039 " "
y[1] (numeric) = -16.33295903563044 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 3.0452529388400140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.904999999999968 " "
y[1] (analytic) = -16.331325821388898 " "
y[1] (numeric) = -16.33132582138895 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 3.26309729931500500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.903999999999968 " "
y[1] (analytic) = -16.329692770460667 " "
y[1] (numeric) = -16.32969277046072 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 3.26342362536096660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.902999999999968 " "
y[1] (analytic) = -16.32805988282936 " "
y[1] (numeric) = -16.328059882829418 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 3.4813333163105760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.901999999999967 " "
y[1] (analytic) = -16.326427158478655 " "
y[1] (numeric) = -16.32642715847871 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 3.48168146704945450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.900999999999967 " "
y[1] (analytic) = -16.324794597392223 " "
y[1] (numeric) = -16.32479459739228 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 3.4820296526051464000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.899999999999967 " "
y[1] (analytic) = -16.323162199553735 " "
y[1] (numeric) = -16.323162199553792 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 3.4823778729811355000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.898999999999966 " "
y[1] (analytic) = -16.32152996494687 " "
y[1] (numeric) = -16.321529964946926 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 3.4827261281809040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.897999999999966 " "
y[1] (analytic) = -16.319897893555307 " "
y[1] (numeric) = -16.31989789355536 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 3.2653822670699370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.896999999999966 " "
y[1] (analytic) = -16.318265985362718 " "
y[1] (numeric) = -16.318265985362775 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 3.48342274306570670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.895999999999965 " "
y[1] (analytic) = -16.31663424035279 " "
y[1] (numeric) = -16.316634240352847 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 3.4837711027577080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.894999999999965 " "
y[1] (analytic) = -16.315002658509208 " "
y[1] (numeric) = -16.315002658509265 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 3.48411949728741950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.893999999999965 " "
y[1] (analytic) = -16.313371239815652 " "
y[1] (numeric) = -16.31337123981571 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 3.48446792665832670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.892999999999964 " "
y[1] (analytic) = -16.311739984255805 " "
y[1] (numeric) = -16.311739984255865 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 3.70261741530353240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.891999999999964 " "
y[1] (analytic) = -16.31010889181336 " "
y[1] (numeric) = -16.31010889181342 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 3.7029876955587670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.890999999999964 " "
y[1] (analytic) = -16.308477962472004 " "
y[1] (numeric) = -16.308477962472065 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 3.7033580128438790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.889999999999963 " "
y[1] (analytic) = -16.30684719621543 " "
y[1] (numeric) = -16.30684719621549 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 3.70372836716257040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.888999999999963 " "
y[1] (analytic) = -16.305216593027325 " "
y[1] (numeric) = -16.305216593027385 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 3.70409875851854640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.887999999999963 " "
y[1] (analytic) = -16.30358615289139 " "
y[1] (numeric) = -16.303586152891448 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 3.4865592347440080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.886999999999962 " "
y[1] (analytic) = -16.30195587579131 " "
y[1] (numeric) = -16.30195587579137 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 3.70483965235716500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.885999999999962 " "
y[1] (analytic) = -16.300325761710795 " "
y[1] (numeric) = -16.300325761710855 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 3.7052101548472160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.884999999999962 " "
y[1] (analytic) = -16.298695810633536 " "
y[1] (numeric) = -16.298695810633596 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 3.7055806943893690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.883999999999961 " "
y[1] (analytic) = -16.297066022543234 " "
y[1] (numeric) = -16.297066022543294 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 3.70595127098732930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.882999999999961 " "
y[1] (analytic) = -16.295436397423593 " "
y[1] (numeric) = -16.295436397423654 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 3.70632188464480200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.881999999999960 " "
y[1] (analytic) = -16.293806935258317 " "
y[1] (numeric) = -16.293806935258377 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 3.70669253536549340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.88099999999996 " "
y[1] (analytic) = -16.29217763603111 " "
y[1] (numeric) = -16.29217763603117 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 3.7070632231531110000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87999999999996 " "
y[1] (analytic) = -16.29054849972568 " "
y[1] (numeric) = -16.29054849972574 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 3.707433948011360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87899999999996 " "
y[1] (analytic) = -16.28891952632573 " "
y[1] (numeric) = -16.288919526325795 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 3.92591086935241750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.877999999999960 " "
y[1] (analytic) = -16.287290715814983 " "
y[1] (numeric) = -16.287290715815047 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 3.9263034800695606000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.876999999999959 " "
y[1] (analytic) = -16.28566206817714 " "
y[1] (numeric) = -16.285662068177203 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 3.926696130049740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.875999999999959 " "
y[1] (analytic) = -16.284033583395917 " "
y[1] (numeric) = -16.28403358339598 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 3.927088819296880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.874999999999958 " "
y[1] (analytic) = -16.282405261455033 " "
y[1] (numeric) = -16.282405261455096 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 3.92748154781490830000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.873999999999958 " "
y[1] (analytic) = -16.2807771023382 " "
y[1] (numeric) = -16.280777102338263 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 3.9278743156077520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.872999999999958 " "
y[1] (analytic) = -16.279149106029138 " "
y[1] (numeric) = -16.2791491060292 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 3.9282671226793390000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.871999999999957 " "
y[1] (analytic) = -16.277521272511564 " "
y[1] (numeric) = -16.27752127251163 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 4.14691885620213140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.870999999999957 " "
y[1] (analytic) = -16.275893601769205 " "
y[1] (numeric) = -16.275893601769273 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 4.14733356882303800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.869999999999957 " "
y[1] (analytic) = -16.274266093785783 " "
y[1] (numeric) = -16.27426609378585 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 4.1477483229172790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.868999999999956 " "
y[1] (analytic) = -16.272638748545024 " "
y[1] (numeric) = -16.27263874854509 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 4.14816311848900330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.867999999999956 " "
y[1] (analytic) = -16.271011566030648 " "
y[1] (numeric) = -16.27101156603072 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 4.36692416372880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.866999999999956 " "
y[1] (analytic) = -16.26938454622639 " "
y[1] (numeric) = -16.269384546226462 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 4.36736087798052100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.865999999999955 " "
y[1] (analytic) = -16.267757689115978 " "
y[1] (numeric) = -16.26775768911605 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 4.36779763590585230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.864999999999955 " "
y[1] (analytic) = -16.266130994683145 " "
y[1] (numeric) = -16.266130994683216 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 4.36823443750915860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.863999999999955 " "
y[1] (analytic) = -16.26450446291162 " "
y[1] (numeric) = -16.26450446291169 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 4.36867128279481000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.862999999999954 " "
y[1] (analytic) = -16.26287809378514 " "
y[1] (numeric) = -16.26287809378521 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 4.3691081717671737000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.861999999999954 " "
y[1] (analytic) = -16.261251887287443 " "
y[1] (numeric) = -16.261251887287514 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 4.36954510443061940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.860999999999954 " "
y[1] (analytic) = -16.25962584340226 " "
y[1] (numeric) = -16.259625843402336 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 4.5884811848289925000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.859999999999953 " "
y[1] (analytic) = -16.25799996211334 " "
y[1] (numeric) = -16.257999962113416 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 4.5889400558906457000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.858999999999953 " "
y[1] (analytic) = -16.25637424340442 " "
y[1] (numeric) = -16.256374243404494 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 4.5893989728417006000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.857999999999953 " "
y[1] (analytic) = -16.25474868725924 " "
y[1] (numeric) = -16.254748687259315 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 4.5898579356867440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.856999999999952 " "
y[1] (analytic) = -16.253123293661545 " "
y[1] (numeric) = -16.253123293661623 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 4.808903465593720000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.855999999999952 " "
y[1] (analytic) = -16.25149806259509 " "
y[1] (numeric) = -16.251498062595164 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 4.5907759990771607000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.854999999999952 " "
y[1] (analytic) = -16.24987299404361 " "
y[1] (numeric) = -16.249872994043688 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 4.809865342471320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.853999999999951 " "
y[1] (analytic) = -16.248248087990863 " "
y[1] (numeric) = -16.24824808799094 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 4.8103463530556950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.852999999999951 " "
y[1] (analytic) = -16.2466233444206 " "
y[1] (numeric) = -16.246623344420673 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 4.5921534384824636000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.851999999999950 " "
y[1] (analytic) = -16.24499876331656 " "
y[1] (numeric) = -16.24499876331664 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 5.0300043602914500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.85099999999995 " "
y[1] (analytic) = -16.243374344662517 " "
y[1] (numeric) = -16.243374344662595 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 4.8117896734488470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.84999999999995 " "
y[1] (analytic) = -16.241750088442217 " "
y[1] (numeric) = -16.24175008844229 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 4.593531291181580000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.84899999999995 " "
y[1] (analytic) = -16.240125994639413 " "
y[1] (numeric) = -16.24012599463949 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 4.8127521276257460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.847999999999950 " "
y[1] (analytic) = -16.23850206323787 " "
y[1] (numeric) = -16.238502063237952 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 5.0320167644895750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.846999999999949 " "
y[1] (analytic) = -16.236878294221352 " "
y[1] (numeric) = -16.236878294221434 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 5.0325199913269460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.845999999999949 " "
y[1] (analytic) = -16.23525468757361 " "
y[1] (numeric) = -16.235254687573697 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 5.2518503671194980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.844999999999948 " "
y[1] (analytic) = -16.233631243278424 " "
y[1] (numeric) = -16.233631243278506 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 5.0335265959823230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.843999999999948 " "
y[1] (analytic) = -16.232007961319542 " "
y[1] (numeric) = -16.232007961319628 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 5.2529008422369330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.842999999999948 " "
y[1] (analytic) = -16.23038484168075 " "
y[1] (numeric) = -16.23038484168083 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 5.0345334019787620000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.841999999999947 " "
y[1] (analytic) = -16.2287618843458 " "
y[1] (numeric) = -16.228761884345882 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 5.0350368804924660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.840999999999947 " "
y[1] (analytic) = -16.22713908929847 " "
y[1] (numeric) = -16.227139089298554 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 5.2544769488937810000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.839999999999947 " "
y[1] (analytic) = -16.225516456522524 " "
y[1] (numeric) = -16.225516456522616 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 5.6929192914337600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.838999999999946 " "
y[1] (analytic) = -16.223893986001755 " "
y[1] (numeric) = -16.22389398600184 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 5.2555279493801050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.837999999999946 " "
y[1] (analytic) = -16.222271677719917 " "
y[1] (numeric) = -16.222271677720006 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 5.4750557588057910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.836999999999946 " "
y[1] (analytic) = -16.2206495316608 " "
y[1] (numeric) = -16.22064953166089 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 5.4756032917578620000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.835999999999945 " "
y[1] (analytic) = -16.219027547808174 " "
y[1] (numeric) = -16.219027547808267 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 5.6951969146446080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.834999999999945 " "
y[1] (analytic) = -16.21740572614583 " "
y[1] (numeric) = -16.21740572614592 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 5.4766985219355820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.833999999999945 " "
y[1] (analytic) = -16.215784066657545 " "
y[1] (numeric) = -16.21578406665763 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 5.2581563704052940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.832999999999944 " "
y[1] (analytic) = -16.214162569327094 " "
y[1] (numeric) = -16.214162569327183 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 5.4777939711812420000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.831999999999944 " "
y[1] (analytic) = -16.21254123413827 " "
y[1] (numeric) = -16.21254123413836 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 5.4783417779682430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.830999999999944 " "
y[1] (analytic) = -16.210920061074862 " "
y[1] (numeric) = -16.21092006107495 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 5.4788896395386620000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.829999999999943 " "
y[1] (analytic) = -16.209299050120652 " "
y[1] (numeric) = -16.20929905012074 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 5.4794375558979780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.828999999999943 " "
y[1] (analytic) = -16.207678201259434 " "
y[1] (numeric) = -16.207678201259522 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 5.4799855270516700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.827999999999943 " "
y[1] (analytic) = -16.206057514474995 " "
y[1] (numeric) = -16.206057514475088 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 5.6997548951254240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.826999999999942 " "
y[1] (analytic) = -16.204436989751134 " "
y[1] (numeric) = -16.204436989751226 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 5.7003248991146630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.825999999999942 " "
y[1] (analytic) = -16.202816627071645 " "
y[1] (numeric) = -16.202816627071737 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 5.7008949601071480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.824999999999942 " "
y[1] (analytic) = -16.20119642642032 " "
y[1] (numeric) = -16.201196426420413 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 5.7014650781085830000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.823999999999941 " "
y[1] (analytic) = -16.199576387780958 " "
y[1] (numeric) = -16.199576387781054 " "
absolute error = 9.59232693276135300000000000000E-14 " "
relative error = 5.9213443013217730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.822999999999941 " "
y[1] (analytic) = -16.19795651113736 " "
y[1] (numeric) = -16.19795651113746 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 6.1412674455581180000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.821999999999940 " "
y[1] (analytic) = -16.19633679647333 " "
y[1] (numeric) = -16.196336796473428 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 6.1418816030100350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.82099999999994 " "
y[1] (analytic) = -16.194717243772665 " "
y[1] (numeric) = -16.194717243772764 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 6.1424958218807680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.81999999999994 " "
y[1] (analytic) = -16.193097853019175 " "
y[1] (numeric) = -16.193097853019275 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 6.1431101021764590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8189999999999396 " "
y[1] (analytic) = -16.191478624196662 " "
y[1] (numeric) = -16.191478624196762 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 6.1437244439032510000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.817999999999940 " "
y[1] (analytic) = -16.189859557288937 " "
y[1] (numeric) = -16.189859557289036 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 6.1443388470672890000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.816999999999939 " "
y[1] (analytic) = -16.188240652279806 " "
y[1] (numeric) = -16.18824065227991 " "
absolute error = 1.03028696685214530000000000000E-13 " "
relative error = 6.3644159299488110000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8159999999999386 " "
y[1] (analytic) = -16.186621909153086 " "
y[1] (numeric) = -16.186621909153185 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 6.1455678377316710000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.814999999999938 " "
y[1] (analytic) = -16.18500332789258 " "
y[1] (numeric) = -16.18500332789268 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 6.1461824252443080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.813999999999938 " "
y[1] (analytic) = -16.18338490848211 " "
y[1] (numeric) = -16.18338490848221 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 6.1467970742187690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8129999999999376 " "
y[1] (analytic) = -16.18176665090549 " "
y[1] (numeric) = -16.18176665090559 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 6.1474117846612010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.811999999999937 " "
y[1] (analytic) = -16.180148555146534 " "
y[1] (numeric) = -16.180148555146637 " "
absolute error = 1.03028696685214530000000000000E-13 " "
relative error = 6.3675989335983860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.810999999999937 " "
y[1] (analytic) = -16.178530621189065 " "
y[1] (numeric) = -16.178530621189168 " "
absolute error = 1.03028696685214530000000000000E-13 " "
relative error = 6.3682357253308020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8099999999999365 " "
y[1] (analytic) = -16.1769128490169 " "
y[1] (numeric) = -16.176912849017008 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 6.5884888766333540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.808999999999936 " "
y[1] (analytic) = -16.175295238613867 " "
y[1] (numeric) = -16.175295238613973 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 6.589147758464560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.807999999999936 " "
y[1] (analytic) = -16.173677789963786 " "
y[1] (numeric) = -16.173677789963893 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 6.5898067061872420000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8069999999999355 " "
y[1] (analytic) = -16.17206050305048 " "
y[1] (numeric) = -16.17206050305059 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 6.810147910468260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.805999999999935 " "
y[1] (analytic) = -16.170443377857787 " "
y[1] (numeric) = -16.170443377857893 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 6.5911247993334010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.804999999999935 " "
y[1] (analytic) = -16.16882641436952 " "
y[1] (numeric) = -16.16882641436963 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 6.8115100762623940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8039999999999345 " "
y[1] (analytic) = -16.16720961256952 " "
y[1] (numeric) = -16.16720961256963 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 6.8121912613287060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.802999999999934 " "
y[1] (analytic) = -16.16559297244162 " "
y[1] (numeric) = -16.165592972441726 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 6.593102433403479000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.801999999999934 " "
y[1] (analytic) = -16.163976493969646 " "
y[1] (numeric) = -16.163976493969752 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 6.5937617766134320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8009999999999335 " "
y[1] (analytic) = -16.162360177137433 " "
y[1] (numeric) = -16.162360177137543 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 6.8142352252863680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.799999999999933 " "
y[1] (analytic) = -16.160744021928824 " "
y[1] (numeric) = -16.160744021928938 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 7.0347527049096360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.798999999999933 " "
y[1] (analytic) = -16.15912802832766 " "
y[1] (numeric) = -16.15912802832777 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 6.8155982086252160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7979999999999325 " "
y[1] (analytic) = -16.157512196317775 " "
y[1] (numeric) = -16.157512196317885 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 6.8162798025252060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.796999999999932 " "
y[1] (analytic) = -16.15589652588301 " "
y[1] (numeric) = -16.155896525883122 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 7.036863447316640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.795999999999932 " "
y[1] (analytic) = -16.15428101700721 " "
y[1] (numeric) = -16.154281017007325 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 7.0375671688468610000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7949999999999315 " "
y[1] (analytic) = -16.15266566967422 " "
y[1] (numeric) = -16.152665669674338 " "
absolute error = 1.17239551400416530000000000000E-13 " "
relative error = 7.2582169282762790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.793999999999931 " "
y[1] (analytic) = -16.15105048386789 " "
y[1] (numeric) = -16.15105048386801 " "
absolute error = 1.17239551400416530000000000000E-13 " "
relative error = 7.2589427862614010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.792999999999930 " "
y[1] (analytic) = -16.149435459572064 " "
y[1] (numeric) = -16.14943545957218 " "
absolute error = 1.17239551400416530000000000000E-13 " "
relative error = 7.259668716835951000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7919999999999305 " "
y[1] (analytic) = -16.14782059677059 " "
y[1] (numeric) = -16.14782059677071 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 7.4804066812195280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.79099999999993 " "
y[1] (analytic) = -16.146205895447327 " "
y[1] (numeric) = -16.146205895447444 " "
absolute error = 1.17239551400416530000000000000E-13 " "
relative error = 7.2611207957823730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.78999999999993 " "
y[1] (analytic) = -16.14459135558612 " "
y[1] (numeric) = -16.14459135558624 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 7.481902912173880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7889999999999295 " "
y[1] (analytic) = -16.142976977170825 " "
y[1] (numeric) = -16.142976977170946 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 7.482651139875860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.787999999999930 " "
y[1] (analytic) = -16.141362760185302 " "
y[1] (numeric) = -16.141362760185423 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 7.483399442404350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.786999999999929 " "
y[1] (analytic) = -16.139748704613407 " "
y[1] (numeric) = -16.139748704613528 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 7.4841478197668350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7859999999999285 " "
y[1] (analytic) = -16.138134810439 " "
y[1] (numeric) = -16.13813481043912 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 7.4848962719707980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.784999999999928 " "
y[1] (analytic) = -16.136521077645938 " "
y[1] (numeric) = -16.13652107764606 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 7.4856447990237250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE for equation 1"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = exp(0.1 * x) / exp(0.2 * x);"
Iterations = 216
"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 58 Seconds
"Expected Time Remaining "= 0 Years 0 Days 2 Hours 15 Minutes 33 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 2 Hours 14 Minutes 16 Seconds
"Expected Total Time "= 0 Years 0 Days 2 Hours 17 Minutes 16 Seconds
"Time to Timeout " Unknown
Percent Done = 2.1700000000007247 "%"
(%o58) true
(%o58) diffeq.max