(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr # 0.0 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr # 0.0 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
elseif (omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 5
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
elseif (omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 5
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_0D2 array_x ,
1 1 1
array_tmp2 : array_const_0D3 + array_tmp1 , array_tmp3 : exp(array_x ),
1 1 1 1 1
array_tmp2
1
array_tmp4 : -----------, array_tmp5 : array_tmp4 + array_const_0D0 ,
1 array_tmp3 1 1 1
1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1),
1
temporary
array_y : temporary, array_y_higher : temporary, temporary : ---------,
2 1, 2 glob_h
array_y_higher : temporary, 0)), kkk : 2,
2, 1
array_tmp1 : array_const_0D2 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp3 array_x
1 2
array_tmp3 : --------------------, array_tmp4 :
2 1 2
array_tmp2 - array_tmp4 array_tmp3
2 1 2
-------------------------------------, array_tmp5 : array_tmp4 ,
array_tmp3 2 2
1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(1, 2),
2
temporary
array_y : temporary, array_y_higher : temporary, temporary : ---------,
3 1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp3 array_x
2 2
array_tmp3 : --------------------, array_tmp4 :
3 2 3
- ats(3, array_tmp3, array_tmp4, 2)
-----------------------------------, array_tmp5 : array_tmp4 ,
array_tmp3 3 3
1
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp3 array_x
3 2
array_tmp3 : --------------------, array_tmp4 :
4 3 4
- ats(4, array_tmp3, array_tmp4, 2)
-----------------------------------, array_tmp5 : array_tmp4 ,
array_tmp3 4 4
1
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp3 array_x
4 2
array_tmp3 : --------------------, array_tmp4 :
5 4 5
- ats(5, array_tmp3, array_tmp4, 2)
-----------------------------------, array_tmp5 : array_tmp4 ,
array_tmp3 5 5
1
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
array_tmp3 array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp3 : --------------------------,
kkk kkk - 1
- ats(kkk, array_tmp3, array_tmp4, 2)
array_tmp4 : -------------------------------------,
kkk array_tmp3
1
array_tmp5 : array_tmp4 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
array_tmp5 expt(glob_h, order_d)
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y : temporary, array_y_higher : temporary,
order_d + kkk 1, order_d + kkk
term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2,
while term >= 1 do (if adj3 <= 1 + order_d
temporary convfp(adj2)
then (if adj2 > 1 then temporary : ----------------------
glob_h
temporary
else temporary : ---------, array_y_higher : temporary),
glob_h adj3, term
term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_0D2 array_x ,
1 1 1
array_tmp2 : array_const_0D3 + array_tmp1 , array_tmp3 : exp(array_x ),
1 1 1 1 1
array_tmp2
1
array_tmp4 : -----------, array_tmp5 : array_tmp4 + array_const_0D0 ,
1 array_tmp3 1 1 1
1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1),
1
temporary
array_y : temporary, array_y_higher : temporary, temporary : ---------,
2 1, 2 glob_h
array_y_higher : temporary, 0)), kkk : 2,
2, 1
array_tmp1 : array_const_0D2 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp3 array_x
1 2
array_tmp3 : --------------------, array_tmp4 :
2 1 2
array_tmp2 - array_tmp4 array_tmp3
2 1 2
-------------------------------------, array_tmp5 : array_tmp4 ,
array_tmp3 2 2
1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(1, 2),
2
temporary
array_y : temporary, array_y_higher : temporary, temporary : ---------,
3 1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp3 array_x
2 2
array_tmp3 : --------------------, array_tmp4 :
3 2 3
- ats(3, array_tmp3, array_tmp4, 2)
-----------------------------------, array_tmp5 : array_tmp4 ,
array_tmp3 3 3
1
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp3 array_x
3 2
array_tmp3 : --------------------, array_tmp4 :
4 3 4
- ats(4, array_tmp3, array_tmp4, 2)
-----------------------------------, array_tmp5 : array_tmp4 ,
array_tmp3 4 4
1
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp3 array_x
4 2
array_tmp3 : --------------------, array_tmp4 :
5 4 5
- ats(5, array_tmp3, array_tmp4, 2)
-----------------------------------, array_tmp5 : array_tmp4 ,
array_tmp3 5 5
1
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
array_tmp3 array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp3 : --------------------------,
kkk kkk - 1
- ats(kkk, array_tmp3, array_tmp4, 2)
array_tmp4 : -------------------------------------,
kkk array_tmp3
1
array_tmp5 : array_tmp4 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
array_tmp5 expt(glob_h, order_d)
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y : temporary, array_y_higher : temporary,
order_d + kkk 1, order_d + kkk
term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2,
while term >= 1 do (if adj3 <= 1 + order_d
temporary convfp(adj2)
then (if adj2 > 1 then temporary : ----------------------
glob_h
temporary
else temporary : ---------, array_y_higher : temporary),
glob_h adj3, term
term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error # 0.0
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error # 0.0
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i32) log_revs(file, revs) := printf(file, revs)
(%o32) log_revs(file, revs) := printf(file, revs)
(%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i35) logstart(file) := printf(file, "")
(%o35) logstart(file) := printf(file, "
")
(%i36) logend(file) := printf(file, "
~%")
(%o36) logend(file) := printf(file, "~%")
(%i37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i40) factorial_2(nnn) := nnn!
(%o40) factorial_2(nnn) := nnn!
(%i41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i46) arcsin(x) := asin(x)
(%o46) arcsin(x) := asin(x)
(%i47) arccos(x) := acos(x)
(%o47) arccos(x) := acos(x)
(%i48) arctan(x) := atan(x)
(%o48) arctan(x) := atan(x)
(%i49) omniabs(x) := abs(x)
(%o49) omniabs(x) := abs(x)
y
(%i50) expt(x, y) := x
y
(%o50) expt(x, y) := x
(%i51) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%o51) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
- 0.1 (2.0 x + 5.0)
(%i52) exact_soln_y(x) := block(-------------------)
exp(x)
- 0.1 (2.0 x + 5.0)
(%o52) exact_soln_y(x) := block(-------------------)
exp(x)
(%i53) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h], define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\
########temp/div_lin_exppostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(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:1.0,"), omniout_str(ALWAYS,
"/* # did poorly with 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_h:0.005,"), 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, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (-(0.1 * (5.0 + 2.0*x))/exp(x)) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5, 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_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_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_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_const_0D3, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term),
term
array_const_0D3 : 0.3, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 1.0,
iiif, jjjf
x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.005,
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_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"),
if glob_iter >= glob_max_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-12-14T21:31:09-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "div_lin_exp"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 151 | "), logitem_str(html_log_file, "div_lin_exp diffeq.max"),
logitem_str(html_log_file,
"div_lin_exp maxima results"),
logitem_str(html_log_file, "Languages compared"), logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%o53) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h], define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\
########temp/div_lin_exppostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(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:1.0,"), omniout_str(ALWAYS,
"/* # did poorly with 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_h:0.005,"), 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, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (-(0.1 * (5.0 + 2.0*x))/exp(x)) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5, 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_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_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_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_const_0D3, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term),
term
array_const_0D3 : 0.3, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 1.0,
iiif, jjjf
x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.005,
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_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"),
if glob_iter >= glob_max_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-12-14T21:31:09-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "div_lin_exp"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 151 | "), logitem_str(html_log_file, "div_lin_exp diffeq.max"),
logitem_str(html_log_file,
"div_lin_exp maxima results"),
logitem_str(html_log_file, "Languages compared"), logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i54) main()
"##############ECHO OF PROBLEM#################"
"##############temp/div_lin_exppostode.ode#################"
"diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:1.0,"
"/* # did poorly with x_start := -5.0; */"
"x_end:5.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.005,"
"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,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (-(0.1 * (5.0 + 2.0*x))/exp(x)) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 4. ""
estimated_steps = 4000. ""
step_error = 2.500000000000000E-14 ""
est_needed_step_err = 2.500000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 2.7748300768159917000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-102 ""
max_value3 = 2.7748300768159917000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-102 ""
value3 = 2.7748300768159917000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-102 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = 1. " "
y[1] (analytic) = -0.2575156088200097 " "
y[1] (numeric) = -0.2575156088200097 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.001 " "
y[1] (analytic) = -0.2573317242752073 " "
y[1] (numeric) = -0.2573317242752073 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0019999999999998 " "
y[1] (analytic) = -0.25714795005742785 " "
y[1] (numeric) = -0.25714795005742785 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0029999999999997 " "
y[1] (analytic) = -0.2569642861298284 " "
y[1] (numeric) = -0.2569642861298284 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0039999999999996 " "
y[1] (analytic) = -0.25678073245552946 " "
y[1] (numeric) = -0.2567807324555294 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.161811390614033800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0049999999999994 " "
y[1] (analytic) = -0.2565972889976149 " "
y[1] (numeric) = -0.2565972889976148 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.32671377379780560000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 211.52112314597645 " "
Order of pole = 61842.862830748396 " "
x[1] = 1.0059999999999993 " "
y[1] (analytic) = -0.2564139557191324 " "
y[1] (numeric) = -0.2564139557191323 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.32980732858885050000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0069999999999992 " "
y[1] (analytic) = -0.2562307325830933 " "
y[1] (numeric) = -0.2562307325830932 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.33290344773580700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 86.00488177324283 " "
Order of pole = 13604.34004973253 " "
x[1] = 1.0079999999999991 " "
y[1] (analytic) = -0.25604761955247296 " "
y[1] (numeric) = -0.25604761955247285 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.336002133375169700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.008999999999999 " "
y[1] (analytic) = -0.2558646165902106 " "
y[1] (numeric) = -0.2558646165902105 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.33910338764533100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.009999999999999 " "
y[1] (analytic) = -0.2556817236592096 " "
y[1] (numeric) = -0.25568172365920944 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 6.51331081902986700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0109999999999988 " "
y[1] (analytic) = -0.2554989407223374 " "
y[1] (numeric) = -0.25549894072233725 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 6.51797041596165100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 34.791264323716966 " "
Order of pole = 5557.044433514180 " "
x[1] = 1.0119999999999987 " "
y[1] (analytic) = -0.25531626774242594 " "
y[1] (numeric) = -0.2553162677424258 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 6.52263387547947400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 170.83182182733543 " "
Order of pole = 40925.85019408974 " "
x[1] = 1.0129999999999986 " "
y[1] (analytic) = -0.2551337046822714 " "
y[1] (numeric) = -0.25513370468227126 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 6.5273012008023200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 186.0342949342033 " "
Order of pole = 47542.42227409368 " "
x[1] = 1.0139999999999985 " "
y[1] (analytic) = -0.25495125150463466 " "
y[1] (numeric) = -0.25495125150463444 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 8.70929652686936800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0149999999999983 " "
y[1] (analytic) = -0.25476890817224107 " "
y[1] (numeric) = -0.2547689081722408 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 1.08944124362554730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0159999999999982 " "
y[1] (analytic) = -0.2545866746477807 " "
y[1] (numeric) = -0.25458667464778045 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 8.72176853844486700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0169999999999981 " "
y[1] (analytic) = -0.25440455089390873 " "
y[1] (numeric) = -0.25440455089390845 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 1.09100153743725630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.017999999999998 " "
y[1] (analytic) = -0.254222536873245 " "
y[1] (numeric) = -0.2542225368732447 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 1.09178265455937160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 72.72051607708512 " "
Order of pole = 10617.854948308024 " "
x[1] = 1.018999999999998 " "
y[1] (analytic) = -0.25404063254837456 " "
y[1] (numeric) = -0.2540406325483742 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 1.31107730305357440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 95.84198850585395 " "
Order of pole = 15450.643761723524 " "
x[1] = 1.0199999999999978 " "
y[1] (analytic) = -0.25385883788184754 " "
y[1] (numeric) = -0.2538588378818472 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 1.31201619831949640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0209999999999977 " "
y[1] (analytic) = -0.2536771528361795 " "
y[1] (numeric) = -0.25367715283617914 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 1.31295587191738980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0219999999999976 " "
y[1] (analytic) = -0.2534955773738512 " "
y[1] (numeric) = -0.2534955773738508 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 1.53287904524557480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0229999999999975 " "
y[1] (analytic) = -0.25331411145730903 " "
y[1] (numeric) = -0.2533141114573086 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.75311674227396880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0239999999999974 " "
y[1] (analytic) = -0.2531327550489649 " "
y[1] (numeric) = -0.25313275504896443 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.75437275892706970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0249999999999972 " "
y[1] (analytic) = -0.2529515081111964 " "
y[1] (numeric) = -0.25295150811119593 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.75562981682181930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 237.9429468778699 " "
Order of pole = 73920.35690395272 " "
x[1] = 1.0259999999999971 " "
y[1] (analytic) = -0.25277037060634705 " "
y[1] (numeric) = -0.25277037060634655 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 1.976498906429880200000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 232.3673199416182 " "
Order of pole = 71091.20799494727 " "
x[1] = 1.026999999999997 " "
y[1] (analytic) = -0.2525893424967261 " "
y[1] (numeric) = -0.2525893424967256 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 1.97791544228670680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.027999999999997 " "
y[1] (analytic) = -0.25240842374460903 " "
y[1] (numeric) = -0.25240842374460853 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 1.97933315247364430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0289999999999968 " "
y[1] (analytic) = -0.2522276143122373 " "
y[1] (numeric) = -0.2522276143122368 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 1.98075203797017960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0299999999999967 " "
y[1] (analytic) = -0.2520469141618187 " "
y[1] (numeric) = -0.2520469141618181 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 2.2024134441740740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 13.578434678391938 " "
Order of pole = 4174.877319804057 " "
x[1] = 1.0309999999999966 " "
y[1] (analytic) = -0.25186632325552716 " "
y[1] (numeric) = -0.2518663232555266 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 2.2039925986825890000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 124.61917571468359 " "
Order of pole = 23207.939818098715 " "
x[1] = 1.0319999999999965 " "
y[1] (analytic) = -0.2516858415555033 " "
y[1] (numeric) = -0.2516858415555027 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 2.20557306236140300000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0329999999999964 " "
y[1] (analytic) = -0.25150546902385407 " "
y[1] (numeric) = -0.2515054690238535 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 2.20715483630269970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0339999999999963 " "
y[1] (analytic) = -0.2513252056226533 " "
y[1] (numeric) = -0.2513252056226527 " "
absolute error = 6.1062266354383610000000000000000E-16 " "
relative error = 2.429611713759590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 693.4037320279019 " "
Order of pole = 591265.9602200632 " "
x[1] = 1.0349999999999961 " "
y[1] (analytic) = -0.25114505131394144 " "
y[1] (numeric) = -0.25114505131394077 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 2.6523867832155680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.035999999999996 " "
y[1] (analytic) = -0.2509650060597257 " "
y[1] (numeric) = -0.25096500605972505 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 2.6542896367653930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.036999999999996 " "
y[1] (analytic) = -0.2507850698219805 " "
y[1] (numeric) = -0.2507850698219798 " "
absolute error = 7.2164496600635180000000000000000E-16 " "
relative error = 2.8775435735413220000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 17.38457139510408 " "
Order of pole = 4283.786098746107 " "
x[1] = 1.0379999999999958 " "
y[1] (analytic) = -0.2506052425626471 " "
y[1] (numeric) = -0.2506052425626464 " "
absolute error = 7.2164496600635180000000000000000E-16 " "
relative error = 2.87960841771278060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 65.23478029378687 " "
Order of pole = 9219.935617204792 " "
x[1] = 1.0389999999999957 " "
y[1] (analytic) = -0.25042552424363407 " "
y[1] (numeric) = -0.2504255242436333 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 3.10334227944564330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0399999999999956 " "
y[1] (analytic) = -0.2502459148268172 " "
y[1] (numeric) = -0.2502459148268164 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 3.10556964646332370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 72.16136299828754 " "
Order of pole = 10245.9353180402 " "
x[1] = 1.0409999999999955 " "
y[1] (analytic) = -0.2500664142740396 " "
y[1] (numeric) = -0.2500664142740388 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 3.1077988601298120000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0419999999999954 " "
y[1] (analytic) = -0.24988702254711204 " "
y[1] (numeric) = -0.24988702254711123 " "
absolute error = 8.0491169285323850000000000000000E-16 " "
relative error = 3.2211024192002036000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0429999999999953 " "
y[1] (analytic) = -0.24970773960781273 " "
y[1] (numeric) = -0.2497077396078119 " "
absolute error = 8.3266726846886740000000000000000E-16 " "
relative error = 3.33456732168831540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0439999999999952 " "
y[1] (analytic) = -0.24952856541788757 " "
y[1] (numeric) = -0.24952856541788673 " "
absolute error = 8.3266726846886740000000000000000E-16 " "
relative error = 3.3369617104734790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.044999999999995 " "
y[1] (analytic) = -0.24934949993905034 " "
y[1] (numeric) = -0.24934949993904948 " "
absolute error = 8.6042284408449630000000000000000E-16 " "
relative error = 3.45067002057278470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.045999999999995 " "
y[1] (analytic) = -0.2491705431329826 " "
y[1] (numeric) = -0.24917054313298173 " "
absolute error = 8.6042284408449630000000000000000E-16 " "
relative error = 3.4531483267076546000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 55.606393724699494 " "
Order of pole = 7653.372864412444 " "
x[1] = 1.0469999999999948 " "
y[1] (analytic) = -0.24899169496133403 " "
y[1] (numeric) = -0.24899169496133314 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.5671005807565210000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0479999999999947 " "
y[1] (analytic) = -0.2488129553857223 " "
y[1] (numeric) = -0.24881295538572137 " "
absolute error = 9.1593399531575410000000000000000E-16 " "
relative error = 3.6812150472463440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0489999999999946 " "
y[1] (analytic) = -0.2486343243677333 " "
y[1] (numeric) = -0.2486343243677324 " "
absolute error = 9.1593399531575410000000000000000E-16 " "
relative error = 3.6838598115724210000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0499999999999945 " "
y[1] (analytic) = -0.24845580186892133 " "
y[1] (numeric) = -0.24845580186892038 " "
absolute error = 9.436895709313831000000000000000E-16 " "
relative error = 3.7982190950374690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0509999999999944 " "
y[1] (analytic) = -0.2482773878508089 " "
y[1] (numeric) = -0.24827738785080797 " "
absolute error = 9.436895709313831000000000000000E-16 " "
relative error = 3.8009485241501360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0519999999999943 " "
y[1] (analytic) = -0.24809908227488725 " "
y[1] (numeric) = -0.24809908227488628 " "
absolute error = 9.714451465470120000000000000000E-16 " "
relative error = 3.91555316383910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0529999999999942 " "
y[1] (analytic) = -0.24792088510261603 " "
y[1] (numeric) = -0.24792088510261504 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 4.0303208894606250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 56.472242126733306 " "
Order of pole = 7728.435917595700 " "
x[1] = 1.053999999999994 " "
y[1] (analytic) = -0.24774279629542373 " "
y[1] (numeric) = -0.2477427962954227 " "
absolute error = 1.0269562977782698000000000000000E-15 " "
relative error = 4.14525190291976900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.054999999999994 " "
y[1] (analytic) = -0.24756481581470755 " "
y[1] (numeric) = -0.24756481581470652 " "
absolute error = 1.0269562977782698000000000000000E-15 " "
relative error = 4.14823202723163140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0559999999999938 " "
y[1] (analytic) = -0.24738694362183372 " "
y[1] (numeric) = -0.24738694362183264 " "
absolute error = 1.0824674490095276000000000000000E-15 " "
relative error = 4.37560460209344640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0569999999999937 " "
y[1] (analytic) = -0.24720917967813733 " "
y[1] (numeric) = -0.24720917967813624 " "
absolute error = 1.0824674490095276000000000000000E-15 " "
relative error = 4.37875102542261640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 71.74524199760098 " "
Order of pole = 10004.466267442398 " "
x[1] = 1.0579999999999936 " "
y[1] (analytic) = -0.24703152394492273 " "
y[1] (numeric) = -0.24703152394492162 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 4.4942564693593030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 584.5364528421578 " "
Order of pole = 415762.2233653164 " "
x[1] = 1.0589999999999935 " "
y[1] (analytic) = -0.24685397638346337 " "
y[1] (numeric) = -0.24685397638346224 " "
absolute error = 1.1379786002407855000000000000000E-15 " "
relative error = 4.6099261470799550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 71.92622378657897 " "
Order of pole = 9971.299016043415 " "
x[1] = 1.0599999999999934 " "
y[1] (analytic) = -0.2466765369550021 " "
y[1] (numeric) = -0.24667653695500094 " "
absolute error = 1.1657341758564144000000000000000E-15 " "
relative error = 4.7257602617838906000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 37.2288326821965 " "
Order of pole = 5469.6395371277395 " "
x[1] = 1.0609999999999933 " "
y[1] (analytic) = -0.24649920562075112 " "
y[1] (numeric) = -0.24649920562074992 " "
absolute error = 1.1934897514720433000000000000000E-15 " "
relative error = 4.8417590168962860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0619999999999932 " "
y[1] (analytic) = -0.2463219823418921 " "
y[1] (numeric) = -0.2463219823418909 " "
absolute error = 1.1934897514720433000000000000000E-15 " "
relative error = 4.8452425566123175000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 69.07835883441862 " "
Order of pole = 9438.926268769877 " "
x[1] = 1.062999999999993 " "
y[1] (analytic) = -0.24614486707957647 " "
y[1] (numeric) = -0.24614486707957525 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 4.9614901239961840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 324.4764333062545 " "
Order of pole = 128916.91537170221 " "
x[1] = 1.063999999999993 " "
y[1] (analytic) = -0.24596785979492522 " "
y[1] (numeric) = -0.245967859794924 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 4.9650605900538430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0649999999999928 " "
y[1] (analytic) = -0.24579096044902926 " "
y[1] (numeric) = -0.245790960449028 " "
absolute error = 1.2490009027033011000000000000000E-15 " "
relative error = 5.0815575170931150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0659999999999927 " "
y[1] (analytic) = -0.24561416900294933 " "
y[1] (numeric) = -0.24561416900294808 " "
absolute error = 1.2490009027033011000000000000000E-15 " "
relative error = 5.0852151884132670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 121.36601643368432 " "
Order of pole = 21169.929677560704 " "
x[1] = 1.0669999999999926 " "
y[1] (analytic) = -0.24543748541771626 " "
y[1] (numeric) = -0.24543748541771496 " "
absolute error = 1.304512053934559000000000000000E-15 " "
relative error = 5.3150481545815090000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0679999999999925 " "
y[1] (analytic) = -0.2452609096543309 " "
y[1] (numeric) = -0.24526090965432956 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.4320422746041220000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0689999999999924 " "
y[1] (analytic) = -0.2450844416737643 " "
y[1] (numeric) = -0.24508444167376298 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.4359535042358590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 101.83246372710168 " "
Order of pole = 16055.224636123383 " "
x[1] = 1.0699999999999923 " "
y[1] (analytic) = -0.24490808143695794 " "
y[1] (numeric) = -0.24490808143695658 " "
absolute error = 1.3600232051658168000000000000000E-15 " "
relative error = 5.5531985599907700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 312.1480343629363 " "
Order of pole = 118499.83862131274 " "
x[1] = 1.0709999999999922 " "
y[1] (analytic) = -0.2447318289048236 " "
y[1] (numeric) = -0.2447318289048222 " "
absolute error = 1.3877787807814457000000000000000E-15 " "
relative error = 5.6706101000093200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.071999999999992 " "
y[1] (analytic) = -0.24455568403824357 " "
y[1] (numeric) = -0.24455568403824215 " "
absolute error = 1.4155343563970746000000000000000E-15 " "
relative error = 5.788188330048030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 59.59853605187178 " "
Order of pole = 8015.760217895717 " "
x[1] = 1.072999999999992 " "
y[1] (analytic) = -0.24437964679807073 " "
y[1] (numeric) = -0.2443796467980693 " "
absolute error = 1.4155343563970746000000000000000E-15 " "
relative error = 5.7923578127057420000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 105.47349770707307 " "
Order of pole = 16883.423606983066 " "
x[1] = 1.0739999999999919 " "
y[1] (analytic) = -0.24420371714512876 " "
y[1] (numeric) = -0.24420371714512729 " "
absolute error = 1.4710455076283324000000000000000E-15 " "
relative error = 6.0238456843558160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0749999999999917 " "
y[1] (analytic) = -0.24402789504021197 " "
y[1] (numeric) = -0.2440278950402105 " "
absolute error = 1.4710455076283324000000000000000E-15 " "
relative error = 6.0281858653328440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 71.1377163767661 " "
Order of pole = 9718.041889296232 " "
x[1] = 1.0759999999999916 " "
y[1] (analytic) = -0.2438521804440857 " "
y[1] (numeric) = -0.2438521804440842 " "
absolute error = 1.4988010832439613000000000000000E-15 " "
relative error = 6.1463509594806780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0769999999999915 " "
y[1] (analytic) = -0.24367657331748616 " "
y[1] (numeric) = -0.24367657331748466 " "
absolute error = 1.4988010832439613000000000000000E-15 " "
relative error = 6.1507803677589210000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0779999999999914 " "
y[1] (analytic) = -0.2435010736211208 " "
y[1] (numeric) = -0.24350107362111928 " "
absolute error = 1.5265566588595902000000000000000E-15 " "
relative error = 6.269198883430220000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0789999999999913 " "
y[1] (analytic) = -0.24332568131566815 " "
y[1] (numeric) = -0.2433256813156666 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 6.3877853996792010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0799999999999912 " "
y[1] (analytic) = -0.243150396361778 " "
y[1] (numeric) = -0.24315039636177643 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 6.3923902972487570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.080999999999991 " "
y[1] (analytic) = -0.24297521872007158 " "
y[1] (numeric) = -0.24297521872007 " "
absolute error = 1.582067810090848000000000000000E-15 " "
relative error = 6.5112311388163690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.081999999999991 " "
y[1] (analytic) = -0.24280014835114155 " "
y[1] (numeric) = -0.24280014835113997 " "
absolute error = 1.582067810090848000000000000000E-15 " "
relative error = 6.5159260438458870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0829999999999909 " "
y[1] (analytic) = -0.2426251852155522 " "
y[1] (numeric) = -0.2426251852155506 " "
absolute error = 1.609823385706477000000000000000E-15 " "
relative error = 6.6350217693859080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0839999999999907 " "
y[1] (analytic) = -0.24245032927383944 " "
y[1] (numeric) = -0.2424503292738378 " "
absolute error = 1.6375789613221060000000000000000E-15 " "
relative error = 6.7542863984833610000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 76.20813612822629 " "
Order of pole = 10472.51857698632 " "
x[1] = 1.0849999999999906 " "
y[1] (analytic) = -0.24227558048651088 " "
y[1] (numeric) = -0.24227558048650927 " "
absolute error = 1.609823385706477000000000000000E-15 " "
relative error = 6.6445961350038200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0859999999999905 " "
y[1] (analytic) = -0.24210093881404615 " "
y[1] (numeric) = -0.24210093881404451 " "
absolute error = 1.6375789613221060000000000000000E-15 " "
relative error = 6.7640339163653730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 162.7252977651437 " "
Order of pole = 34163.80347143093 " "
x[1] = 1.0869999999999904 " "
y[1] (analytic) = -0.24192640421689673 " "
y[1] (numeric) = -0.24192640421689504 " "
absolute error = 1.6930901125533637000000000000000E-15 " "
relative error = 6.9983684419805640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0879999999999903 " "
y[1] (analytic) = -0.2417519766554861 " "
y[1] (numeric) = -0.2417519766554844 " "
absolute error = 1.6930901125533637000000000000000E-15 " "
relative error = 7.0034178664281970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0889999999999902 " "
y[1] (analytic) = -0.24157765609020995 " "
y[1] (numeric) = -0.24157765609020826 " "
absolute error = 1.6930901125533637000000000000000E-15 " "
relative error = 7.0084714785092950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.08999999999999 " "
y[1] (analytic) = -0.24140344248143628 " "
y[1] (numeric) = -0.24140344248143455 " "
absolute error = 1.7208456881689926000000000000000E-15 " "
relative error = 7.1285051715918430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.09099999999999 " "
y[1] (analytic) = -0.2412293357895053 " "
y[1] (numeric) = -0.24122933578950356 " "
absolute error = 1.7486012637846216000000000000000E-15 " "
relative error = 7.2487090264611780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 99.36952951115846 " "
Order of pole = 14955.29857466062 " "
x[1] = 1.0919999999999899 " "
y[1] (analytic) = -0.24105533597472975 " "
y[1] (numeric) = -0.24105533597472797 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.3690832530936760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 84.91537904954646 " "
Order of pole = 12040.664999650846 " "
x[1] = 1.0929999999999898 " "
y[1] (analytic) = -0.24088144299739478 " "
y[1] (numeric) = -0.24088144299739297 " "
absolute error = 1.8041124150158794000000000000000E-15 " "
relative error = 7.489628061699181000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 170.9700337072005 " "
Order of pole = 37476.431550191155 " "
x[1] = 1.0939999999999896 " "
y[1] (analytic) = -0.24070765681775824 " "
y[1] (numeric) = -0.24070765681775644 " "
absolute error = 1.8041124150158794000000000000000E-15 " "
relative error = 7.4950354254072930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 56.90612095512654 " "
Order of pole = 7412.737646090328 " "
x[1] = 1.0949999999999895 " "
y[1] (analytic) = -0.2405339773960507 " "
y[1] (numeric) = -0.2405339773960489 " "
absolute error = 1.8041124150158794000000000000000E-15 " "
relative error = 7.5004472737975060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 231.00945699645538 " "
Order of pole = 65596.96942478431 " "
x[1] = 1.0959999999999894 " "
y[1] (analytic) = -0.24036040469247555 " "
y[1] (numeric) = -0.24036040469247372 " "
absolute error = 1.8318679906315083000000000000000E-15 " "
relative error = 7.6213384354018550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0969999999999893 " "
y[1] (analytic) = -0.240186938667209 " "
y[1] (numeric) = -0.24018693866720714 " "
absolute error = 1.8596235662471372000000000000000E-15 " "
relative error = 7.7424008839370670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.0979999999999892 " "
y[1] (analytic) = -0.24001357928040035 " "
y[1] (numeric) = -0.24001357928039846 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 7.8636348306684780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.098999999999989 " "
y[1] (analytic) = -0.2398403264921719 " "
y[1] (numeric) = -0.23984032649217 " "
absolute error = 1.915134717478395000000000000000E-15 " "
relative error = 7.985040487096330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.099999999999989 " "
y[1] (analytic) = -0.2396671802626192 " "
y[1] (numeric) = -0.2396671802626173 " "
absolute error = 1.915134717478395000000000000000E-15 " "
relative error = 7.9908092354566650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1009999999999889 " "
y[1] (analytic) = -0.2394941405518111 " "
y[1] (numeric) = -0.23949414055180915 " "
absolute error = 1.942890293094024000000000000000E-15 " "
relative error = 8.1124752723280410000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 236.75448078554763 " "
Order of pole = 67434.66364963785 " "
x[1] = 1.1019999999999888 " "
y[1] (analytic) = -0.23932120731978973 " "
y[1] (numeric) = -0.23932120731978776 " "
absolute error = 1.970645868709652900000000000000E-15 " "
relative error = 8.2343135854082660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 101.39690075725152 " "
Order of pole = 15531.536790459393 " "
x[1] = 1.1029999999999887 " "
y[1] (analytic) = -0.23914838052657073 " "
y[1] (numeric) = -0.23914838052656875 " "
absolute error = 1.970645868709652900000000000000E-15 " "
relative error = 8.2402643261500290000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 192.67044138824045 " "
Order of pole = 46048.24120676925 " "
x[1] = 1.1039999999999885 " "
y[1] (analytic) = -0.2389756601321433 " "
y[1] (numeric) = -0.23897566013214133 " "
absolute error = 1.970645868709652900000000000000E-15 " "
relative error = 8.2462200025725220000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1049999999999884 " "
y[1] (analytic) = -0.23880304609647032 " "
y[1] (numeric) = -0.23880304609646832 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 8.3684085148477490000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1059999999999883 " "
y[1] (analytic) = -0.23863053837948836 " "
y[1] (numeric) = -0.23863053837948633 " "
absolute error = 2.0261570199409107000000000000000E-15 " "
relative error = 8.4907700150211370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 151.43481514404698 " "
Order of pole = 29723.33502050777 " "
x[1] = 1.1069999999999882 " "
y[1] (analytic) = -0.23845813694110782 " "
y[1] (numeric) = -0.2384581369411058 " "
absolute error = 2.0261570199409107000000000000000E-15 " "
relative error = 8.4969087066268250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.107999999999988 " "
y[1] (analytic) = -0.23828584174121312 " "
y[1] (numeric) = -0.23828584174121104 " "
absolute error = 2.0816681711721685000000000000000E-15 " "
relative error = 8.7360128321553150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.108999999999988 " "
y[1] (analytic) = -0.23811365273966253 " "
y[1] (numeric) = -0.23811365273966045 " "
absolute error = 2.0816681711721685000000000000000E-15 " "
relative error = 8.7423301739364120000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 171.7558287542028 " "
Order of pole = 37083.24873976984 " "
x[1] = 1.1099999999999879 " "
y[1] (analytic) = -0.2379415698962886 " "
y[1] (numeric) = -0.2379415698962865 " "
absolute error = 2.0816681711721685000000000000000E-15 " "
relative error = 8.748652755714370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 119.16103493740094 " "
Order of pole = 19666.673736377485 " "
x[1] = 1.1109999999999878 " "
y[1] (analytic) = -0.23776959317089802 " "
y[1] (numeric) = -0.23776959317089588 " "
absolute error = 2.1371793224034263000000000000000E-15 " "
relative error = 8.9884467307277540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 44.31138645882181 " "
Order of pole = 5763.082291253584 " "
x[1] = 1.1119999999999877 " "
y[1] (analytic) = -0.2375977225232717 " "
y[1] (numeric) = -0.23759772252326955 " "
absolute error = 2.1371793224034263000000000000000E-15 " "
relative error = 8.9949486876672350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1129999999999876 " "
y[1] (analytic) = -0.2374259579131651 " "
y[1] (numeric) = -0.2374259579131629 " "
absolute error = 2.192690473634684200000000000000E-15 " "
relative error = 9.2352600907969250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1139999999999874 " "
y[1] (analytic) = -0.23725429930030795 " "
y[1] (numeric) = -0.23725429930030575 " "
absolute error = 2.192690473634684200000000000000E-15 " "
relative error = 9.241942001056240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1149999999999873 " "
y[1] (analytic) = -0.2370827466444047 " "
y[1] (numeric) = -0.23708274664440251 " "
absolute error = 2.192690473634684200000000000000E-15 " "
relative error = 9.248629453932610000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1159999999999872 " "
y[1] (analytic) = -0.2369112999051345 " "
y[1] (numeric) = -0.23691129990513227 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.372478434500330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1169999999999871 " "
y[1] (analytic) = -0.23673995904215106 " "
y[1] (numeric) = -0.2367399590421488 " "
absolute error = 2.248201624865942000000000000000E-15 " "
relative error = 9.496502550571340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.117999999999987 " "
y[1] (analytic) = -0.23656872401508305 " "
y[1] (numeric) = -0.2365687240150808 " "
absolute error = 2.248201624865942000000000000000E-15 " "
relative error = 9.5033763834419720000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 65.73040660522437 " "
Order of pole = 8378.57613577682 " "
x[1] = 1.118999999999987 " "
y[1] (analytic) = -0.23639759478353414 " "
y[1] (numeric) = -0.23639759478353187 " "
absolute error = 2.275957200481571000000000000000E-15 " "
relative error = 9.6276664852095140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 47.74442810312485 " "
Order of pole = 6110.166104468192 " "
x[1] = 1.1199999999999868 " "
y[1] (analytic) = -0.23622657130708286 " "
y[1] (numeric) = -0.23622657130708058 " "
absolute error = 2.275957200481571000000000000000E-15 " "
relative error = 9.634636729849240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 74.49549827258166 " "
Order of pole = 9831.071714684002 " "
x[1] = 1.1209999999999867 " "
y[1] (analytic) = -0.236055653545283 " "
y[1] (numeric) = -0.23605565354528069 " "
absolute error = 2.3037127760971998000000000000E-15 " "
relative error = 9.7591933999380980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1219999999999866 " "
y[1] (analytic) = -0.23588484145766342 " "
y[1] (numeric) = -0.23588484145766112 " "
absolute error = 2.3037127760971998000000000000E-15 " "
relative error = 9.7662603576443470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1229999999999865 " "
y[1] (analytic) = -0.23571413500372843 " "
y[1] (numeric) = -0.2357141350037261 " "
absolute error = 2.3314683517128287000000000000000E-15 " "
relative error = 9.891084179894221000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1239999999999863 " "
y[1] (analytic) = -0.23554353414295756 " "
y[1] (numeric) = -0.2355435341429552 " "
absolute error = 2.3592239273284576000000000000000E-15 " "
relative error = 1.0016084440240175000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1249999999999862 " "
y[1] (analytic) = -0.23537303883480593 " "
y[1] (numeric) = -0.23537303883480354 " "
absolute error = 2.3869795029440866000000000000000E-15 " "
relative error = 1.0141261355848676000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 133.87721736619517 " "
Order of pole = 23535.565296892648 " "
x[1] = 1.1259999999999861 " "
y[1] (analytic) = -0.23520264903870416 " "
y[1] (numeric) = -0.23520264903870175 " "
absolute error = 2.4147350785597155000000000000000E-15 " "
relative error = 1.0266615144127712000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.126999999999986 " "
y[1] (analytic) = -0.23503236471405853 " "
y[1] (numeric) = -0.2350323647140561 " "
absolute error = 2.4147350785597155000000000000000E-15 " "
relative error = 1.0274053454287002000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.127999999999986 " "
y[1] (analytic) = -0.23486218582025106 " "
y[1] (numeric) = -0.23486218582024865 " "
absolute error = 2.4147350785597155000000000000000E-15 " "
relative error = 1.0281497935166982000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1289999999999858 " "
y[1] (analytic) = -0.23469211231663967 " "
y[1] (numeric) = -0.23469211231663722 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.0407212368858856000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1299999999999857 " "
y[1] (analytic) = -0.2345221441625581 " "
y[1] (numeric) = -0.23452214416255562 " "
absolute error = 2.4702462297909733000000000000000E-15 " "
relative error = 1.0533104405180314000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1309999999999856 " "
y[1] (analytic) = -0.2343522813173161 " "
y[1] (numeric) = -0.23435228131731362 " "
absolute error = 2.4980018054066022000000000000000E-15 " "
relative error = 1.065917426263188000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 99.87230840654281 " "
Order of pole = 14587.64367332975 " "
x[1] = 1.1319999999999855 " "
y[1] (analytic) = -0.2341825237401996 " "
y[1] (numeric) = -0.2341825237401971 " "
absolute error = 2.4980018054066022000000000000000E-15 " "
relative error = 1.066690103732022000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1329999999999854 " "
y[1] (analytic) = -0.23401287139047064 " "
y[1] (numeric) = -0.2340128713904681 " "
absolute error = 2.525757381022231000000000000000E-15 " "
relative error = 1.0793241269228251000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1339999999999852 " "
y[1] (analytic) = -0.23384332422736756 " "
y[1] (numeric) = -0.233843324227365 " "
absolute error = 2.55351295663786000000000000000E-15 " "
relative error = 1.091975990794187100000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 236.12534649670724 " "
Order of pole = 65322.82825447247 " "
x[1] = 1.1349999999999851 " "
y[1] (analytic) = -0.23367388221010504 " "
y[1] (numeric) = -0.2336738822101025 " "
absolute error = 2.55351295663786000000000000000E-15 " "
relative error = 1.092767806348978000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.135999999999985 " "
y[1] (analytic) = -0.23350454529787426 " "
y[1] (numeric) = -0.23350454529787168 " "
absolute error = 2.581268532253489000000000000000E-15 " "
relative error = 1.1054468035988967000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.136999999999985 " "
y[1] (analytic) = -0.2333353134498429 " "
y[1] (numeric) = -0.2333353134498403 " "
absolute error = 2.609024107869118000000000000000E-15 " "
relative error = 1.1181437002804749000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 56.99536375861019 " "
Order of pole = 7020.412637432055 " "
x[1] = 1.1379999999999848 " "
y[1] (analytic) = -0.2331661866251552 " "
y[1] (numeric) = -0.2331661866251526 " "
absolute error = 2.609024107869118000000000000000E-15 " "
relative error = 1.11895474452454000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1389999999999847 " "
y[1] (analytic) = -0.23299716478293225 " "
y[1] (numeric) = -0.23299716478292962 " "
absolute error = 2.6367796834847470000000000000000E-15 " "
relative error = 1.1316788708314354000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1399999999999846 " "
y[1] (analytic) = -0.23282824788227188 " "
y[1] (numeric) = -0.2328282478822692 " "
absolute error = 2.6922908347160046000000000000000E-15 " "
relative error = 1.1563420071250738000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1409999999999845 " "
y[1] (analytic) = -0.2326594358822487 " "
y[1] (numeric) = -0.232659435882246 " "
absolute error = 2.6922908347160046000000000000000E-15 " "
relative error = 1.1571810206221768000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 54.25318152514393 " "
Order of pole = 6708.606019647350 " "
x[1] = 1.1419999999999844 " "
y[1] (analytic) = -0.2324907287419144 " "
y[1] (numeric) = -0.2324907287419117 " "
absolute error = 2.6922908347160046000000000000000E-15 " "
relative error = 1.1580207302393934000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 173.3696707888814 " "
Order of pole = 36401.62192374385 " "
x[1] = 1.1429999999999843 " "
y[1] (analytic) = -0.2323221264202978 " "
y[1] (numeric) = -0.23232212642029507 " "
absolute error = 2.7200464103316335000000000000000E-15 " "
relative error = 1.1708081585869926000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 49.68003716212351 " "
Order of pole = 6080.920803936474 " "
x[1] = 1.1439999999999841 " "
y[1] (analytic) = -0.23215362887640467 " "
y[1] (numeric) = -0.23215362887640195 " "
absolute error = 2.7200464103316335000000000000000E-15 " "
relative error = 1.1716579333677994000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.144999999999984 " "
y[1] (analytic) = -0.2319852360692182 " "
y[1] (numeric) = -0.23198523606921548 " "
absolute error = 2.7200464103316335000000000000000E-15 " "
relative error = 1.1725084132164533000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 36.65058181456074 " "
Order of pole = 4930.269279863176 " "
x[1] = 1.145999999999984 " "
y[1] (analytic) = -0.23181694795769883 " "
y[1] (numeric) = -0.23181694795769606 " "
absolute error = 2.7755575615628914000000000000000E-15 " "
relative error = 1.1973057129840937000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1469999999999838 " "
y[1] (analytic) = -0.23164876450078437 " "
y[1] (numeric) = -0.23164876450078156 " "
absolute error = 2.8033131371785200000000000000000E-15 " "
relative error = 1.210156740192339000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1479999999999837 " "
y[1] (analytic) = -0.2314806856573901 " "
y[1] (numeric) = -0.2314806856573873 " "
absolute error = 2.8033131371785200000000000000000E-15 " "
relative error = 1.2110354387526084000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 34.16668622280269 " "
Order of pole = 4733.479577341246 " "
x[1] = 1.1489999999999836 " "
y[1] (analytic) = -0.23131271138640902 " "
y[1] (numeric) = -0.2313127113864062 " "
absolute error = 2.831068712794149000000000000000E-15 " "
relative error = 1.2239140234990524000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1499999999999835 " "
y[1] (analytic) = -0.23114484164671162 " "
y[1] (numeric) = -0.23114484164670882 " "
absolute error = 2.8033131371785200000000000000000E-15 " "
relative error = 1.2127950237640105000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1509999999999834 " "
y[1] (analytic) = -0.23097707639714632 " "
y[1] (numeric) = -0.2309770763971435 " "
absolute error = 2.831068712794149000000000000000E-15 " "
relative error = 1.2256925046216952000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 107.85031003673315 " "
Order of pole = 15982.154254478924 " "
x[1] = 1.1519999999999833 " "
y[1] (analytic) = -0.2308094155965392 " "
y[1] (numeric) = -0.23080941559653637 " "
absolute error = 2.831068712794149000000000000000E-15 " "
relative error = 1.2265828521237324000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 70.88298337675289 " "
Order of pole = 8850.093216967785 " "
x[1] = 1.1529999999999831 " "
y[1] (analytic) = -0.23064185920369437 " "
y[1] (numeric) = -0.2306418592036915 " "
absolute error = 2.858824288409778000000000000000E-15 " "
relative error = 1.2395079966316824000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 131.43149218169054 " "
Order of pole = 22024.449949426657 " "
x[1] = 1.153999999999983 " "
y[1] (analytic) = -0.23047440717739393 " "
y[1] (numeric) = -0.23047440717739104 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 1.25245136732411000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 86.4710015357014 " "
Order of pole = 11499.76000875315 " "
x[1] = 1.154999999999983 " "
y[1] (analytic) = -0.23030705947639804 " "
y[1] (numeric) = -0.23030705947639513 " "
absolute error = 2.914335439641036000000000000000E-15 " "
relative error = 1.2654129865870212000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1559999999999828 " "
y[1] (analytic) = -0.23013981605944503 " "
y[1] (numeric) = -0.23013981605944211 " "
absolute error = 2.914335439641036000000000000000E-15 " "
relative error = 1.2663325666725414000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1569999999999827 " "
y[1] (analytic) = -0.22997267688525155 " "
y[1] (numeric) = -0.2299726768852486 " "
absolute error = 2.942091015256665000000000000000E-15 " "
relative error = 1.279321985161162000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1579999999999826 " "
y[1] (analytic) = -0.22980564191251254 " "
y[1] (numeric) = -0.2298056419125096 " "
absolute error = 2.942091015256665000000000000000E-15 " "
relative error = 1.2802518644762972000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 272.9220455223663 " "
Order of pole = 83617.01404609531 " "
x[1] = 1.1589999999999825 " "
y[1] (analytic) = -0.2296387110999014 " "
y[1] (numeric) = -0.22963871109989845 " "
absolute error = 2.942091015256665000000000000000E-15 " "
relative error = 1.2811825154238676000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1599999999999824 " "
y[1] (analytic) = -0.22947188440607003 " "
y[1] (numeric) = -0.22947188440606706 " "
absolute error = 2.9698465908722940000000000000000E-15 " "
relative error = 1.2942093531671606000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 318.6147346448063 " "
Order of pole = 113325.02459536467 " "
x[1] = 1.1609999999999823 " "
y[1] (analytic) = -0.22930516178964896 " "
y[1] (numeric) = -0.22930516178964594 " "
absolute error = 3.0253577421035516000000000000000E-15 " "
relative error = 1.3193587612645355000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 138.30652630961671 " "
Order of pole = 24014.65444706564 " "
x[1] = 1.1619999999999822 " "
y[1] (analytic) = -0.22913854320924731 " "
y[1] (numeric) = -0.2291385432092443 " "
absolute error = 3.0253577421035516000000000000000E-15 " "
relative error = 1.3203181358017196000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 163.23098608031466 " "
Order of pole = 31830.669913903115 " "
x[1] = 1.162999999999982 " "
y[1] (analytic) = -0.22897202862345312 " "
y[1] (numeric) = -0.22897202862345006 " "
absolute error = 3.0531133177191805000000000000000E-15 " "
relative error = 1.333400125803163900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.163999999999982 " "
y[1] (analytic) = -0.22880561799083313 " "
y[1] (numeric) = -0.22880561799083005 " "
absolute error = 3.0808688933348094000000000000000E-15 " "
relative error = 1.3465005450426665000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1649999999999818 " "
y[1] (analytic) = -0.22863931126993312 " "
y[1] (numeric) = -0.22863931126993 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.3596194161381003000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1659999999999817 " "
y[1] (analytic) = -0.22847310841927781 " "
y[1] (numeric) = -0.22847310841927468 " "
absolute error = 3.1363800445660670000000000000000E-15 " "
relative error = 1.3727567617325023000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1669999999999816 " "
y[1] (analytic) = -0.22830700939737106 " "
y[1] (numeric) = -0.22830700939736792 " "
absolute error = 3.1363800445660670000000000000000E-15 " "
relative error = 1.3737554763845033000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1679999999999815 " "
y[1] (analytic) = -0.22814101416269592 " "
y[1] (numeric) = -0.22814101416269278 " "
absolute error = 3.1363800445660670000000000000000E-15 " "
relative error = 1.3747550198621442000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 206.49982891242814 " "
Order of pole = 48723.08555058117 " "
x[1] = 1.1689999999999814 " "
y[1] (analytic) = -0.22797512267371475 " "
y[1] (numeric) = -0.22797512267371156 " "
absolute error = 3.191891195797325000000000000000E-15 " "
relative error = 1.400105045832418000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 58.999509482253956 " "
Order of pole = 7044.96326957809 " "
x[1] = 1.1699999999999813 " "
y[1] (analytic) = -0.22780933488886912 " "
y[1] (numeric) = -0.22780933488886593 " "
absolute error = 3.191891195797325000000000000000E-15 " "
relative error = 1.401123969460868200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1709999999999812 " "
y[1] (analytic) = -0.2276436507665802 " "
y[1] (numeric) = -0.22764365076657697 " "
absolute error = 3.219646771412954000000000000000E-15 " "
relative error = 1.4143362929609202000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.171999999999981 " "
y[1] (analytic) = -0.22747807026524852 " "
y[1] (numeric) = -0.2274780702652453 " "
absolute error = 3.219646771412954000000000000000E-15 " "
relative error = 1.4153657834615518000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 123.66194736188415 " "
Order of pole = 19634.07832612207 " "
x[1] = 1.172999999999981 " "
y[1] (analytic) = -0.22731259334325432 " "
y[1] (numeric) = -0.22731259334325113 " "
absolute error = 3.191891195797325000000000000000E-15 " "
relative error = 1.4041858169192573000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 310.07688438182186 " "
Order of pole = 105654.99863864957 " "
x[1] = 1.1739999999999808 " "
y[1] (analytic) = -0.22714721995895756 " "
y[1] (numeric) = -0.22714721995895432 " "
absolute error = 3.247402347028583000000000000000E-15 " "
relative error = 1.4296465295130378000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1749999999999807 " "
y[1] (analytic) = -0.2269819500706978 " "
y[1] (numeric) = -0.22698195007069455 " "
absolute error = 3.247402347028583000000000000000E-15 " "
relative error = 1.4306874824262980000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1759999999999806 " "
y[1] (analytic) = -0.22681678363679456 " "
y[1] (numeric) = -0.22681678363679128 " "
absolute error = 3.2751579226442120000000000000000E-15 " "
relative error = 1.4439663018450943000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1769999999999805 " "
y[1] (analytic) = -0.22665172061554725 " "
y[1] (numeric) = -0.22665172061554398 " "
absolute error = 3.2751579226442120000000000000000E-15 " "
relative error = 1.4450178951871373000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 209.29453464955193 " "
Order of pole = 49896.87160917166 " "
x[1] = 1.1779999999999804 " "
y[1] (analytic) = -0.22648676096523532 " "
y[1] (numeric) = -0.22648676096523204 " "
absolute error = 3.2751579226442120000000000000000E-15 " "
relative error = 1.446070361325417000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1789999999999803 " "
y[1] (analytic) = -0.2263219046441183 " "
y[1] (numeric) = -0.226321904644115 " "
absolute error = 3.3029134982598407000000000000000E-15 " "
relative error = 1.4593874611710844000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1799999999999802 " "
y[1] (analytic) = -0.22615715161043587 " "
y[1] (numeric) = -0.22615715161043254 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 1.4727233033128537000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.18099999999998 " "
y[1] (analytic) = -0.22599250182240796 " "
y[1] (numeric) = -0.2259925018224046 " "
absolute error = 3.3584246494910985000000000000000E-15 " "
relative error = 1.486077910730974000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.18199999999998 " "
y[1] (analytic) = -0.22582795523823487 " "
y[1] (numeric) = -0.2258279552382315 " "
absolute error = 3.3861802251067274000000000000000E-15 " "
relative error = 1.499451306431266000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1829999999999798 " "
y[1] (analytic) = -0.22566351181609728 " "
y[1] (numeric) = -0.22566351181609387 " "
absolute error = 3.4139358007223564000000000000000E-15 " "
relative error = 1.5128435134451496000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1839999999999797 " "
y[1] (analytic) = -0.22549917151415635 " "
y[1] (numeric) = -0.22549917151415294 " "
absolute error = 3.4139358007223564000000000000000E-15 " "
relative error = 1.5139460503552390000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1849999999999796 " "
y[1] (analytic) = -0.22533493429055393 " "
y[1] (numeric) = -0.2253349342905505 " "
absolute error = 3.4416913763379850000000000000000E-15 " "
relative error = 1.5273669780381946000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1859999999999795 " "
y[1] (analytic) = -0.22517080010341237 " "
y[1] (numeric) = -0.22517080010340892 " "
absolute error = 3.4416913763379850000000000000000E-15 " "
relative error = 1.5284803246057427000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 201.3075283393434 " "
Order of pole = 45790.94207754672 " "
x[1] = 1.1869999999999794 " "
y[1] (analytic) = -0.22500676891083488 " "
y[1] (numeric) = -0.2250067689108314 " "
absolute error = 3.469446951953614000000000000000E-15 " "
relative error = 1.5419300355930526000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1879999999999793 " "
y[1] (analytic) = -0.2248428406709054 " "
y[1] (numeric) = -0.2248428406709019 " "
absolute error = 3.497202527569243000000000000000E-15 " "
relative error = 1.5553986585180962000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1889999999999792 " "
y[1] (analytic) = -0.22467901534168885 " "
y[1] (numeric) = -0.22467901534168533 " "
absolute error = 3.524958103184872000000000000000E-15 " "
relative error = 1.5688862165539416000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.189999999999979 " "
y[1] (analytic) = -0.22451529288123104 " "
y[1] (numeric) = -0.2245152928812275 " "
absolute error = 3.524958103184872000000000000000E-15 " "
relative error = 1.5700302896736665000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.190999999999979 " "
y[1] (analytic) = -0.2243516732475589 " "
y[1] (numeric) = -0.22435167324755537 " "
absolute error = 3.524958103184872000000000000000E-15 " "
relative error = 1.5711753124726144000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1919999999999789 " "
y[1] (analytic) = -0.22418815639868053 " "
y[1] (numeric) = -0.22418815639867698 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.5847017683140244000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1929999999999787 " "
y[1] (analytic) = -0.22402474229258518 " "
y[1] (numeric) = -0.2240247422925816 " "
absolute error = 3.58046925441613000000000000000E-15 " "
relative error = 1.598247237235918800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 191.32420524507515 " "
Order of pole = 41430.33937564263 " "
x[1] = 1.1939999999999786 " "
y[1] (analytic) = -0.22386143088724336 " "
y[1] (numeric) = -0.22386143088723978 " "
absolute error = 3.58046925441613000000000000000E-15 " "
relative error = 1.5994131906623854000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 128.42305048622808 " "
Order of pole = 20350.981895124118 " "
x[1] = 1.1949999999999785 " "
y[1] (analytic) = -0.2236982221406071 " "
y[1] (numeric) = -0.2236982221406035 " "
absolute error = 3.608224830031759000000000000000E-15 " "
relative error = 1.6129877097386064000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.1959999999999784 " "
y[1] (analytic) = -0.2235351160106098 " "
y[1] (numeric) = -0.22353511601060616 " "
absolute error = 3.635980405647387700000000000000E-15 " "
relative error = 1.6265813043328775000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 82.80924565243976 " "
Order of pole = 10378.90455323495 " "
x[1] = 1.1969999999999783 " "
y[1] (analytic) = -0.2233721124551663 " "
y[1] (numeric) = -0.22337211245516267 " "
absolute error = 3.635980405647387700000000000000E-15 " "
relative error = 1.6277682857018136000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 89.89448561124333 " "
Order of pole = 11625.862761855797 " "
x[1] = 1.1979999999999782 " "
y[1] (analytic) = -0.22320921143217326 " "
y[1] (numeric) = -0.2232092114321696 " "
absolute error = 3.6637359812630166000000000000000E-15 " "
relative error = 1.6413910329934203000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.198999999999978 " "
y[1] (analytic) = -0.22304641289950886 " "
y[1] (numeric) = -0.2230464128995052 " "
absolute error = 3.6637359812630166000000000000000E-15 " "
relative error = 1.6425890619068925000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.199999999999978 " "
y[1] (analytic) = -0.22288371681503316 " "
y[1] (numeric) = -0.22288371681502947 " "
absolute error = 3.6914915568786455000000000000000E-15 " "
relative error = 1.6562410254231996000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.2009999999999779 " "
y[1] (analytic) = -0.22272112313658798 " "
y[1] (numeric) = -0.2227211231365843 " "
absolute error = 3.6914915568786455000000000000000E-15 " "
relative error = 1.6574501353492040000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.2019999999999778 " "
y[1] (analytic) = -0.22255863182199717 " "
y[1] (numeric) = -0.22255863182199345 " "
absolute error = 3.7192471324942744000000000000000E-15 " "
relative error = 1.6711313787500884000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 248.59210529936126 " "
Order of pole = 66785.88081225975 " "
x[1] = 1.2029999999999776 " "
y[1] (analytic) = -0.22239624282906648 " "
y[1] (numeric) = -0.22239624282906276 " "
absolute error = 3.7192471324942744000000000000000E-15 " "
relative error = 1.6723516032385870000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 167.59730943291154 " "
Order of pole = 32528.48310273424 " "
x[1] = 1.2039999999999775 " "
y[1] (analytic) = -0.2222339561155838 " "
y[1] (numeric) = -0.22223395611558008 " "
absolute error = 3.7192471324942744000000000000000E-15 " "
relative error = 1.673572840758815200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 137.64916829449436 " "
Order of pole = 22971.65592192499 " "
x[1] = 1.2049999999999774 " "
y[1] (analytic) = -0.2220717716393192 " "
y[1] (numeric) = -0.22207177163931546 " "
absolute error = 3.747002708109903300000000000000E-15 " "
relative error = 1.6872935629998248000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 1.2059999999999773 " "
y[1] (analytic) = -0.22190968935802496 " "
y[1] (numeric) = -0.22190968935802122 " "
absolute error = 3.747002708109903300000000000000E-15 " "
relative error = 1.6885259579921086000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);"
Iterations = 206
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds
"Expected Time Remaining "= 0 Years 0 Days 0 Hours 55 Minutes 28 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 54 Minutes 57 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 57 Minutes 58 Seconds
"Time to Timeout " Unknown
Percent Done = 5.1749999999994305 "%"
(%o54) true
(%o54) diffeq.max