(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, 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 (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : 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 (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : 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 : sin(array_const_0D1 ),
1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
array_tmp3 : cos(array_const_0D05 ), array_tmp4 : array_tmp3 + array_tmp2 ,
1 1 1 1 1
array_tmp5 : tan(array_const_0D02 ), array_tmp6 : array_tmp4 - array_tmp5 ,
1 1 1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (order_d : 1,
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp6 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : sin(array_const_0D1 ),
1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
array_tmp3 : cos(array_const_0D05 ), array_tmp4 : array_tmp3 + array_tmp2 ,
1 1 1 1 1
array_tmp5 : tan(array_const_0D02 ), array_tmp6 : array_tmp4 - array_tmp5 ,
1 1 1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (order_d : 1,
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp6 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole() := 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 > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%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) Si(x) := 0.0
(%o46) Si(x) := 0.0
(%i47) Ci(x) := 0.0
(%o47) Ci(x) := 0.0
(%i48) ln(x) := log(x)
(%o48) ln(x) := log(x)
(%i49) arcsin(x) := asin(x)
(%o49) arcsin(x) := asin(x)
(%i50) arccos(x) := acos(x)
(%o50) arccos(x) := acos(x)
(%i51) arctan(x) := atan(x)
(%o51) arctan(x) := atan(x)
(%i52) omniabs(x) := abs(x)
(%o52) omniabs(x) := abs(x)
(%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i54) 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)
(%o54) 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)
(%i55) exact_soln_y(x) := block((- tan(0.02) + cos(0.05) + sin(0.1)) x)
(%o55) exact_soln_y(x) := block((- tan(0.02) + cos(0.05) + sin(0.1)) x)
(%i56) 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, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_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/add_sub_sin_c_cos_c_tan_cpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(0.1) + cos(0.05) - tan(0.02);"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS,
"glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "glob_display_interval:0.1,"),
omniout_str(ALWAYS, "glob_max_minutes:10,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " ((sin(0.1) + cos(0.05) - tan(0.02)) * 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_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3_g, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5_g, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_tmp6, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3_g : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp5_g : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_g : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp5_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5_g : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D05, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D05 : 0.0, term : 1 + term),
term
array_const_0D05 : 0.05, array(array_const_0D02, 1 + 1 + max_terms),
1
term : 1, while term <= 1 + max_terms do (array_const_0D02 : 0.0,
term
term : 1 + term), array_const_0D02 : 0.02,
1
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 0.05, glob_look_poles : true, glob_max_iter : 1000000,
glob_display_interval : 0.1, glob_max_minutes : 10,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
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(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = sin(0.1) + cos(0.05) - tan(0.02);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-12T20:47:56-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file,
"add_sub_sin_c_cos_c_tan_c"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sin(0.1) + cos(0.05) - tan(0.02);"),
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, " 156 | "), logitem_str(html_log_file, "add_sub_sin_c_cos_c_tan_c diff\
eq.max"), logitem_str(html_log_file, "add_sub_sin_c_cos_c_tan_c maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%o56) 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, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_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/add_sub_sin_c_cos_c_tan_cpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(0.1) + cos(0.05) - tan(0.02);"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS,
"glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "glob_display_interval:0.1,"),
omniout_str(ALWAYS, "glob_max_minutes:10,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " ((sin(0.1) + cos(0.05) - tan(0.02)) * 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_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3_g, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5_g, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_tmp6, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3_g : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp5_g : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_g : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp5_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5_g : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D05, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D05 : 0.0, term : 1 + term),
term
array_const_0D05 : 0.05, array(array_const_0D02, 1 + 1 + max_terms),
1
term : 1, while term <= 1 + max_terms do (array_const_0D02 : 0.0,
term
term : 1 + term), array_const_0D02 : 0.02,
1
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 0.05, glob_look_poles : true, glob_max_iter : 1000000,
glob_display_interval : 0.1, glob_max_minutes : 10,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
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(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = sin(0.1) + cos(0.05) - tan(0.02);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-12T20:47:56-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file,
"add_sub_sin_c_cos_c_tan_c"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sin(0.1) + cos(0.05) - tan(0.02);"),
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, " 156 | "), logitem_str(html_log_file, "add_sub_sin_c_cos_c_tan_c diff\
eq.max"), logitem_str(html_log_file, "add_sub_sin_c_cos_c_tan_c maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i57) main()
"##############ECHO OF PROBLEM#################"
"##############temp/add_sub_sin_c_cos_c_tan_cpostode.ode#################"
"diff ( y , x , 1 ) = sin(0.1) + cos(0.05) - tan(0.02);"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:-5.0,"
"x_end:5.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.05,"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"glob_display_interval:0.1,"
"glob_max_minutes:10,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" ((sin(0.1) + cos(0.05) - tan(0.02)) * x) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 10. ""
estimated_steps = 10000. ""
step_error = 1.00000000000000E-14 ""
est_needed_step_err = 1.00000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_value3 = 0.0 ""
value3 = 0.0 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = -5. " "
y[1] (analytic) = -5.392905049741960 " "
y[1] (numeric) = -5.392905049741960 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -5. " "
y[1] (analytic) = -5.392905049741960 " "
y[1] (numeric) = -5.392905049741960 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.999 " "
y[1] (analytic) = -5.391826468732011 " "
y[1] (numeric) = -5.391826468732012 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.647268184261495600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.998000000000000 " "
y[1] (analytic) = -5.390747887722063 " "
y[1] (numeric) = -5.390747887722064 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.647597769732536000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.996999999999999 " "
y[1] (analytic) = -5.389669306712114 " "
y[1] (numeric) = -5.389669306712116 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.295854974233828000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.995999999999999 " "
y[1] (analytic) = -5.388590725702166 " "
y[1] (numeric) = -5.3885907257021675 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.29651467298767700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.994999999999998 " "
y[1] (analytic) = -5.3875121446922165 " "
y[1] (numeric) = -5.387512144692220 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.94576195382775900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.993999999999998 " "
y[1] (analytic) = -5.386433563682268 " "
y[1] (numeric) = -5.386433563682270 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.946752294627484400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.992999999999998 " "
y[1] (analytic) = -5.385354982672319 " "
y[1] (numeric) = -5.385354982672323 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 6.59699070949186500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.991999999999997 " "
y[1] (analytic) = -5.384276401662370 " "
y[1] (numeric) = -5.384276401662374 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 6.59831222205386100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.990999999999997 " "
y[1] (analytic) = -5.383197820652422 " "
y[1] (numeric) = -5.383197820652426 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 8.24954283021761300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.989999999999997 " "
y[1] (analytic) = -5.382119239642473 " "
y[1] (numeric) = -5.382119239642478 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 8.25119604521364800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.988999999999996 " "
y[1] (analytic) = -5.381040658632524 " "
y[1] (numeric) = -5.3810406586325294 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 9.90341990754446400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.987999999999996 " "
y[1] (analytic) = -5.379962077622576 " "
y[1] (numeric) = -5.379962077622581 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 9.90540535660371500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.986999999999996 " "
y[1] (analytic) = -5.378883496612627 " "
y[1] (numeric) = -5.378883496612633 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.15586235355649810000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.985999999999995 " "
y[1] (analytic) = -5.377804915602678 " "
y[1] (numeric) = -5.377804915602685 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.15609417512760850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.984999999999995 " "
y[1] (analytic) = -5.376726334592730 " "
y[1] (numeric) = -5.376726334592736 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 1.32151553109299500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.983999999999995 " "
y[1] (analytic) = -5.375647753582781 " "
y[1] (numeric) = -5.375647753582788 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 1.32178068268430570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.982999999999994 " "
y[1] (analytic) = -5.374569172572832 " "
y[1] (numeric) = -5.37456917257284 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 1.48730168328535080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.981999999999994 " "
y[1] (analytic) = -5.3734905915628834 " "
y[1] (numeric) = -5.373490591562891 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 1.4876002183482340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.980999999999994 " "
y[1] (analytic) = -5.372412010552934 " "
y[1] (numeric) = -5.372412010552943 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 1.65322097031183030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.979999999999993 " "
y[1] (analytic) = -5.371333429542986 " "
y[1] (numeric) = -5.371333429542995 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 1.6535529423942220000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.978999999999993 " "
y[1] (analytic) = -5.370254848533037 " "
y[1] (numeric) = -5.370254848533047 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 1.8192735526080640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.977999999999993 " "
y[1] (analytic) = -5.369176267523088 " "
y[1] (numeric) = -5.369176267523098 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 1.9850607440232770000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.976999999999992 " "
y[1] (analytic) = -5.368097686513140 " "
y[1] (numeric) = -5.36809768651315 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 1.98545959086756540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.975999999999992 " "
y[1] (analytic) = -5.36701910550319 " "
y[1] (numeric) = -5.367019105503202 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 2.1513468145217440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.974999999999992 " "
y[1] (analytic) = -5.365940524493242 " "
y[1] (numeric) = -5.365940524493253 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 2.1517792460422508000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.973999999999991 " "
y[1] (analytic) = -5.364861943483293 " "
y[1] (numeric) = -5.364861943483305 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 2.31776660924256560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.972999999999991 " "
y[1] (analytic) = -5.363783362473344 " "
y[1] (numeric) = -5.363783362473357 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 2.31823267934295640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.971999999999990 " "
y[1] (analytic) = -5.362704781463395 " "
y[1] (numeric) = -5.362704781463409 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 2.4843202895584970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.97099999999999 " "
y[1] (analytic) = -5.361626200453447 " "
y[1] (numeric) = -5.36162620045346 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 2.4848200522399610000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96999999999999 " "
y[1] (analytic) = -5.360547619443498 " "
y[1] (numeric) = -5.360547619443512 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 2.65100801710204670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96899999999999 " "
y[1] (analytic) = -5.3594690384335495 " "
y[1] (numeric) = -5.359469038433564 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 2.6515415264635084000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.967999999999990 " "
y[1] (analytic) = -5.3583904574236 " "
y[1] (numeric) = -5.358390457423615 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 2.8178299537660020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.966999999999989 " "
y[1] (analytic) = -5.357311876413652 " "
y[1] (numeric) = -5.357311876413667 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 2.8183972640043280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.965999999999989 " "
y[1] (analytic) = -5.356233295403703 " "
y[1] (numeric) = -5.356233295403719 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 2.98478626170395170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.964999999999988 " "
y[1] (analytic) = -5.355154714393755 " "
y[1] (numeric) = -5.3551547143937706 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 2.98538742711416400000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.963999999999988 " "
y[1] (analytic) = -5.354076133383805 " "
y[1] (numeric) = -5.354076133383822 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 3.1518771033308113000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.962999999999988 " "
y[1] (analytic) = -5.352997552373857 " "
y[1] (numeric) = -5.352997552373874 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 3.1525121783062960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.961999999999987 " "
y[1] (analytic) = -5.351918971363908 " "
y[1] (numeric) = -5.351918971363926 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 3.3191026413233520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.960999999999987 " "
y[1] (analytic) = -5.35084039035396 " "
y[1] (numeric) = -5.350840390353977 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 3.3197716803560723000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.959999999999987 " "
y[1] (analytic) = -5.3497618093440105 " "
y[1] (numeric) = -5.349761809344030 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 3.48646303862072570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.958999999999986 " "
y[1] (analytic) = -5.348683228334062 " "
y[1] (numeric) = -5.348683228334080 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 3.48716609630143100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.957999999999986 " "
y[1] (analytic) = -5.347604647324113 " "
y[1] (numeric) = -5.3476046473241325 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 3.6539584584249946000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.956999999999986 " "
y[1] (analytic) = -5.346526066314164 " "
y[1] (numeric) = -5.346526066314184 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 3.8208181162363230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.955999999999985 " "
y[1] (analytic) = -5.3454474853042155 " "
y[1] (numeric) = -5.345447485304236 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 3.8215890642016650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.954999999999985 " "
y[1] (analytic) = -5.344368904294266 " "
y[1] (numeric) = -5.344368904294288 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 3.98854990262276050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.953999999999985 " "
y[1] (analytic) = -5.343290323284318 " "
y[1] (numeric) = -5.343290323284340 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 3.98935501968021360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.952999999999984 " "
y[1] (analytic) = -5.342211742274369 " "
y[1] (numeric) = -5.342211742274391 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 4.15641714775047600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.951999999999984 " "
y[1] (analytic) = -5.341133161264420 " "
y[1] (numeric) = -5.341133161264443 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 4.15725648885462540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.950999999999984 " "
y[1] (analytic) = -5.340054580254471 " "
y[1] (numeric) = -5.3400545802544945 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 4.32442001577871770000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.949999999999983 " "
y[1] (analytic) = -5.338975999244523 " "
y[1] (numeric) = -5.338975999244546 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 4.32529363598392560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.948999999999983 " "
y[1] (analytic) = -5.337897418234574 " "
y[1] (numeric) = -5.337897418234598 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 4.49255867113209900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.947999999999983 " "
y[1] (analytic) = -5.336818837224626 " "
y[1] (numeric) = -5.33681883722465 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 4.4934666255927160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.946999999999982 " "
y[1] (analytic) = -5.3357402562146765 " "
y[1] (numeric) = -5.335740256214701 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 4.660833278501129700000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.945999999999982 " "
y[1] (analytic) = -5.334661675204728 " "
y[1] (numeric) = -5.334661675204753 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 4.6617756224717116000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.944999999999982 " "
y[1] (analytic) = -5.333583094194779 " "
y[1] (numeric) = -5.333583094194805 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 4.8292440028427530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.943999999999981 " "
y[1] (analytic) = -5.332504513184830 " "
y[1] (numeric) = -5.3325045131848565 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 4.830220791678279700000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.942999999999981 " "
y[1] (analytic) = -5.331425932174882 " "
y[1] (numeric) = -5.331425932174908 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 4.9977910093808910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.941999999999980 " "
y[1] (analytic) = -5.330347351164933 " "
y[1] (numeric) = -5.33034735116496 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 4.9988022985369773000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.94099999999998 " "
y[1] (analytic) = -5.329268770154984 " "
y[1] (numeric) = -5.329268770155012 " "
absolute error = 2.753353101070388000000000000000E-14 " "
relative error = 5.1664744636069760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93999999999998 " "
y[1] (analytic) = -5.328190189145036 " "
y[1] (numeric) = -5.328190189145063 " "
absolute error = 2.753353101070388000000000000000E-14 " "
relative error = 5.1675203086400960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93899999999998 " "
y[1] (analytic) = -5.327111608135087 " "
y[1] (numeric) = -5.327111608135115 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 5.3352945312805010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.937999999999980 " "
y[1] (analytic) = -5.326033027125138 " "
y[1] (numeric) = -5.326033027125167 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 5.3363749878481970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.936999999999979 " "
y[1] (analytic) = -5.324954446115190 " "
y[1] (numeric) = -5.3249544461152185 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 5.5042513784295580000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.935999999999979 " "
y[1] (analytic) = -5.32387586510524 " "
y[1] (numeric) = -5.32387586510527 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 5.6721957902388690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.934999999999978 " "
y[1] (analytic) = -5.322797284095292 " "
y[1] (numeric) = -5.322797284095322 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 5.6733451713513790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.933999999999978 " "
y[1] (analytic) = -5.321718703085343 " "
y[1] (numeric) = -5.321718703085374 " "
absolute error = 3.10862446895043830000000000000E-14 " "
relative error = 5.8413919306711360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.932999999999978 " "
y[1] (analytic) = -5.320640122075394 " "
y[1] (numeric) = -5.320640122075425 " "
absolute error = 3.10862446895043830000000000000E-14 " "
relative error = 5.842576076612890000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.931999999999977 " "
y[1] (analytic) = -5.319561541065445 " "
y[1] (numeric) = -5.319561541065477 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 6.010725294250551000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.930999999999977 " "
y[1] (analytic) = -5.318482960055497 " "
y[1] (numeric) = -5.318482960055529 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 6.011944261051251000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.929999999999977 " "
y[1] (analytic) = -5.317404379045548 " "
y[1] (numeric) = -5.3174043790455805 " "
absolute error = 3.286260152890463400000000000000E-14 " "
relative error = 6.180196047982970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.928999999999976 " "
y[1] (analytic) = -5.316325798035600 " "
y[1] (numeric) = -5.316325798035632 " "
absolute error = 3.286260152890463400000000000000E-14 " "
relative error = 6.1814498917744040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.927999999999976 " "
y[1] (analytic) = -5.31524721702565 " "
y[1] (numeric) = -5.315247217025684 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 6.3498043591453680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.926999999999976 " "
y[1] (analytic) = -5.314168636015702 " "
y[1] (numeric) = -5.314168636015736 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 6.3510931361616340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.925999999999975 " "
y[1] (analytic) = -5.313090055005753 " "
y[1] (numeric) = -5.313090055005787 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 6.5195503952863790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.924999999999975 " "
y[1] (analytic) = -5.312011473995804 " "
y[1] (numeric) = -5.312011473995839 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 6.5208741618641020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.923999999999975 " "
y[1] (analytic) = -5.310932892985855 " "
y[1] (numeric) = -5.310932892985890 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 6.6894343242268550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.922999999999974 " "
y[1] (analytic) = -5.309854311975907 " "
y[1] (numeric) = -5.3098543119759425 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 6.6907931368054100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.921999999999974 " "
y[1] (analytic) = -5.308775730965958 " "
y[1] (numeric) = -5.308775730965994 " "
absolute error = 3.641531520770513500000000000000E-14 " "
relative error = 6.8594563140604150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.920999999999974 " "
y[1] (analytic) = -5.3076971499560095 " "
y[1] (numeric) = -5.307697149956046 " "
absolute error = 3.641531520770513500000000000000E-14 " "
relative error = 6.860850229182150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.919999999999973 " "
y[1] (analytic) = -5.30661856894606 " "
y[1] (numeric) = -5.306618568946098 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 7.0296165331540030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.918999999999973 " "
y[1] (analytic) = -5.305539987936112 " "
y[1] (numeric) = -5.305539987936150 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 7.0310456074644620000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.917999999999973 " "
y[1] (analytic) = -5.304461406926163 " "
y[1] (numeric) = -5.304461406926201 " "
absolute error = 3.819167204710538500000000000000E-14 " "
relative error = 7.1999151501484390000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.916999999999972 " "
y[1] (analytic) = -5.303382825916215 " "
y[1] (numeric) = -5.303382825916253 " "
absolute error = 3.819167204710538500000000000000E-14 " "
relative error = 7.2013794403965880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.915999999999972 " "
y[1] (analytic) = -5.302304244906265 " "
y[1] (numeric) = -5.3023042449063045 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 7.3703523339589820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.914999999999972 " "
y[1] (analytic) = -5.301225663896316 " "
y[1] (numeric) = -5.301225663896356 " "
absolute error = 3.996802888650563500000000000000E-14 " "
relative error = 7.5393939855655510000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.913999999999971 " "
y[1] (analytic) = -5.300147082886368 " "
y[1] (numeric) = -5.300147082886408 " "
absolute error = 3.996802888650563500000000000000E-14 " "
relative error = 7.5409282537758830000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.912999999999971 " "
y[1] (analytic) = -5.299068501876419 " "
y[1] (numeric) = -5.29906850187646 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 7.7100734387069040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.911999999999970 " "
y[1] (analytic) = -5.2979899208664705 " "
y[1] (numeric) = -5.297989920866511 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 7.7116430790649470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.91099999999997 " "
y[1] (analytic) = -5.296911339856521 " "
y[1] (numeric) = -5.296911339856563 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 7.8808919099326720000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90999999999997 " "
y[1] (analytic) = -5.295832758846573 " "
y[1] (numeric) = -5.295832758846615 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 7.8824969795680950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90899999999997 " "
y[1] (analytic) = -5.294754177836624 " "
y[1] (numeric) = -5.2947541778366665 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 8.0518495691569940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.907999999999970 " "
y[1] (analytic) = -5.2936755968266755 " "
y[1] (numeric) = -5.293675596826718 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 8.0534901253039280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.906999999999969 " "
y[1] (analytic) = -5.292597015816726 " "
y[1] (numeric) = -5.29259701581677 " "
absolute error = 4.352074256530613600000000000000E-14 " "
relative error = 8.2229465865710240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.905999999999969 " "
y[1] (analytic) = -5.291518434806778 " "
y[1] (numeric) = -5.291518434806822 " "
absolute error = 4.352074256530613600000000000000E-14 " "
relative error = 8.2246226865682860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.904999999999968 " "
y[1] (analytic) = -5.290439853796829 " "
y[1] (numeric) = -5.290439853796873 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 8.3941831326434960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.903999999999968 " "
y[1] (analytic) = -5.289361272786880 " "
y[1] (numeric) = -5.289361272786925 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 8.3958948339348170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.902999999999968 " "
y[1] (analytic) = -5.288282691776931 " "
y[1] (numeric) = -5.288282691776977 " "
absolute error = 4.52970994047063870000000000000E-14 " "
relative error = 8.5655593781212880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.901999999999967 " "
y[1] (analytic) = -5.287204110766983 " "
y[1] (numeric) = -5.2872041107670285 " "
absolute error = 4.52970994047063870000000000000E-14 " "
relative error = 8.5673067382555430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.900999999999967 " "
y[1] (analytic) = -5.286125529757034 " "
y[1] (numeric) = -5.28612552975708 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 8.7370754940299960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.899999999999967 " "
y[1] (analytic) = -5.285046948747086 " "
y[1] (numeric) = -5.285046948747132 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 8.7388585706614310000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.898999999999966 " "
y[1] (analytic) = -5.2839683677371365 " "
y[1] (numeric) = -5.283968367737184 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 8.9087316516744930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.897999999999966 " "
y[1] (analytic) = -5.282889786727188 " "
y[1] (numeric) = -5.282889786727235 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 8.9105505025629530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.896999999999966 " "
y[1] (analytic) = -5.281811205717239 " "
y[1] (numeric) = -5.281811205717287 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 9.0805280226395090000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.895999999999965 " "
y[1] (analytic) = -5.280732624707290 " "
y[1] (numeric) = -5.280732624707339 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 9.0823827056506690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.894999999999965 " "
y[1] (analytic) = -5.279654043697342 " "
y[1] (numeric) = -5.27965404369739 " "
absolute error = 4.88498130835068900000000000000E-14 " "
relative error = 9.2524647787901960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.893999999999965 " "
y[1] (analytic) = -5.278575462687393 " "
y[1] (numeric) = -5.278575462687442 " "
absolute error = 4.88498130835068900000000000000E-14 " "
relative error = 9.2543553518957930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.892999999999964 " "
y[1] (analytic) = -5.277496881677444 " "
y[1] (numeric) = -5.277496881677494 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 9.4245420922727050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.891999999999964 " "
y[1] (analytic) = -5.276418300667495 " "
y[1] (numeric) = -5.276418300667546 " "
absolute error = 5.06261699229071400000000000000E-14 " "
relative error = 9.5947984102213160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.890999999999964 " "
y[1] (analytic) = -5.275339719657547 " "
y[1] (numeric) = -5.275339719657597 " "
absolute error = 5.06261699229071400000000000000E-14 " "
relative error = 9.5967601355147570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.889999999999963 " "
y[1] (analytic) = -5.2742611386475975 " "
y[1] (numeric) = -5.274261138647649 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 9.7671213063629880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.888999999999963 " "
y[1] (analytic) = -5.273182557637650 " "
y[1] (numeric) = -5.273182557637700 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 9.7691190812262240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.887999999999963 " "
y[1] (analytic) = -5.2721039766277 " "
y[1] (numeric) = -5.272103976627752 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 9.9395852196046130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.886999999999962 " "
y[1] (analytic) = -5.271025395617752 " "
y[1] (numeric) = -5.271025395617804 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 9.9416191023997020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.885999999999962 " "
y[1] (analytic) = -5.269946814607803 " "
y[1] (numeric) = -5.269946814607856 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.0112190323114957000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.884999999999962 " "
y[1] (analytic) = -5.268868233597854 " "
y[1] (numeric) = -5.268868233597908 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.0114260372311092000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.883999999999961 " "
y[1] (analytic) = -5.267789652587905 " "
y[1] (numeric) = -5.267789652587960 " "
absolute error = 5.41788836017076400000000000000E-14 " "
relative error = 1.028493679034644000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.882999999999961 " "
y[1] (analytic) = -5.266711071577957 " "
y[1] (numeric) = -5.266711071578011 " "
absolute error = 5.41788836017076400000000000000E-14 " "
relative error = 1.0287043064520175000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.881999999999960 " "
y[1] (analytic) = -5.265632490568008 " "
y[1] (numeric) = -5.265632490568063 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 1.0457824795035714000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.88099999999996 " "
y[1] (analytic) = -5.264553909558060 " "
y[1] (numeric) = -5.264553909558114 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 1.0459967352871205000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87999999999996 " "
y[1] (analytic) = -5.26347532854811 " "
y[1] (numeric) = -5.263475328548166 " "
absolute error = 5.59552404411078900000000000000E-14 " "
relative error = 1.0630854511204240000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87899999999996 " "
y[1] (analytic) = -5.262396747538162 " "
y[1] (numeric) = -5.262396747538218 " "
absolute error = 5.59552404411078900000000000000E-14 " "
relative error = 1.0633033411493478000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.877999999999960 " "
y[1] (analytic) = -5.261318166528213 " "
y[1] (numeric) = -5.26131816652827 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 1.0804026113158881000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.876999999999959 " "
y[1] (analytic) = -5.260239585518264 " "
y[1] (numeric) = -5.260239585518321 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 1.080624141480193000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.875999999999959 " "
y[1] (analytic) = -5.259161004508315 " "
y[1] (numeric) = -5.259161004508373 " "
absolute error = 5.77315972805081400000000000000E-14 " "
relative error = 1.0977339775492485000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.874999999999958 " "
y[1] (analytic) = -5.258082423498367 " "
y[1] (numeric) = -5.258082423498425 " "
absolute error = 5.77315972805081400000000000000E-14 " "
relative error = 1.0979591537497713000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.873999999999958 " "
y[1] (analytic) = -5.257003842488418 " "
y[1] (numeric) = -5.257003842488476 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 1.1150795673084467000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.872999999999958 " "
y[1] (analytic) = -5.2559252614784695 " "
y[1] (numeric) = -5.255925261478528 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 1.1153083954568786000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.871999999999957 " "
y[1] (analytic) = -5.25484668046852 " "
y[1] (numeric) = -5.25484668046858 " "
absolute error = 5.95079541199083900000000000000E-14 " "
relative error = 1.1324393981101401000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.870999999999957 " "
y[1] (analytic) = -5.253768099458571 " "
y[1] (numeric) = -5.2537680994586315 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 1.1495774346384391000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.869999999999957 " "
y[1] (analytic) = -5.252689518448623 " "
y[1] (numeric) = -5.252689518448683 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 1.149813487499761000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.868999999999956 " "
y[1] (analytic) = -5.251610937438674 " "
y[1] (numeric) = -5.251610937438735 " "
absolute error = 6.12843109593086400000000000000E-14 " "
relative error = 1.1669621319891292000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.867999999999956 " "
y[1] (analytic) = -5.250532356428725 " "
y[1] (numeric) = -5.250532356428787 " "
absolute error = 6.12843109593086400000000000000E-14 " "
relative error = 1.1672018530515757000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.866999999999956 " "
y[1] (analytic) = -5.249453775418776 " "
y[1] (numeric) = -5.249453775418838 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 1.1843611171535451000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.865999999999955 " "
y[1] (analytic) = -5.248375194408828 " "
y[1] (numeric) = -5.24837519440889 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 1.184604512368743000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.864999999999955 " "
y[1] (analytic) = -5.247296613398879 " "
y[1] (numeric) = -5.247296613398942 " "
absolute error = 6.30606677987088900000000000000E-14 " "
relative error = 1.201774407752834000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.863999999999955 " "
y[1] (analytic) = -5.2462180323889305 " "
y[1] (numeric) = -5.2462180323889935 " "
absolute error = 6.30606677987088900000000000000E-14 " "
relative error = 1.2020214830833753000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.862999999999954 " "
y[1] (analytic) = -5.245139451378981 " "
y[1] (numeric) = -5.245139451379045 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 1.2192020214371316000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.861999999999954 " "
y[1] (analytic) = -5.244060870369033 " "
y[1] (numeric) = -5.244060870369097 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 1.2194527828565963000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.860999999999954 " "
y[1] (analytic) = -5.242982289359084 " "
y[1] (numeric) = -5.242982289359149 " "
absolute error = 6.48370246381091400000000000000E-14 " "
relative error = 1.2366439758856212000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.859999999999953 " "
y[1] (analytic) = -5.2419037083491355 " "
y[1] (numeric) = -5.2419037083492 " "
absolute error = 6.48370246381091400000000000000E-14 " "
relative error = 1.2368984293786019000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.858999999999953 " "
y[1] (analytic) = -5.240825127339186 " "
y[1] (numeric) = -5.240825127339252 " "
absolute error = 6.57252030578092700000000000000E-14 " "
relative error = 1.2541002888065936000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.857999999999953 " "
y[1] (analytic) = -5.239746546329238 " "
y[1] (numeric) = -5.239746546329304 " "
absolute error = 6.57252030578092700000000000000E-14 " "
relative error = 1.2543584403687194000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.856999999999952 " "
y[1] (analytic) = -5.238667965319289 " "
y[1] (numeric) = -5.2386679653193555 " "
absolute error = 6.66133814775093900000000000000E-14 " "
relative error = 1.2715709779375070000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.855999999999952 " "
y[1] (analytic) = -5.237589384309340 " "
y[1] (numeric) = -5.237589384309407 " "
absolute error = 6.66133814775093900000000000000E-14 " "
relative error = 1.271832833575467800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.854999999999952 " "
y[1] (analytic) = -5.2365108032993914 " "
y[1] (numeric) = -5.236510803299459 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 1.2890560610450474000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.853999999999951 " "
y[1] (analytic) = -5.235432222289443 " "
y[1] (numeric) = -5.235432222289510 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 1.2893216267766186000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.852999999999951 " "
y[1] (analytic) = -5.234353641279494 " "
y[1] (numeric) = -5.234353641279562 " "
absolute error = 6.83897383169096400000000000000E-14 " "
relative error = 1.3065555559251885000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.851999999999950 " "
y[1] (analytic) = -5.233275060269546 " "
y[1] (numeric) = -5.233275060269614 " "
absolute error = 6.83897383169096400000000000000E-14 " "
relative error = 1.3068248377792538000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.85099999999995 " "
y[1] (analytic) = -5.2321964792595965 " "
y[1] (numeric) = -5.232196479259666 " "
absolute error = 6.92779167366097700000000000000E-14 " "
relative error = 1.3240694804032518000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.84999999999995 " "
y[1] (analytic) = -5.231117898249647 " "
y[1] (numeric) = -5.2311178982497175 " "
absolute error = 7.01660951563098900000000000000E-14 " "
relative error = 1.3413212342200842000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.84899999999995 " "
y[1] (analytic) = -5.230039317239699 " "
y[1] (numeric) = -5.230039317239770 " "
absolute error = 7.01660951563098900000000000000E-14 " "
relative error = 1.3415978523339675000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.847999999999950 " "
y[1] (analytic) = -5.22896073622975 " "
y[1] (numeric) = -5.228960736229821 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 1.3588603387992249000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.846999999999949 " "
y[1] (analytic) = -5.227882155219802 " "
y[1] (numeric) = -5.227882155219873 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 1.3591406896015354000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.845999999999949 " "
y[1] (analytic) = -5.226803574209852 " "
y[1] (numeric) = -5.226803574209924 " "
absolute error = 7.19424519957101400000000000000E-14 " "
relative error = 1.3764139205591985000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.844999999999948 " "
y[1] (analytic) = -5.225724993199904 " "
y[1] (numeric) = -5.225724993199976 " "
absolute error = 7.19424519957101400000000000000E-14 " "
relative error = 1.3766980101196855000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.843999999999948 " "
y[1] (analytic) = -5.224646412189955 " "
y[1] (numeric) = -5.224646412190028 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 1.3939819974321035000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.842999999999948 " "
y[1] (analytic) = -5.223567831180007 " "
y[1] (numeric) = -5.2235678311800795 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 1.3942698318317387000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.841999999999947 " "
y[1] (analytic) = -5.2224892501700575 " "
y[1] (numeric) = -5.222489250170131 " "
absolute error = 7.3718808835110390000000000000E-14 " "
relative error = 1.4115645873796662000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.840999999999947 " "
y[1] (analytic) = -5.221410669160110 " "
y[1] (numeric) = -5.221410669160183 " "
absolute error = 7.3718808835110390000000000000E-14 " "
relative error = 1.411856172710668000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.839999999999947 " "
y[1] (analytic) = -5.22033208815016 " "
y[1] (numeric) = -5.220332088150235 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 1.4291617083933011000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.838999999999946 " "
y[1] (analytic) = -5.219253507140212 " "
y[1] (numeric) = -5.219253507140286 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 1.4294570507591606000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.837999999999946 " "
y[1] (analytic) = -5.218174926130263 " "
y[1] (numeric) = -5.218174926130338 " "
absolute error = 7.54951656745106400000000000000E-14 " "
relative error = 1.4467733784941736000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.836999999999946 " "
y[1] (analytic) = -5.217096345120314 " "
y[1] (numeric) = -5.21709634512039 " "
absolute error = 7.54951656745106400000000000000E-14 " "
relative error = 1.4470724840096777000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.835999999999945 " "
y[1] (analytic) = -5.216017764110365 " "
y[1] (numeric) = -5.2160177641104415 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 1.46439961573326000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.834999999999945 " "
y[1] (analytic) = -5.214939183100417 " "
y[1] (numeric) = -5.214939183100493 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 1.4647024905245182000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.833999999999945 " "
y[1] (analytic) = -5.213860602090468 " "
y[1] (numeric) = -5.213860602090545 " "
absolute error = 7.7271522513910900000000000000E-14 " "
relative error = 1.4820404381914107000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.832999999999944 " "
y[1] (analytic) = -5.212782021080520 " "
y[1] (numeric) = -5.212782021080597 " "
absolute error = 7.7271522513910900000000000000E-14 " "
relative error = 1.4823470883958780000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.831999999999944 " "
y[1] (analytic) = -5.21170344007057 " "
y[1] (numeric) = -5.211703440070648 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 1.499695863979410800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.830999999999944 " "
y[1] (analytic) = -5.210624859060622 " "
y[1] (numeric) = -5.2106248590607 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 1.5000062957459145000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.829999999999943 " "
y[1] (analytic) = -5.209546278050673 " "
y[1] (numeric) = -5.209546278050752 " "
absolute error = 7.90478793533111500000000000000E-14 " "
relative error = 1.517365911238043000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.828999999999943 " "
y[1] (analytic) = -5.2084676970407235 " "
y[1] (numeric) = -5.2084676970408035 " "
absolute error = 7.99360577730112700000000000000E-14 " "
relative error = 1.53473271646531000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.827999999999943 " "
y[1] (analytic) = -5.207389116030775 " "
y[1] (numeric) = -5.207389116030855 " "
absolute error = 7.99360577730112700000000000000E-14 " "
relative error = 1.5350505981381488000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.826999999999942 " "
y[1] (analytic) = -5.206310535020826 " "
y[1] (numeric) = -5.206310535020907 " "
absolute error = 8.0824236192711400000000000000E-14 " "
relative error = 1.5524282627599373000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.825999999999942 " "
y[1] (analytic) = -5.205231954010878 " "
y[1] (numeric) = -5.205231954010959 " "
absolute error = 8.0824236192711400000000000000E-14 " "
relative error = 1.5527499428806912000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.824999999999942 " "
y[1] (analytic) = -5.204153373000929 " "
y[1] (numeric) = -5.20415337300101 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 1.5701384789375025000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.823999999999941 " "
y[1] (analytic) = -5.20307479199098 " "
y[1] (numeric) = -5.203074791991062 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 1.570463963696818200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.822999999999941 " "
y[1] (analytic) = -5.201996210981031 " "
y[1] (numeric) = -5.201996210981114 " "
absolute error = 8.26005930321116500000000000000E-14 " "
relative error = 1.587863383247913000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.821999999999940 " "
y[1] (analytic) = -5.200917629971083 " "
y[1] (numeric) = -5.2009176299711655 " "
absolute error = 8.26005930321116500000000000000E-14 " "
relative error = 1.5881926788479228000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.82099999999994 " "
y[1] (analytic) = -5.199839048961134 " "
y[1] (numeric) = -5.199839048961217 " "
absolute error = 8.34887714518117700000000000000E-14 " "
relative error = 1.6056029939713584000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.81999999999994 " "
y[1] (analytic) = -5.198760467951185 " "
y[1] (numeric) = -5.198760467951269 " "
absolute error = 8.34887714518117700000000000000E-14 " "
relative error = 1.6059361066257094000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8189999999999396 " "
y[1] (analytic) = -5.197681886941236 " "
y[1] (numeric) = -5.197681886941320 " "
absolute error = 8.4376949871511900000000000000E-14 " "
relative error = 1.6233573294183760000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.817999999999940 " "
y[1] (analytic) = -5.196603305931288 " "
y[1] (numeric) = -5.196603305931372 " "
absolute error = 8.4376949871511900000000000000E-14 " "
relative error = 1.6236942653522526000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.816999999999939 " "
y[1] (analytic) = -5.195524724921339 " "
y[1] (numeric) = -5.195524724921424 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 1.6411264079299120000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8159999999999386 " "
y[1] (analytic) = -5.1944461439113905 " "
y[1] (numeric) = -5.194446143911476 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 1.6414671733800637000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.814999999999938 " "
y[1] (analytic) = -5.193367562901441 " "
y[1] (numeric) = -5.1933675629015275 " "
absolute error = 8.61533067109121500000000000000E-14 " "
relative error = 1.6589102478773876000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.813999999999938 " "
y[1] (analytic) = -5.192288981891493 " "
y[1] (numeric) = -5.192288981891580 " "
absolute error = 8.61533067109121500000000000000E-14 " "
relative error = 1.6592548490921524000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8129999999999376 " "
y[1] (analytic) = -5.191210400881544 " "
y[1] (numeric) = -5.191210400881630 " "
absolute error = 8.70414851306122700000000000000E-14 " "
relative error = 1.6767088676627584000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.811999999999937 " "
y[1] (analytic) = -5.1901318198715956 " "
y[1] (numeric) = -5.190131819871683 " "
absolute error = 8.70414851306122700000000000000E-14 " "
relative error = 1.6770573109020898000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.810999999999937 " "
y[1] (analytic) = -5.189053238861646 " "
y[1] (numeric) = -5.189053238861734 " "
absolute error = 8.7929663550312400000000000000E-14 " "
relative error = 1.6945222857185804000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8099999999999365 " "
y[1] (analytic) = -5.187974657851698 " "
y[1] (numeric) = -5.187974657851786 " "
absolute error = 8.7929663550312400000000000000E-14 " "
relative error = 1.6948745772540730000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.808999999999936 " "
y[1] (analytic) = -5.186896076841749 " "
y[1] (numeric) = -5.186896076841838 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 1.7123505205080733000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.807999999999936 " "
y[1] (analytic) = -5.1858174958318 " "
y[1] (numeric) = -5.1858174958318894 " "
absolute error = 8.97060203897126500000000000000E-14 " "
relative error = 1.7298337332892177000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8069999999999355 " "
y[1] (analytic) = -5.1847389148218515 " "
y[1] (numeric) = -5.184738914821941 " "
absolute error = 8.97060203897126500000000000000E-14 " "
relative error = 1.7301935905251840000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.805999999999935 " "
y[1] (analytic) = -5.183660333811902 " "
y[1] (numeric) = -5.183660333811993 " "
absolute error = 9.05941988094127700000000000000E-14 " "
relative error = 1.7476877915492703000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.804999999999935 " "
y[1] (analytic) = -5.182581752801954 " "
y[1] (numeric) = -5.182581752802045 " "
absolute error = 9.05941988094127700000000000000E-14 " "
relative error = 1.74805151429465000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8039999999999345 " "
y[1] (analytic) = -5.181503171792005 " "
y[1] (numeric) = -5.181503171792096 " "
absolute error = 9.1482377229112900000000000000E-14 " "
relative error = 1.7655567158028784000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.802999999999934 " "
y[1] (analytic) = -5.1804245907820565 " "
y[1] (numeric) = -5.180424590782148 " "
absolute error = 9.1482377229112900000000000000E-14 " "
relative error = 1.765924310372065000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.801999999999934 " "
y[1] (analytic) = -5.179346009772107 " "
y[1] (numeric) = -5.1793460097722 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 1.7834405246247945000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8009999999999335 " "
y[1] (analytic) = -5.178267428762159 " "
y[1] (numeric) = -5.178267428762251 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 1.7838119973439415000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.799999999999933 " "
y[1] (analytic) = -5.17718884775221 " "
y[1] (numeric) = -5.177188847752303 " "
absolute error = 9.32587340685131500000000000000E-14 " "
relative error = 1.8013392366207284000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.798999999999933 " "
y[1] (analytic) = -5.176110266742262 " "
y[1] (numeric) = -5.176110266742355 " "
absolute error = 9.32587340685131500000000000000E-14 " "
relative error = 1.801714593827776000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7979999999999325 " "
y[1] (analytic) = -5.175031685732312 " "
y[1] (numeric) = -5.175031685732407 " "
absolute error = 9.41469124882132700000000000000E-14 " "
relative error = 1.819252870427413800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.796999999999932 " "
y[1] (analytic) = -5.173953104722364 " "
y[1] (numeric) = -5.173953104722458 " "
absolute error = 9.41469124882132700000000000000E-14 " "
relative error = 1.819632118472114000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.795999999999932 " "
y[1] (analytic) = -5.172874523712415 " "
y[1] (numeric) = -5.17287452371251 " "
absolute error = 9.5035090907913400000000000000E-14 " "
relative error = 1.83718144471267000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7949999999999315 " "
y[1] (analytic) = -5.171795942702467 " "
y[1] (numeric) = -5.171795942702562 " "
absolute error = 9.5035090907913400000000000000E-14 " "
relative error = 1.8375645899566145000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.793999999999931 " "
y[1] (analytic) = -5.1707173616925175 " "
y[1] (numeric) = -5.170717361692613 " "
absolute error = 9.59232693276135300000000000000E-14 " "
relative error = 1.8551249781754695000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.792999999999930 " "
y[1] (analytic) = -5.169638780682570 " "
y[1] (numeric) = -5.169638780682665 " "
absolute error = 9.59232693276135300000000000000E-14 " "
relative error = 1.8555120269921135000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7919999999999305 " "
y[1] (analytic) = -5.16856019967262 " "
y[1] (numeric) = -5.168560199672717 " "
absolute error = 9.68114477473136500000000000000E-14 " "
relative error = 1.8730834895460005000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.79099999999993 " "
y[1] (analytic) = -5.167481618662672 " "
y[1] (numeric) = -5.167481618662769 " "
absolute error = 9.68114477473136500000000000000E-14 " "
relative error = 1.873474448320692000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.78999999999993 " "
y[1] (analytic) = -5.166403037652723 " "
y[1] (numeric) = -5.16640303765282 " "
absolute error = 9.76996261670137800000000000000E-14 " "
relative error = 1.891056997585735000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7889999999999295 " "
y[1] (analytic) = -5.165324456642774 " "
y[1] (numeric) = -5.165324456642872 " "
absolute error = 9.76996261670137800000000000000E-14 " "
relative error = 1.891451872715738000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.787999999999930 " "
y[1] (analytic) = -5.164245875632825 " "
y[1] (numeric) = -5.164245875632924 " "
absolute error = 9.8587804586713900000000000000E-14 " "
relative error = 1.9090455210874904000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.786999999999929 " "
y[1] (analytic) = -5.163167294622876 " "
y[1] (numeric) = -5.163167294622975 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 1.926646520053924800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7859999999999285 " "
y[1] (analytic) = -5.162088713612928 " "
y[1] (numeric) = -5.162088713613027 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 1.9270490788754993000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.784999999999928 " "
y[1] (analytic) = -5.1610101326029785 " "
y[1] (numeric) = -5.161010132603079 " "
absolute error = 1.00364161426114150000000000000E-13 " "
relative error = 1.944661197080329000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.783999999999928 " "
y[1] (analytic) = -5.15993155159303 " "
y[1] (numeric) = -5.1599315515931305 " "
absolute error = 1.00364161426114150000000000000E-13 " "
relative error = 1.945067689805470800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7829999999999275 " "
y[1] (analytic) = -5.158852970583081 " "
y[1] (numeric) = -5.158852970583182 " "
absolute error = 1.01252339845814280000000000000E-13 " "
relative error = 1.9626909396948794000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.781999999999927 " "
y[1] (analytic) = -5.157774389573133 " "
y[1] (numeric) = -5.157774389573234 " "
absolute error = 1.01252339845814280000000000000E-13 " "
relative error = 1.9631013727646607000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.780999999999927 " "
y[1] (analytic) = -5.1566958085631835 " "
y[1] (numeric) = -5.156695808563286 " "
absolute error = 1.0214051826551440000000000000E-13 " "
relative error = 1.9807357668044015000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7799999999999265 " "
y[1] (analytic) = -5.155617227553235 " "
y[1] (numeric) = -5.155617227553337 " "
absolute error = 1.0214051826551440000000000000E-13 " "
relative error = 1.9811501466719336000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.778999999999926 " "
y[1] (analytic) = -5.154538646543286 " "
y[1] (numeric) = -5.154538646543390 " "
absolute error = 1.03028696685214530000000000000E-13 " "
relative error = 1.9987956973473694000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.777999999999926 " "
y[1] (analytic) = -5.153460065533338 " "
y[1] (numeric) = -5.153460065533440 " "
absolute error = 1.03028696685214530000000000000E-13 " "
relative error = 1.9992140304778314000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7769999999999255 " "
y[1] (analytic) = -5.152381484523389 " "
y[1] (numeric) = -5.1523814845234925 " "
absolute error = 1.03916875104914650000000000000E-13 " "
relative error = 2.016870750293974000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.775999999999925 " "
y[1] (analytic) = -5.15130290351344 " "
y[1] (numeric) = -5.151302903513544 " "
absolute error = 1.03916875104914650000000000000E-13 " "
relative error = 2.017293043164638300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.774999999999925 " "
y[1] (analytic) = -5.150224322503491 " "
y[1] (numeric) = -5.150224322503596 " "
absolute error = 1.04805053524614780000000000000E-13 " "
relative error = 2.034960944646188000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7739999999999245 " "
y[1] (analytic) = -5.149145741493543 " "
y[1] (numeric) = -5.149145741493648 " "
absolute error = 1.04805053524614780000000000000E-13 " "
relative error = 2.035387203746449000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.772999999999924 " "
y[1] (analytic) = -5.148067160483594 " "
y[1] (numeric) = -5.148067160483700 " "
absolute error = 1.0569323194431490000000000000E-13 " "
relative error = 2.053066299437834000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.771999999999924 " "
y[1] (analytic) = -5.146988579473645 " "
y[1] (numeric) = -5.146988579473751 " "
absolute error = 1.0569323194431490000000000000E-13 " "
relative error = 2.0534965312692335000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7709999999999235 " "
y[1] (analytic) = -5.145909998463696 " "
y[1] (numeric) = -5.145909998463803 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 2.0711868337346503000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.769999999999923 " "
y[1] (analytic) = -5.144831417453748 " "
y[1] (numeric) = -5.1448314174538545 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 2.071621044810905100000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.768999999999923 " "
y[1] (analytic) = -5.143752836443799 " "
y[1] (numeric) = -5.143752836443906 " "
absolute error = 1.07469588783715150000000000000E-13 " "
relative error = 2.089322566634358000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7679999999999225 " "
y[1] (analytic) = -5.1426742554338505 " "
y[1] (numeric) = -5.142674255433958 " "
absolute error = 1.07469588783715150000000000000E-13 " "
relative error = 2.0897607634813867000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.766999999999922 " "
y[1] (analytic) = -5.141595674423901 " "
y[1] (numeric) = -5.14159567442401 " "
absolute error = 1.08357767203415280000000000000E-13 " "
relative error = 2.107473517266727000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.765999999999922 " "
y[1] (analytic) = -5.140517093413952 " "
y[1] (numeric) = -5.140517093414061 " "
absolute error = 1.0924594562311540000000000000E-13 " "
relative error = 2.1251937040163074000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7649999999999215 " "
y[1] (analytic) = -5.139438512404004 " "
y[1] (numeric) = -5.139438512404113 " "
absolute error = 1.0924594562311540000000000000E-13 " "
relative error = 2.1256397047936457000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.763999999999921 " "
y[1] (analytic) = -5.138359931394055 " "
y[1] (numeric) = -5.138359931394165 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 2.1433711439699743000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.762999999999920 " "
y[1] (analytic) = -5.137281350384106 " "
y[1] (numeric) = -5.1372813503842165 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 2.143821148409187000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7619999999999205 " "
y[1] (analytic) = -5.136202769374157 " "
y[1] (numeric) = -5.136202769374268 " "
absolute error = 1.11022302462515650000000000000E-13 " "
relative error = 2.161563852667826900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.76099999999992 " "
y[1] (analytic) = -5.135124188364209 " "
y[1] (numeric) = -5.13512418836432 " "
absolute error = 1.11022302462515650000000000000E-13 " "
relative error = 2.1620178673396748000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.75999999999992 " "
y[1] (analytic) = -5.13404560735426 " "
y[1] (numeric) = -5.134045607354372 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 2.179771849356182000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7589999999999195 " "
y[1] (analytic) = -5.1329670263443115 " "
y[1] (numeric) = -5.132967026344423 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 2.180229880843754200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.757999999999920 " "
y[1] (analytic) = -5.131888445334362 " "
y[1] (numeric) = -5.131888445334475 " "
absolute error = 1.1279865930191590000000000000E-13 " "
relative error = 2.1979951533137163000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.756999999999919 " "
y[1] (analytic) = -5.130809864324414 " "
y[1] (numeric) = -5.130809864324527 " "
absolute error = 1.1279865930191590000000000000E-13 " "
relative error = 2.198457208212458000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7559999999999185 " "
y[1] (analytic) = -5.129731283314465 " "
y[1] (numeric) = -5.1297312833145785 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 2.2162337838515345000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.754999999999918 " "
y[1] (analytic) = -5.1286527023045165 " "
y[1] (numeric) = -5.12865270230463 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 2.2166998687692738000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.753999999999918 " "
y[1] (analytic) = -5.127574121294567 " "
y[1] (numeric) = -5.127574121294682 " "
absolute error = 1.14575016141316150000000000000E-13 " "
relative error = 2.234487760313238000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7529999999999175 " "
y[1] (analytic) = -5.126495540284619 " "
y[1] (numeric) = -5.126495540284734 " "
absolute error = 1.14575016141316150000000000000E-13 " "
relative error = 2.234957881870214800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.751999999999917 " "
y[1] (analytic) = -5.12541695927467 " "
y[1] (numeric) = -5.125416959274785 " "
absolute error = 1.15463194561016280000000000000E-13 " "
relative error = 2.252757102074993000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.750999999999917 " "
y[1] (analytic) = -5.124338378264722 " "
y[1] (numeric) = -5.124338378264837 " "
absolute error = 1.15463194561016280000000000000E-13 " "
relative error = 2.253231266903887000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7499999999999165 " "
y[1] (analytic) = -5.123259797254772 " "
y[1] (numeric) = -5.123259797254889 " "
absolute error = 1.1635137298071640000000000000E-13 " "
relative error = 2.2710418285456005000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.748999999999916 " "
y[1] (analytic) = -5.122181216244824 " "
y[1] (numeric) = -5.1221812162449405 " "
absolute error = 1.1635137298071640000000000000E-13 " "
relative error = 2.2715200432915564000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.747999999999916 " "
y[1] (analytic) = -5.121102635234875 " "
y[1] (numeric) = -5.121102635234992 " "
absolute error = 1.17239551400416530000000000000E-13 " "
relative error = 2.2893419591665623000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7469999999999155 " "
y[1] (analytic) = -5.120024054224927 " "
y[1] (numeric) = -5.120024054225044 " "
absolute error = 1.17239551400416530000000000000E-13 " "
relative error = 2.2898242304872204000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.745999999999915 " "
y[1] (analytic) = -5.1189454732149775 " "
y[1] (numeric) = -5.118945473215096 " "
absolute error = 1.18127729820116660000000000000E-13 " "
relative error = 2.3076575134121516000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.744999999999915 " "
y[1] (analytic) = -5.117866892205028 " "
y[1] (numeric) = -5.117866892205147 " "
absolute error = 1.19015908239816780000000000000E-13 " "
relative error = 2.325498313000065000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7439999999999145 " "
y[1] (analytic) = -5.11678831119508 " "
y[1] (numeric) = -5.116788311195199 " "
absolute error = 1.19015908239816780000000000000E-13 " "
relative error = 2.3259885107894832000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.742999999999914 " "
y[1] (analytic) = -5.115709730185130 " "
y[1] (numeric) = -5.115709730185250 " "
absolute error = 1.1990408665951690000000000000E-13 " "
relative error = 2.343840698232457000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.741999999999914 " "
y[1] (analytic) = -5.114631149175183 " "
y[1] (numeric) = -5.1146311491753025 " "
absolute error = 1.1990408665951690000000000000E-13 " "
relative error = 2.344334970838579000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7409999999999135 " "
y[1] (analytic) = -5.113552568165233 " "
y[1] (numeric) = -5.113552568165354 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 2.36219855900607000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.739999999999913 " "
y[1] (analytic) = -5.112473987155285 " "
y[1] (numeric) = -5.112473987155406 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 2.3626969131324424000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.738999999999913 " "
y[1] (analytic) = -5.111395406145336 " "
y[1] (numeric) = -5.111395406145458 " "
absolute error = 1.21680443498917160000000000000E-13 " "
relative error = 2.3805719149143306000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7379999999999125 " "
y[1] (analytic) = -5.110316825135388 " "
y[1] (numeric) = -5.110316825135510 " "
absolute error = 1.21680443498917160000000000000E-13 " "
relative error = 2.381074357277124000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.736999999999912 " "
y[1] (analytic) = -5.1092382441254385 " "
y[1] (numeric) = -5.109238244125561 " "
absolute error = 1.22568621918617280000000000000E-13 " "
relative error = 2.398960785583755000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.735999999999912 " "
y[1] (analytic) = -5.10815966311549 " "
y[1] (numeric) = -5.108159663115613 " "
absolute error = 1.22568621918617280000000000000E-13 " "
relative error = 2.3994673229117924000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7349999999999115 " "
y[1] (analytic) = -5.107081082105541 " "
y[1] (numeric) = -5.1070810821056645 " "
absolute error = 1.2345680033831741000000000000E-13 " "
relative error = 2.41736519067401980000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.733999999999911 " "
y[1] (analytic) = -5.106002501095593 " "
y[1] (numeric) = -5.106002501095716 " "
absolute error = 1.2345680033831741000000000000E-13 " "
relative error = 2.417875829708805000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.732999999999910 " "
y[1] (analytic) = -5.1049239200856436 " "
y[1] (numeric) = -5.104923920085768 " "
absolute error = 1.24344978758017530000000000000E-13 " "
relative error = 2.4357851498780306000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7319999999999105 " "
y[1] (analytic) = -5.103845339075695 " "
y[1] (numeric) = -5.10384533907582 " "
absolute error = 1.24344978758017530000000000000E-13 " "
relative error = 2.4362998973737782000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.73099999999991 " "
y[1] (analytic) = -5.102766758065746 " "
y[1] (numeric) = -5.102766758065871 " "
absolute error = 1.25233157177717660000000000000E-13 " "
relative error = 2.4542206829219942000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.72999999999991 " "
y[1] (analytic) = -5.101688177055798 " "
y[1] (numeric) = -5.101688177055923 " "
absolute error = 1.25233157177717660000000000000E-13 " "
relative error = 2.4547395456456564000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7289999999999095 " "
y[1] (analytic) = -5.100609596045849 " "
y[1] (numeric) = -5.100609596045975 " "
absolute error = 1.26121335597417780000000000000E-13 " "
relative error = 2.4726718095654876000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.727999999999910 " "
y[1] (analytic) = -5.0995310150359 " "
y[1] (numeric) = -5.0995310150360265 " "
absolute error = 1.26121335597417780000000000000E-13 " "
relative error = 2.473194794296783000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.726999999999909 " "
y[1] (analytic) = -5.098452434025951 " "
y[1] (numeric) = -5.098452434026078 " "
absolute error = 1.2700951401711790000000000000E-13 " "
relative error = 2.4911385496015284000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7259999999999085 " "
y[1] (analytic) = -5.097373853016003 " "
y[1] (numeric) = -5.09737385301613 " "
absolute error = 1.2700951401711790000000000000E-13 " "
relative error = 2.491665663132972000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.724999999999908 " "
y[1] (analytic) = -5.096295272006054 " "
y[1] (numeric) = -5.096295272006182 " "
absolute error = 1.27897692436818030000000000000E-13 " "
relative error = 2.509620922856648000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.723999999999908 " "
y[1] (analytic) = -5.095216690996105 " "
y[1] (numeric) = -5.095216690996233 " "
absolute error = 1.27897692436818030000000000000E-13 " "
relative error = 2.5101521719935777000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7229999999999075 " "
y[1] (analytic) = -5.094138109986156 " "
y[1] (numeric) = -5.094138109986285 " "
absolute error = 1.28785870856518160000000000000E-13 " "
relative error = 2.5281189491909584000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.721999999999907 " "
y[1] (analytic) = -5.093059528976207 " "
y[1] (numeric) = -5.093059528976337 " "
absolute error = 1.29674049276218280000000000000E-13 " "
relative error = 2.5460933362050260000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.720999999999907 " "
y[1] (analytic) = -5.091980947966259 " "
y[1] (numeric) = -5.0919809479663884 " "
absolute error = 1.29674049276218280000000000000E-13 " "
relative error = 2.5466326484982270000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7199999999999065 " "
y[1] (analytic) = -5.09090236695631 " "
y[1] (numeric) = -5.09090236695644 " "
absolute error = 1.3056222769591840000000000000E-13 " "
relative error = 2.5646185741718996000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.718999999999906 " "
y[1] (analytic) = -5.089823785946361 " "
y[1] (numeric) = -5.089823785946492 " "
absolute error = 1.3056222769591840000000000000E-13 " "
relative error = 2.5651620407059480000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.717999999999906 " "
y[1] (analytic) = -5.088745204936412 " "
y[1] (numeric) = -5.088745204936544 " "
absolute error = 1.31450406115618530000000000000E-13 " "
relative error = 2.583159518148071500000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7169999999999055 " "
y[1] (analytic) = -5.087666623926464 " "
y[1] (numeric) = -5.087666623926595 " "
absolute error = 1.31450406115618530000000000000E-13 " "
relative error = 2.5837071457754085000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.715999999999905 " "
y[1] (analytic) = -5.086588042916515 " "
y[1] (numeric) = -5.086588042916647 " "
absolute error = 1.32338584535318660000000000000E-13 " "
relative error = 2.601716188115742000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.714999999999905 " "
y[1] (analytic) = -5.085509461906566 " "
y[1] (numeric) = -5.085509461906699 " "
absolute error = 1.32338584535318660000000000000E-13 " "
relative error = 2.6022679837017680000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7139999999999045 " "
y[1] (analytic) = -5.084430880896617 " "
y[1] (numeric) = -5.08443088089675 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 2.620288604091021000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.712999999999904 " "
y[1] (analytic) = -5.083352299886669 " "
y[1] (numeric) = -5.083352299886802 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 2.6208445745141257000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.711999999999904 " "
y[1] (analytic) = -5.08227371887672 " "
y[1] (numeric) = -5.082273718876854 " "
absolute error = 1.3411494137471890000000000000E-13 " "
relative error = 2.6388767861240050000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7109999999999035 " "
y[1] (analytic) = -5.0811951378667715 " "
y[1] (numeric) = -5.081195137866906 " "
absolute error = 1.3411494137471890000000000000E-13 " "
relative error = 2.639436938275591000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.709999999999903 " "
y[1] (analytic) = -5.080116556856822 " "
y[1] (numeric) = -5.080116556856957 " "
absolute error = 1.35003119794419040000000000000E-13 " "
relative error = 2.657480754298842000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.708999999999903 " "
y[1] (analytic) = -5.079037975846874 " "
y[1] (numeric) = -5.079037975847009 " "
absolute error = 1.35003119794419040000000000000E-13 " "
relative error = 2.6580450950833606000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7079999999999025 " "
y[1] (analytic) = -5.077959394836925 " "
y[1] (numeric) = -5.077959394837060 " "
absolute error = 1.35891298214119160000000000000E-13 " "
relative error = 2.6761005287338110000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.706999999999902 " "
y[1] (analytic) = -5.0768808138269765 " "
y[1] (numeric) = -5.076880813827112 " "
absolute error = 1.35891298214119160000000000000E-13 " "
relative error = 2.676669065068787400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.705999999999902 " "
y[1] (analytic) = -5.075802232817027 " "
y[1] (numeric) = -5.075802232817164 " "
absolute error = 1.36779476633819290000000000000E-13 " "
relative error = 2.694736129581389300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7049999999999015 " "
y[1] (analytic) = -5.074723651807079 " "
y[1] (numeric) = -5.074723651807216 " "
absolute error = 1.36779476633819290000000000000E-13 " "
relative error = 2.695308868397453000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.703999999999901 " "
y[1] (analytic) = -5.07364507079713 " "
y[1] (numeric) = -5.073645070797268 " "
absolute error = 1.3766765505351940000000000000E-13 " "
relative error = 2.7133875770283270000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.702999999999900 " "
y[1] (analytic) = -5.072566489787182 " "
y[1] (numeric) = -5.072566489787320 " "
absolute error = 1.3766765505351940000000000000E-13 " "
relative error = 2.7139645252692435000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7019999999999005 " "
y[1] (analytic) = -5.071487908777232 " "
y[1] (numeric) = -5.071487908777371 " "
absolute error = 1.38555833473219540000000000000E-13 " "
relative error = 2.732054891295722700000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7009999999999 " "
y[1] (analytic) = -5.070409327767283 " "
y[1] (numeric) = -5.070409327767423 " "
absolute error = 1.39444011892919660000000000000E-13 " "
relative error = 2.7501529537127684000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6999999999999 " "
y[1] (analytic) = -5.069330746757335 " "
y[1] (numeric) = -5.069330746757474 " "
absolute error = 1.39444011892919660000000000000E-13 " "
relative error = 2.7507380926390900000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6989999999998995 " "
y[1] (analytic) = -5.068252165747386 " "
y[1] (numeric) = -5.068252165747526 " "
absolute error = 1.40332190312619800000000000000E-13 " "
relative error = 2.768847833993394000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.697999999999900 " "
y[1] (analytic) = -5.0671735847374375 " "
y[1] (numeric) = -5.067173584737578 " "
absolute error = 1.40332190312619800000000000000E-13 " "
relative error = 2.7694372013484375000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.696999999999899 " "
y[1] (analytic) = -5.066095003727488 " "
y[1] (numeric) = -5.0660950037276296 " "
absolute error = 1.4122036873231990000000000000E-13 " "
relative error = 2.7875586349725770000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6959999999998985 " "
y[1] (analytic) = -5.06501642271754 " "
y[1] (numeric) = -5.065016422717681 " "
absolute error = 1.4122036873231990000000000000E-13 " "
relative error = 2.788152237748338000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.694999999999898 " "
y[1] (analytic) = -5.063937841707590 " "
y[1] (numeric) = -5.063937841707733 " "
absolute error = 1.42108547152020040000000000000E-13 " "
relative error = 2.806285376996258000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.693999999999898 " "
y[1] (analytic) = -5.062859260697643 " "
y[1] (numeric) = -5.062859260697785 " "
absolute error = 1.42108547152020040000000000000E-13 " "
relative error = 2.806883222198004000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6929999999998975 " "
y[1] (analytic) = -5.061780679687693 " "
y[1] (numeric) = -5.061780679687836 " "
absolute error = 1.42996725571720160000000000000E-13 " "
relative error = 2.82502808044506000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.691999999999897 " "
y[1] (analytic) = -5.060702098677745 " "
y[1] (numeric) = -5.060702098677888 " "
absolute error = 1.42996725571720160000000000000E-13 " "
relative error = 2.825630175091361000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.690999999999897 " "
y[1] (analytic) = -5.059623517667796 " "
y[1] (numeric) = -5.05962351766794 " "
absolute error = 1.4388490399142030000000000000E-13 " "
relative error = 2.8437867657343640000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6899999999998965 " "
y[1] (analytic) = -5.058544936657848 " "
y[1] (numeric) = -5.0585449366579915 " "
absolute error = 1.4388490399142030000000000000E-13 " "
relative error = 2.844393116857122400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.688999999999896 " "
y[1] (analytic) = -5.0574663556478985 " "
y[1] (numeric) = -5.057466355648043 " "
absolute error = 1.44773082411120400000000000000E-13 " "
relative error = 2.8625614533143830000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.687999999999896 " "
y[1] (analytic) = -5.05638777463795 " "
y[1] (numeric) = -5.056387774638095 " "
absolute error = 1.44773082411120400000000000000E-13 " "
relative error = 2.8631720679588607000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6869999999998955 " "
y[1] (analytic) = -5.055309193628001 " "
y[1] (numeric) = -5.055309193628147 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 2.8813521636702316000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.685999999999895 " "
y[1] (analytic) = -5.054230612618053 " "
y[1] (numeric) = -5.054230612618198 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 2.8819670488950860000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.684999999999895 " "
y[1] (analytic) = -5.053152031608104 " "
y[1] (numeric) = -5.05315203160825 " "
absolute error = 1.46549439250520660000000000000E-13 " "
relative error = 2.900158917322009000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6839999999998945 " "
y[1] (analytic) = -5.052073450598155 " "
y[1] (numeric) = -5.052073450598302 " "
absolute error = 1.46549439250520660000000000000E-13 " "
relative error = 2.900778080199319000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.682999999999894 " "
y[1] (analytic) = -5.050994869588206 " "
y[1] (numeric) = -5.0509948695883535 " "
absolute error = 1.4743761767022080000000000000E-13 " "
relative error = 2.918981734824866000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.681999999999894 " "
y[1] (analytic) = -5.049916288578258 " "
y[1] (numeric) = -5.049916288578405 " "
absolute error = 1.4743761767022080000000000000E-13 " "
relative error = 2.9196051824401636000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6809999999998935 " "
y[1] (analytic) = -5.048837707568309 " "
y[1] (numeric) = -5.048837707568457 " "
absolute error = 1.48325796089920900000000000000E-13 " "
relative error = 2.9378206367690840000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.679999999999893 " "
y[1] (analytic) = -5.0477591265583595 " "
y[1] (numeric) = -5.047759126558509 " "
absolute error = 1.49213974509621040000000000000E-13 " "
relative error = 2.9560438754801965000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.678999999999893 " "
y[1] (analytic) = -5.046680545548411 " "
y[1] (numeric) = -5.04668054554856 " "
absolute error = 1.49213974509621040000000000000E-13 " "
relative error = 2.9566756437801495000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6779999999998925 " "
y[1] (analytic) = -5.045601964538462 " "
y[1] (numeric) = -5.045601964538612 " "
absolute error = 1.50102152929321160000000000000E-13 " "
relative error = 2.974910704099734000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.676999999999892 " "
y[1] (analytic) = -5.044523383528514 " "
y[1] (numeric) = -5.044523383528664 " "
absolute error = 1.50102152929321160000000000000E-13 " "
relative error = 2.975546776518827000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.675999999999892 " "
y[1] (analytic) = -5.0434448025185645 " "
y[1] (numeric) = -5.0434448025187155 " "
absolute error = 1.5099033134902130000000000000E-13 " "
relative error = 2.993793672008082000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6749999999998915 " "
y[1] (analytic) = -5.042366221508616 " "
y[1] (numeric) = -5.042366221508767 " "
absolute error = 1.5099033134902130000000000000E-13 " "
relative error = 2.9944340556812390000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.673999999999891 " "
y[1] (analytic) = -5.041287640498667 " "
y[1] (numeric) = -5.041287640498819 " "
absolute error = 1.51878509768721410000000000000E-13 " "
relative error = 3.012692799923198000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.672999999999890 " "
y[1] (analytic) = -5.040209059488719 " "
y[1] (numeric) = -5.040209059488870 " "
absolute error = 1.51878509768721410000000000000E-13 " "
relative error = 3.013337501998936000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6719999999998905 " "
y[1] (analytic) = -5.03913047847877 " "
y[1] (numeric) = -5.039130478478922 " "
absolute error = 1.52766688188421540000000000000E-13 " "
relative error = 3.0316081085985150000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.67099999999989 " "
y[1] (analytic) = -5.038051897468821 " "
y[1] (numeric) = -5.038051897468974 " "
absolute error = 1.52766688188421540000000000000E-13 " "
relative error = 3.0322571362389780000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.66999999999989 " "
y[1] (analytic) = -5.036973316458872 " "
y[1] (numeric) = -5.036973316459026 " "
absolute error = 1.53654866608121670000000000000E-13 " "
relative error = 3.0505396188230194000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6689999999998895 " "
y[1] (analytic) = -5.035894735448924 " "
y[1] (numeric) = -5.0358947354490775 " "
absolute error = 1.53654866608121670000000000000E-13 " "
relative error = 3.051192979204005000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.667999999999890 " "
y[1] (analytic) = -5.034816154438975 " "
y[1] (numeric) = -5.034816154439130 " "
absolute error = 1.5454304502782180000000000000E-13 " "
relative error = 3.069487351421323000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.666999999999889 " "
y[1] (analytic) = -5.033737573429026 " "
y[1] (numeric) = -5.033737573429181 " "
absolute error = 1.5454304502782180000000000000E-13 " "
relative error = 3.0701450517323200000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6659999999998885 " "
y[1] (analytic) = -5.032658992419077 " "
y[1] (numeric) = -5.032658992419233 " "
absolute error = 1.55431223447521920000000000000E-13 " "
relative error = 3.0884513272537445000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.664999999999888 " "
y[1] (analytic) = -5.031580411409129 " "
y[1] (numeric) = -5.031580411409284 " "
absolute error = 1.55431223447521920000000000000E-13 " "
relative error = 3.0891133746979577000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.663999999999888 " "
y[1] (analytic) = -5.03050183039918 " "
y[1] (numeric) = -5.030501830399336 " "
absolute error = 1.56319401867222040000000000000E-13 " "
relative error = 3.1074315672163827000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6629999999998875 " "
y[1] (analytic) = -5.0294232493892315 " "
y[1] (numeric) = -5.029423249389388 " "
absolute error = 1.56319401867222040000000000000E-13 " "
relative error = 3.1080979690107674000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.661999999999887 " "
y[1] (analytic) = -5.028344668379282 " "
y[1] (numeric) = -5.0283446683794395 " "
absolute error = 1.57207580286922170000000000000E-13 " "
relative error = 3.1264280922411936000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.660999999999887 " "
y[1] (analytic) = -5.027266087369334 " "
y[1] (numeric) = -5.027266087369491 " "
absolute error = 1.57207580286922170000000000000E-13 " "
relative error = 3.1270988556164864000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6599999999998865 " "
y[1] (analytic) = -5.026187506359385 " "
y[1] (numeric) = -5.026187506359543 " "
absolute error = 1.5809575870662230000000000000E-13 " "
relative error = 3.1454409232960684000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.658999999999886 " "
y[1] (analytic) = -5.025108925349436 " "
y[1] (numeric) = -5.025108925349595 " "
absolute error = 1.58983937126322420000000000000E-13 " "
relative error = 3.1637908647973634000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.657999999999886 " "
y[1] (analytic) = -5.024030344339487 " "
y[1] (numeric) = -5.024030344339646 " "
absolute error = 1.58983937126322420000000000000E-13 " "
relative error = 3.1644700813849114000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6569999999998855 " "
y[1] (analytic) = -5.022951763329538 " "
y[1] (numeric) = -5.022951763329698 " "
absolute error = 1.59872115546022540000000000000E-13 " "
relative error = 3.1828319896118000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.655999999999885 " "
y[1] (analytic) = -5.02187318231959 " "
y[1] (numeric) = -5.02187318231975 " "
absolute error = 1.59872115546022540000000000000E-13 " "
relative error = 3.183515587547713400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.654999999999885 " "
y[1] (analytic) = -5.020794601309640 " "
y[1] (numeric) = -5.0207946013098015 " "
absolute error = 1.60760293965722670000000000000E-13 " "
relative error = 3.2018894762950356000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6539999999998845 " "
y[1] (analytic) = -5.019716020299692 " "
y[1] (numeric) = -5.019716020299853 " "
absolute error = 1.60760293965722670000000000000E-13 " "
relative error = 3.202577462860634000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.652999999999884 " "
y[1] (analytic) = -5.018637439289743 " "
y[1] (numeric) = -5.018637439289905 " "
absolute error = 1.6164847238542280000000000000E-13 " "
relative error = 3.2209633459455460000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.651999999999884 " "
y[1] (analytic) = -5.017558858279795 " "
y[1] (numeric) = -5.017558858279957 " "
absolute error = 1.6164847238542280000000000000E-13 " "
relative error = 3.221655728436076400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6509999999998834 " "
y[1] (analytic) = -5.016480277269846 " "
y[1] (numeric) = -5.016480277270008 " "
absolute error = 1.62536650805122920000000000000E-13 " "
relative error = 3.2400536196981000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.649999999999883 " "
y[1] (analytic) = -5.0154016962598975 " "
y[1] (numeric) = -5.01540169626006 " "
absolute error = 1.62536650805122920000000000000E-13 " "
relative error = 3.240750405422766000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.648999999999883 " "
y[1] (analytic) = -5.014323115249948 " "
y[1] (numeric) = -5.014323115250112 " "
absolute error = 1.63424829224823040000000000000E-13 " "
relative error = 3.2591603187238327000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6479999999998824 " "
y[1] (analytic) = -5.01324453424 " "
y[1] (numeric) = -5.0132445342401635 " "
absolute error = 1.63424829224823040000000000000E-13 " "
relative error = 3.25986151500583000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.646999999999882 " "
y[1] (analytic) = -5.012165953230050 " "
y[1] (numeric) = -5.012165953230215 " "
absolute error = 1.64313007644523170000000000000E-13 " "
relative error = 3.278283464230328000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.645999999999882 " "
y[1] (analytic) = -5.011087372220103 " "
y[1] (numeric) = -5.011087372220267 " "
absolute error = 1.64313007644523170000000000000E-13 " "
relative error = 3.2789890784068737000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6449999999998814 " "
y[1] (analytic) = -5.010008791210153 " "
y[1] (numeric) = -5.010008791210319 " "
absolute error = 1.6520118606422330000000000000E-13 " "
relative error = 3.297423077461694700000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.643999999999881 " "
y[1] (analytic) = -5.008930210200205 " "
y[1] (numeric) = -5.00893021020037 " "
absolute error = 1.6520118606422330000000000000E-13 " "
relative error = 3.2981331168840594000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.642999999999880 " "
y[1] (analytic) = -5.007851629190256 " "
y[1] (numeric) = -5.007851629190422 " "
absolute error = 1.66089364483923420000000000000E-13 " "
relative error = 3.316579179698645000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.64199999999988 " "
y[1] (analytic) = -5.006773048180308 " "
y[1] (numeric) = -5.006773048180474 " "
absolute error = 1.66089364483923420000000000000E-13 " "
relative error = 3.317293651732186000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.64099999999988 " "
y[1] (analytic) = -5.0056944671703585 " "
y[1] (numeric) = -5.0056944671705255 " "
absolute error = 1.66977542903623540000000000000E-13 " "
relative error = 3.3357517922585744000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.63999999999988 " "
y[1] (analytic) = -5.00461588616041 " "
y[1] (numeric) = -5.004615886160577 " "
absolute error = 1.66977542903623540000000000000E-13 " "
relative error = 3.3364707042827685000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.638999999999880 " "
y[1] (analytic) = -5.003537305150461 " "
y[1] (numeric) = -5.003537305150629 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 3.3549409364956420000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.637999999999879 " "
y[1] (analytic) = -5.002458724140512 " "
y[1] (numeric) = -5.002458724140680 " "
absolute error = 1.6875389974302380000000000000E-13 " "
relative error = 3.373419133448581400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.636999999999879 " "
y[1] (analytic) = -5.001380143130564 " "
y[1] (numeric) = -5.001380143130732 " "
absolute error = 1.6875389974302380000000000000E-13 " "
relative error = 3.374146633800844700000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.635999999999878 " "
y[1] (analytic) = -5.000301562120614 " "
y[1] (numeric) = -5.000301562120784 " "
absolute error = 1.69642078162723920000000000000E-13 " "
relative error = 3.392636945096151000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.634999999999878 " "
y[1] (analytic) = -4.999222981110666 " "
y[1] (numeric) = -4.999222981110836 " "
absolute error = 1.69642078162723920000000000000E-13 " "
relative error = 3.393368905602105000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.633999999999878 " "
y[1] (analytic) = -4.998144400100717 " "
y[1] (numeric) = -4.9981444001008875 " "
absolute error = 1.70530256582424040000000000000E-13 " "
relative error = 3.411871345273412300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.632999999999877 " "
y[1] (analytic) = -4.997065819090769 " "
y[1] (numeric) = -4.997065819090940 " "
absolute error = 1.70530256582424040000000000000E-13 " "
relative error = 3.412607773364341000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.631999999999877 " "
y[1] (analytic) = -4.9959872380808195 " "
y[1] (numeric) = -4.995987238080990 " "
absolute error = 1.71418435002124170000000000000E-13 " "
relative error = 3.431122355468098000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.630999999999877 " "
y[1] (analytic) = -4.994908657070871 " "
y[1] (numeric) = -4.994908657071043 " "
absolute error = 1.71418435002124170000000000000E-13 " "
relative error = 3.4318632585895550000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.629999999999876 " "
y[1] (analytic) = -4.993830076060922 " "
y[1] (numeric) = -4.993830076061094 " "
absolute error = 1.7230661342182430000000000000E-13 " "
relative error = 3.450389997205068000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.628999999999876 " "
y[1] (analytic) = -4.992751495050974 " "
y[1] (numeric) = -4.992751495051146 " "
absolute error = 1.7230661342182430000000000000E-13 " "
relative error = 3.4511353828169080000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.627999999999876 " "
y[1] (analytic) = -4.9916729140410245 " "
y[1] (numeric) = -4.991672914041198 " "
absolute error = 1.73194791841524420000000000000E-13 " "
relative error = 3.469674292046392000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.626999999999875 " "
y[1] (analytic) = -4.990594333031076 " "
y[1] (numeric) = -4.990594333031250 " "
absolute error = 1.73194791841524420000000000000E-13 " "
relative error = 3.4704241676228015000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.625999999999875 " "
y[1] (analytic) = -4.989515752021127 " "
y[1] (numeric) = -4.989515752021301 " "
absolute error = 1.74082970261224550000000000000E-13 " "
relative error = 3.4889752615914266000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.624999999999875 " "
y[1] (analytic) = -4.988437171011179 " "
y[1] (numeric) = -4.988437171011353 " "
absolute error = 1.74082970261224550000000000000E-13 " "
relative error = 3.4897296346209594000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.623999999999874 " "
y[1] (analytic) = -4.98735859000123 " "
y[1] (numeric) = -4.987358590001405 " "
absolute error = 1.74971148680924670000000000000E-13 " "
relative error = 3.5082929274768976000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.622999999999874 " "
y[1] (analytic) = -4.986280008991281 " "
y[1] (numeric) = -4.986280008991456 " "
absolute error = 1.74971148680924670000000000000E-13 " "
relative error = 3.5090518054625080000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.621999999999874 " "
y[1] (analytic) = -4.985201427981332 " "
y[1] (numeric) = -4.985201427981508 " "
absolute error = 1.7585932710062480000000000000E-13 " "
relative error = 3.5276273113769824000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.620999999999873 " "
y[1] (analytic) = -4.984122846971384 " "
y[1] (numeric) = -4.98412284697156 " "
absolute error = 1.7585932710062480000000000000E-13 " "
relative error = 3.5283907018360555000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.619999999999873 " "
y[1] (analytic) = -4.983044265961435 " "
y[1] (numeric) = -4.983044265961611 " "
absolute error = 1.76747505520324920000000000000E-13 " "
relative error = 3.5469784350033870000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.618999999999873 " "
y[1] (analytic) = -4.981965684951486 " "
y[1] (numeric) = -4.981965684951663 " "
absolute error = 1.76747505520324920000000000000E-13 " "
relative error = 3.547746345467774000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.617999999999872 " "
y[1] (analytic) = -4.980887103941537 " "
y[1] (numeric) = -4.980887103941715 " "
absolute error = 1.77635683940025050000000000000E-13 " "
relative error = 3.566346320105432000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.616999999999872 " "
y[1] (analytic) = -4.979808522931588 " "
y[1] (numeric) = -4.979808522931767 " "
absolute error = 1.78523862359725170000000000000E-13 " "
relative error = 3.5849543519120910000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.615999999999872 " "
y[1] (analytic) = -4.97872994192164 " "
y[1] (numeric) = -4.978729941921818 " "
absolute error = 1.78523862359725170000000000000E-13 " "
relative error = 3.5857309884701305000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.614999999999871 " "
y[1] (analytic) = -4.977651360911690 " "
y[1] (numeric) = -4.97765136091187 " "
absolute error = 1.7941204077942530000000000000E-13 " "
relative error = 3.6043512847907605000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.613999999999871 " "
y[1] (analytic) = -4.976572779901742 " "
y[1] (numeric) = -4.976572779901922 " "
absolute error = 1.7941204077942530000000000000E-13 " "
relative error = 3.605132461922271300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.612999999999870 " "
y[1] (analytic) = -4.975494198891793 " "
y[1] (numeric) = -4.975494198891973 " "
absolute error = 1.80300219199125420000000000000E-13 " "
relative error = 3.6237650370345975000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.61199999999987 " "
y[1] (analytic) = -4.974415617881845 " "
y[1] (numeric) = -4.974415617882025 " "
absolute error = 1.80300219199125420000000000000E-13 " "
relative error = 3.6245507623245010000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = sin(0.1) + cos(0.05) - tan(0.02);"
Iterations = 389
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds
"Expected Time Remaining "= 0 Years 0 Days 1 Hours 14 Minutes 7 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 1 Hours 13 Minutes 32 Seconds
"Expected Total Time "= 0 Years 0 Days 1 Hours 16 Minutes 32 Seconds
"Time to Timeout " Unknown
Percent Done = 3.9000000000013024 "%"
(%o57) true
(%o57) diffeq.max