(%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 : array_const_1D0 + array_const_0D0 ,
1 1 1
array_tmp2 : sin(array_x ), array_tmp2_g : cos(array_x ),
1 1 1 1
array_tmp3 : array_tmp2 + array_tmp1 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp2_g array_x - array_tmp2 array_x
1 2 1 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
2 1 2 1
array_tmp3 : array_tmp2 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp3 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp2_g array_x - array_tmp2 array_x
2 2 2 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
3 2 3 2
array_tmp3 : array_tmp2 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp3 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
array_tmp2_g array_x - array_tmp2 array_x
3 2 3 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
4 3 4 3
array_tmp3 : array_tmp2 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp3 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
array_tmp2_g array_x - array_tmp2 array_x
4 2 4 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
5 4 5 4
array_tmp3 : array_tmp2 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp3 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
array_tmp2_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp2 : ----------------------------,
kkk kkk - 1
- array_tmp2 array_x
kkk - 1 2
array_tmp2_g : ----------------------------, array_tmp3 : array_tmp2 ,
kkk kkk - 1 kkk kkk
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_tmp3 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_1D0 + array_const_0D0 ,
1 1 1
array_tmp2 : sin(array_x ), array_tmp2_g : cos(array_x ),
1 1 1 1
array_tmp3 : array_tmp2 + array_tmp1 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp2_g array_x - array_tmp2 array_x
1 2 1 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
2 1 2 1
array_tmp3 : array_tmp2 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp3 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp2_g array_x - array_tmp2 array_x
2 2 2 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
3 2 3 2
array_tmp3 : array_tmp2 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp3 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
array_tmp2_g array_x - array_tmp2 array_x
3 2 3 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
4 3 4 3
array_tmp3 : array_tmp2 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp3 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
array_tmp2_g array_x - array_tmp2 array_x
4 2 4 2
array_tmp2 : ----------------------, array_tmp2_g : ----------------------,
5 4 5 4
array_tmp3 : array_tmp2 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp3 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
array_tmp2_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp2 : ----------------------------,
kkk kkk - 1
- array_tmp2 array_x
kkk - 1 2
array_tmp2_g : ----------------------------, array_tmp3 : array_tmp2 ,
kkk kkk - 1 kkk kkk
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_tmp3 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole() := 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(x - cos(x) + 2.0)
(%o55) exact_soln_y(x) := block(x - cos(x) + 2.0)
(%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_c_sinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0 + sin(x);"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-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_display_interval:0.1,"), omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
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, " (2.0 - cos(x) + x) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2_g, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2_g : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
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_display_interval : 0.1, glob_look_poles : true,
glob_max_iter : 1000000, 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 ) = 1.0 + sin(x);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-12T20:12:44-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "add_c_sin"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.0 + sin(x);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 156 | "), logitem_str(html_log_file, "add_c_sin diffeq.max"),
logitem_str(html_log_file,
"add_c_sin 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_c_sinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0 + sin(x);"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-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_display_interval:0.1,"), omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
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, " (2.0 - cos(x) + x) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2_g, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2_g : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
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_display_interval : 0.1, glob_look_poles : true,
glob_max_iter : 1000000, 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 ) = 1.0 + sin(x);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-12T20:12:44-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "add_c_sin"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.0 + sin(x);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 156 | "), logitem_str(html_log_file, "add_c_sin diffeq.max"),
logitem_str(html_log_file,
"add_c_sin 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_c_sinpostode.ode#################"
"diff ( y , x , 1 ) = 1.0 + sin(x);"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:-5.0,"
"x_end:5.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.05,"
"glob_display_interval:0.1,"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"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("
" (2.0 - cos(x) + x) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 10. ""
estimated_steps = 10000. ""
step_error = 1.00000000000000E-14 ""
est_needed_step_err = 1.00000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 7.0332366254449390000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 ""
max_value3 = 7.0332366254449390000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 ""
value3 = 7.0332366254449390000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = -5. " "
y[1] (analytic) = -3.283662185463226 " "
y[1] (numeric) = -3.283662185463226 " "
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) = -3.283662185463226 " "
y[1] (numeric) = -3.283662185463226 " "
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) = -3.281703119517302 " "
y[1] (numeric) = -3.281703119517303 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.70645572543675200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.998000000000000 " "
y[1] (analytic) = -3.2797437708682824 " "
y[1] (numeric) = -3.2797437708682837 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.06210887991863500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.996999999999999 " "
y[1] (analytic) = -3.2777841404755153 " "
y[1] (numeric) = -3.277784140475517 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.41938322742189700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.995999999999999 " "
y[1] (analytic) = -3.275824229298631 " "
y[1] (numeric) = -3.275824229298633 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.77828202560709600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.994999999999998 " "
y[1] (analytic) = -3.27386403829754 " "
y[1] (numeric) = -3.2738640382975435 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.08517447189039870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.993999999999998 " "
y[1] (analytic) = -3.2719035684324345 " "
y[1] (numeric) = -3.2719035684324385 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 1.22155277655857920000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.992999999999998 " "
y[1] (analytic) = -3.269942820663784 " "
y[1] (numeric) = -3.2699428206637884 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.35809472582739070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.991999999999997 " "
y[1] (analytic) = -3.267981795952336 " "
y[1] (numeric) = -3.2679817959523407 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.49480064864533220000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.990999999999997 " "
y[1] (analytic) = -3.2660204952591143 " "
y[1] (numeric) = -3.26602049525912 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.76764344756287020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.989999999999997 " "
y[1] (analytic) = -3.2640589195454206 " "
y[1] (numeric) = -3.2640589195454273 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 2.04081430879276270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.988999999999996 " "
y[1] (analytic) = -3.2620970697728304 " "
y[1] (numeric) = -3.2620970697728375 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.17817778123194170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.987999999999996 " "
y[1] (analytic) = -3.260134946903193 " "
y[1] (numeric) = -3.260134946903201 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 2.4519248152271320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.986999999999996 " "
y[1] (analytic) = -3.2581725518986318 " "
y[1] (numeric) = -3.25817255189864 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 2.5897016971167780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.985999999999995 " "
y[1] (analytic) = -3.2562098857215407 " "
y[1] (numeric) = -3.25620988572155 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 2.864027115618440500000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.984999999999995 " "
y[1] (analytic) = -3.2542469493345862 " "
y[1] (numeric) = -3.2542469493345965 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 3.13868369105791500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.983999999999995 " "
y[1] (analytic) = -3.2522837437007057 " "
y[1] (numeric) = -3.252283743700716 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 3.14057832325819240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.982999999999994 " "
y[1] (analytic) = -3.2503202697831033 " "
y[1] (numeric) = -3.2503202697831144 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 3.41573424301120600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.981999999999994 " "
y[1] (analytic) = -3.248356528545253 " "
y[1] (numeric) = -3.248356528545265 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 3.6912231033092563000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.980999999999994 " "
y[1] (analytic) = -3.2463925209508973 " "
y[1] (numeric) = -3.2463925209509097 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 3.8302509002083270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.979999999999993 " "
y[1] (analytic) = -3.2444282479640423 " "
y[1] (numeric) = -3.244428247964055 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 3.9694473421421610000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.978999999999993 " "
y[1] (analytic) = -3.2424637105489613 " "
y[1] (numeric) = -3.242463710548975 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 4.2457731941805370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.977999999999993 " "
y[1] (analytic) = -3.2404989096701917 " "
y[1] (numeric) = -3.2404989096702064 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 4.52243445641017150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.976999999999992 " "
y[1] (analytic) = -3.238533846292534 " "
y[1] (numeric) = -3.2385338462925497 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 4.7994318053973467000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.975999999999992 " "
y[1] (analytic) = -3.2365685213810527 " "
y[1] (numeric) = -3.2365685213810687 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 4.9395560294766966000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.974999999999992 " "
y[1] (analytic) = -3.234602935901071 " "
y[1] (numeric) = -3.234602935901088 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 5.2171442086449970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.973999999999991 " "
y[1] (analytic) = -3.2326370908181756 " "
y[1] (numeric) = -3.232637090818193 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 5.3576936406953460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.972999999999991 " "
y[1] (analytic) = -3.23067098709821 " "
y[1] (numeric) = -3.2306709870982284 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 5.6358749239911590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.971999999999990 " "
y[1] (analytic) = -3.22870462570728 " "
y[1] (numeric) = -3.2287046257072984 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 5.7768513927212460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.97099999999999 " "
y[1] (analytic) = -3.2267380076117447 " "
y[1] (numeric) = -3.226738007611764 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 6.0556280637934850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96999999999999 " "
y[1] (analytic) = -3.2247711337782237 " "
y[1] (numeric) = -3.2247711337782436 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 6.1970334061627010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96899999999999 " "
y[1] (analytic) = -3.2228040051735896 " "
y[1] (numeric) = -3.2228040051736104 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 6.4764077584136880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.967999999999990 " "
y[1] (analytic) = -3.220836622764972 " "
y[1] (numeric) = -3.220836622764993 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 6.6182438196768110000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.966999999999989 " "
y[1] (analytic) = -3.2188689875197523 " "
y[1] (numeric) = -3.2188689875197745 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 6.8982181563134760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.965999999999989 " "
y[1] (analytic) = -3.2169011004055665 " "
y[1] (numeric) = -3.216901100405589 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 7.0404867900656960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.964999999999988 " "
y[1] (analytic) = -3.214932962390301 " "
y[1] (numeric) = -3.2149329623903244 " "
absolute error = 2.35367281220533200000000000000E-14 " "
relative error = 7.3210634241510820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.963999999999988 " "
y[1] (analytic) = -3.2129645744420934 " "
y[1] (numeric) = -3.212964574442118 " "
absolute error = 2.442490654175344400000000000000E-14 " "
relative error = 7.6019843903802280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.962999999999988 " "
y[1] (analytic) = -3.210995937529333 " "
y[1] (numeric) = -3.2109959375293577 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 7.7449477468784010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.961999999999987 " "
y[1] (analytic) = -3.2090270526206552 " "
y[1] (numeric) = -3.2090270526206806 " "
absolute error = 2.53130849614535700000000000000E-14 " "
relative error = 7.8880871199828660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.960999999999987 " "
y[1] (analytic) = -3.2070579206849454 " "
y[1] (numeric) = -3.2070579206849716 " "
absolute error = 2.620126338115369400000000000000E-14 " "
relative error = 8.1698753278387240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.959999999999987 " "
y[1] (analytic) = -3.2050885426913354 " "
y[1] (numeric) = -3.2050885426913625 " "
absolute error = 2.70894418008538200000000000000E-14 " "
relative error = 8.4520104327934190000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.958999999999986 " "
y[1] (analytic) = -3.2031189196092034 " "
y[1] (numeric) = -3.203118919609231 " "
absolute error = 2.753353101070388000000000000000E-14 " "
relative error = 8.5958503888650850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.957999999999986 " "
y[1] (analytic) = -3.201149052408172 " "
y[1] (numeric) = -3.2011490524082 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 8.7398680169256230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.956999999999986 " "
y[1] (analytic) = -3.1991789420581083 " "
y[1] (numeric) = -3.199178942058137 " "
absolute error = 2.88657986402540700000000000000E-14 " "
relative error = 9.0228771703792270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.955999999999985 " "
y[1] (analytic) = -3.197208589529123 " "
y[1] (numeric) = -3.1972085895291524 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 9.1673367656067820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.954999999999985 " "
y[1] (analytic) = -3.195237995791568 " "
y[1] (numeric) = -3.195237995791598 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 9.4509599314911690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.953999999999985 " "
y[1] (analytic) = -3.1932671618160375 " "
y[1] (numeric) = -3.193267161816068 " "
absolute error = 3.06421554796543200000000000000E-14 " "
relative error = 9.5958633984849140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.952999999999984 " "
y[1] (analytic) = -3.191296088573365 " "
y[1] (numeric) = -3.1912960885733965 " "
absolute error = 3.153033389935444600000000000000E-14 " "
relative error = 9.880102950099420000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.951999999999984 " "
y[1] (analytic) = -3.1893247770346234 " "
y[1] (numeric) = -3.1893247770346558 " "
absolute error = 3.24185123190545700000000000000E-14 " "
relative error = 1.0164694593818292000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.950999999999984 " "
y[1] (analytic) = -3.187353228171125 " "
y[1] (numeric) = -3.187353228171158 " "
absolute error = 3.286260152890463400000000000000E-14 " "
relative error = 1.03103105229917990000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.949999999999983 " "
y[1] (analytic) = -3.185381442954418 " "
y[1] (numeric) = -3.1853814429544514 " "
absolute error = 3.330669073875469600000000000000E-14 " "
relative error = 1.0456107482017282000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.948999999999983 " "
y[1] (analytic) = -3.183409422356288 " "
y[1] (numeric) = -3.1834094223563216 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 1.0602085836519008000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.947999999999983 " "
y[1] (analytic) = -3.1814371673487547 " "
y[1] (numeric) = -3.1814371673487893 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 1.088783356270751000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.946999999999982 " "
y[1] (analytic) = -3.1794646789040737 " "
y[1] (numeric) = -3.1794646789041088 " "
absolute error = 3.508304757815494700000000000000E-14 " "
relative error = 1.1034262406163192000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.945999999999982 " "
y[1] (analytic) = -3.177491957994733 " "
y[1] (numeric) = -3.1774919579947687 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 1.1180873864563812000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.944999999999982 " "
y[1] (analytic) = -3.1755190055934537 " "
y[1] (numeric) = -3.17551900559349 " "
absolute error = 3.641531520770513500000000000000E-14 " "
relative error = 1.1467516063850387000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.943999999999981 " "
y[1] (analytic) = -3.173545822673188 " "
y[1] (numeric) = -3.173545822673225 " "
absolute error = 3.6859404417555197000000000000E-14 " "
relative error = 1.1614580811852668000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.942999999999981 " "
y[1] (analytic) = -3.1715724102071188 " "
y[1] (numeric) = -3.1715724102071565 " "
absolute error = 3.77475828372553200000000000000E-14 " "
relative error = 1.1901851181379847000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.941999999999980 " "
y[1] (analytic) = -3.1695987691686582 " "
y[1] (numeric) = -3.169598769168697 " "
absolute error = 3.86357612569554500000000000000E-14 " "
relative error = 1.2189480142651958000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.94099999999998 " "
y[1] (analytic) = -3.167624900531448 " "
y[1] (numeric) = -3.167624900531487 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 1.2337272149947075000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93999999999998 " "
y[1] (analytic) = -3.1656508052693555 " "
y[1] (numeric) = -3.1656508052693955 " "
absolute error = 3.996802888650563500000000000000E-14 " "
relative error = 1.262553305626041000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93899999999998 " "
y[1] (analytic) = -3.1636764843564773 " "
y[1] (numeric) = -3.1636764843565173 " "
absolute error = 3.996802888650563500000000000000E-14 " "
relative error = 1.263341213431167800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.937999999999980 " "
y[1] (analytic) = -3.161701938767133 " "
y[1] (numeric) = -3.1617019387671736 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 1.292221977196786000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.936999999999979 " "
y[1] (analytic) = -3.159727169475868 " "
y[1] (numeric) = -3.15972716947591 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 1.3211389302586650000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.935999999999979 " "
y[1] (analytic) = -3.157752177457453 " "
y[1] (numeric) = -3.1577521774574953 " "
absolute error = 4.21884749357559500000000000000E-14 " "
relative error = 1.3360286863842843000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.934999999999978 " "
y[1] (analytic) = -3.1557769636868787 " "
y[1] (numeric) = -3.1557769636869217 " "
absolute error = 4.307665335545607400000000000000E-14 " "
relative error = 1.3650094366976376000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.933999999999978 " "
y[1] (analytic) = -3.153801529139359 " "
y[1] (numeric) = -3.1538015291394026 " "
absolute error = 4.352074256530613600000000000000E-14 " "
relative error = 1.379945509037232000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.932999999999978 " "
y[1] (analytic) = -3.1518258747903287 " "
y[1] (numeric) = -3.1518258747903727 " "
absolute error = 4.3964831775156200000000000000E-14 " "
relative error = 1.394900401281873000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.931999999999977 " "
y[1] (analytic) = -3.149850001615442 " "
y[1] (numeric) = -3.1498500016154862 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 1.4098741515383453000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.930999999999977 " "
y[1] (analytic) = -3.147873910590571 " "
y[1] (numeric) = -3.1478739105906164 " "
absolute error = 4.52970994047063870000000000000E-14 " "
relative error = 1.4389743900577080000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.929999999999977 " "
y[1] (analytic) = -3.145897602691808 " "
y[1] (numeric) = -3.145897602691854 " "
absolute error = 4.57411886145564500000000000000E-14 " "
relative error = 1.453994833634053900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.928999999999976 " "
y[1] (analytic) = -3.1439210788954606 " "
y[1] (numeric) = -3.1439210788955068 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 1.4690342621651487000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.927999999999976 " "
y[1] (analytic) = -3.141944340178052 " "
y[1] (numeric) = -3.1419443401780986 " "
absolute error = 4.662936703425657500000000000000E-14 " "
relative error = 1.4840927141189940000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.926999999999976 " "
y[1] (analytic) = -3.1399673875163208 " "
y[1] (numeric) = -3.1399673875163683 " "
absolute error = 4.7517545453956700000000000000E-14 " "
relative error = 1.5133133434084023000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.925999999999975 " "
y[1] (analytic) = -3.13799022188722 " "
y[1] (numeric) = -3.137990221887268 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 1.5284188691627643000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.924999999999975 " "
y[1] (analytic) = -3.136012844267915 " "
y[1] (numeric) = -3.1360128442679636 " "
absolute error = 4.840572387365682500000000000000E-14 " "
relative error = 1.5435435464537095000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.923999999999975 " "
y[1] (analytic) = -3.1340352556357836 " "
y[1] (numeric) = -3.1340352556358324 " "
absolute error = 4.88498130835068900000000000000E-14 " "
relative error = 1.5586874141145235000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.922999999999974 " "
y[1] (analytic) = -3.132057456968414 " "
y[1] (numeric) = -3.132057456968463 " "
absolute error = 4.92939022933569500000000000000E-14 " "
relative error = 1.5738505110653234000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.921999999999974 " "
y[1] (analytic) = -3.1300794492436044 " "
y[1] (numeric) = -3.1300794492436546 " "
absolute error = 5.018208071305708000000000000000E-14 " "
relative error = 1.6032206698518073000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.920999999999974 " "
y[1] (analytic) = -3.128101233439363 " "
y[1] (numeric) = -3.128101233439414 " "
absolute error = 5.1070259132757200000000000000E-14 " "
relative error = 1.6326280807928073000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.919999999999973 " "
y[1] (analytic) = -3.1261228105339054 " "
y[1] (numeric) = -3.1261228105339574 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.6620728199601165000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.918999999999973 " "
y[1] (analytic) = -3.1241441815056548 " "
y[1] (numeric) = -3.124144181505707 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.677340216002849200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.917999999999973 " "
y[1] (analytic) = -3.1221653473332394 " "
y[1] (numeric) = -3.1221653473332927 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.7068508311875650000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.916999999999972 " "
y[1] (analytic) = -3.120186308995494 " "
y[1] (numeric) = -3.1201863089955477 " "
absolute error = 5.373479439185758000000000000000E-14 " "
relative error = 1.7221662128617200000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.915999999999972 " "
y[1] (analytic) = -3.1182070674714564 " "
y[1] (numeric) = -3.118207067471511 " "
absolute error = 5.4622972811557700000000000000E-14 " "
relative error = 1.7517429609269436000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.914999999999972 " "
y[1] (analytic) = -3.116227623740368 " "
y[1] (numeric) = -3.1162276237404236 " "
absolute error = 5.55111512312578300000000000000E-14 " "
relative error = 1.7813573953441983000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.913999999999971 " "
y[1] (analytic) = -3.1142479787816733 " "
y[1] (numeric) = -3.114247978781729 " "
absolute error = 5.59552404411078900000000000000E-14 " "
relative error = 1.796749675117335000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.912999999999971 " "
y[1] (analytic) = -3.1122681335750157 " "
y[1] (numeric) = -3.1122681335750726 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 1.826430642256804000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.911999999999970 " "
y[1] (analytic) = -3.1102880891002416 " "
y[1] (numeric) = -3.110288089100299 " "
absolute error = 5.72875080706580800000000000000E-14 " "
relative error = 1.841871441794013000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.91099999999997 " "
y[1] (analytic) = -3.1083078463373948 " "
y[1] (numeric) = -3.1083078463374525 " "
absolute error = 5.77315972805081400000000000000E-14 " "
relative error = 1.8573320319135983000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90999999999997 " "
y[1] (analytic) = -3.106327406266718 " "
y[1] (numeric) = -3.1063274062667765 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 1.887108731099898800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90899999999997 " "
y[1] (analytic) = -3.104346769868651 " "
y[1] (numeric) = -3.1043467698687106 " "
absolute error = 5.95079541199083900000000000000E-14 " "
relative error = 1.916923544028757100000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.907999999999970 " "
y[1] (analytic) = -3.102365938123831 " "
y[1] (numeric) = -3.102365938123891 " "
absolute error = 5.99520433297584500000000000000E-14 " "
relative error = 1.9324620152970962000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.906999999999969 " "
y[1] (analytic) = -3.100384912013089 " "
y[1] (numeric) = -3.1003849120131495 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 1.9480204637040735000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.905999999999969 " "
y[1] (analytic) = -3.0984036925174507 " "
y[1] (numeric) = -3.098403692517512 " "
absolute error = 6.12843109593086400000000000000E-14 " "
relative error = 1.977931768778495900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.904999999999968 " "
y[1] (analytic) = -3.0964222806181363 " "
y[1] (numeric) = -3.096422280618198 " "
absolute error = 6.1728400169158700000000000000E-14 " "
relative error = 1.993539465064045000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.903999999999968 " "
y[1] (analytic) = -3.094440677296557 " "
y[1] (numeric) = -3.0944406772966193 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 2.0091672732703816000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.902999999999968 " "
y[1] (analytic) = -3.0924588835343165 " "
y[1] (numeric) = -3.092458883534379 " "
absolute error = 6.26165785888588300000000000000E-14 " "
relative error = 2.024815234319152800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.901999999999967 " "
y[1] (analytic) = -3.090476900313208 " "
y[1] (numeric) = -3.0904769003132713 " "
absolute error = 6.30606677987088900000000000000E-14 " "
relative error = 2.0404833892244245000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.900999999999967 " "
y[1] (analytic) = -3.088494728615215 " "
y[1] (numeric) = -3.088494728615279 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 2.0705506027229545000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.899999999999967 " "
y[1] (analytic) = -3.0865123694225094 " "
y[1] (numeric) = -3.086512369422574 " "
absolute error = 6.43929354282590800000000000000E-14 " "
relative error = 2.0862685037710405000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.898999999999966 " "
y[1] (analytic) = -3.0845298237174497 " "
y[1] (numeric) = -3.0845298237175145 " "
absolute error = 6.48370246381091400000000000000E-14 " "
relative error = 2.1020067350157146000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.897999999999966 " "
y[1] (analytic) = -3.0825470924825815 " "
y[1] (numeric) = -3.0825470924826472 " "
absolute error = 6.57252030578092700000000000000E-14 " "
relative error = 2.1321719047891774000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.896999999999966 " "
y[1] (analytic) = -3.080564176700636 " "
y[1] (numeric) = -3.080564176700703 " "
absolute error = 6.66133814775093900000000000000E-14 " "
relative error = 2.162376034277398200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.895999999999965 " "
y[1] (analytic) = -3.0785810773545297 " "
y[1] (numeric) = -3.0785810773545967 " "
absolute error = 6.70574706873594600000000000000E-14 " "
relative error = 2.178194077155276000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.894999999999965 " "
y[1] (analytic) = -3.076597795427361 " "
y[1] (numeric) = -3.076597795427429 " "
absolute error = 6.79456491070595800000000000000E-14 " "
relative error = 2.208467067357482200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.893999999999965 " "
y[1] (analytic) = -3.0746143319024117 " "
y[1] (numeric) = -3.0746143319024806 " "
absolute error = 6.8833827526759700000000000000E-14 " "
relative error = 2.2387792450108338000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.892999999999964 " "
y[1] (analytic) = -3.0726306877631457 " "
y[1] (numeric) = -3.0726306877632155 " "
absolute error = 6.97220059464598300000000000000E-14 " "
relative error = 2.269130690653128000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.891999999999964 " "
y[1] (analytic) = -3.0706468639932067 " "
y[1] (numeric) = -3.0706468639932774 " "
absolute error = 7.06101843661599600000000000000E-14 " "
relative error = 2.299521485005127000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.890999999999964 " "
y[1] (analytic) = -3.0686628615764193 " "
y[1] (numeric) = -3.0686628615764904 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 2.3154799592259000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.889999999999963 " "
y[1] (analytic) = -3.066678681496785 " "
y[1] (numeric) = -3.0666786814968563 " "
absolute error = 7.14983627858600800000000000000E-14 " "
relative error = 2.331459217336821000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.888999999999963 " "
y[1] (analytic) = -3.0646943247384835 " "
y[1] (numeric) = -3.0646943247385554 " "
absolute error = 7.19424519957101400000000000000E-14 " "
relative error = 2.347459301731475000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.887999999999963 " "
y[1] (analytic) = -3.062709792285872 " "
y[1] (numeric) = -3.0627097922859448 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 2.377980133764247300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.886999999999962 " "
y[1] (analytic) = -3.0607250851234826 " "
y[1] (numeric) = -3.0607250851235563 " "
absolute error = 7.3718808835110390000000000000E-14 " "
relative error = 2.408540681860561700000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.885999999999962 " "
y[1] (analytic) = -3.058740204236023 " "
y[1] (numeric) = -3.058740204236097 " "
absolute error = 7.41628980449604600000000000000E-14 " "
relative error = 2.4246223311889287000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.884999999999962 " "
y[1] (analytic) = -3.056755150608373 " "
y[1] (numeric) = -3.0567551506084483 " "
absolute error = 7.50510764646605800000000000000E-14 " "
relative error = 2.4552531284595522000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.883999999999961 " "
y[1] (analytic) = -3.054769925225587 " "
y[1] (numeric) = -3.054769925225663 " "
absolute error = 7.59392548843607100000000000000E-14 " "
relative error = 2.485923874569794000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.882999999999961 " "
y[1] (analytic) = -3.0527845290728903 " "
y[1] (numeric) = -3.0527845290729667 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 2.50208763071162000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.881999999999960 " "
y[1] (analytic) = -3.050798963135678 " "
y[1] (numeric) = -3.0507989631357555 " "
absolute error = 7.7271522513910900000000000000E-14 " "
relative error = 2.5328290538846104000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.88099999999996 " "
y[1] (analytic) = -3.0488132283995175 " "
y[1] (numeric) = -3.0488132283995952 " "
absolute error = 7.77156117237609600000000000000E-14 " "
relative error = 2.54904469056499000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87999999999996 " "
y[1] (analytic) = -3.046827325850142 " "
y[1] (numeric) = -3.0468273258502205 " "
absolute error = 7.86037901434610800000000000000E-14 " "
relative error = 2.5798570689111383000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87899999999996 " "
y[1] (analytic) = -3.044841256473455 " "
y[1] (numeric) = -3.044841256473534 " "
absolute error = 7.90478793533111500000000000000E-14 " "
relative error = 2.5961248122624514000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.877999999999960 " "
y[1] (analytic) = -3.0428550212555248 " "
y[1] (numeric) = -3.0428550212556047 " "
absolute error = 7.99360577730112700000000000000E-14 " "
relative error = 2.627008425134515000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.876999999999959 " "
y[1] (analytic) = -3.0408686211825877 " "
y[1] (numeric) = -3.040868621182668 " "
absolute error = 8.03801469828613300000000000000E-14 " "
relative error = 2.6433285023540953000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.875999999999959 " "
y[1] (analytic) = -3.038882057241042 " "
y[1] (numeric) = -3.038882057241124 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 2.688897202104548000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.874999999999958 " "
y[1] (analytic) = -3.0368953304174537 " "
y[1] (numeric) = -3.036895330417536 " "
absolute error = 8.21565038222615800000000000000E-14 " "
relative error = 2.705279401610733000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.873999999999958 " "
y[1] (analytic) = -3.034908441698548 " "
y[1] (numeric) = -3.034908441698631 " "
absolute error = 8.30446822419617100000000000000E-14 " "
relative error = 2.7363159000435633000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.872999999999958 " "
y[1] (analytic) = -3.0329213920712146 " "
y[1] (numeric) = -3.032921392071298 " "
absolute error = 8.34887714518117700000000000000E-14 " "
relative error = 2.7527509176489534000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.871999999999957 " "
y[1] (analytic) = -3.030934182522502 " "
y[1] (numeric) = -3.030934182522586 " "
absolute error = 8.4376949871511900000000000000E-14 " "
relative error = 2.783859522851433000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.870999999999957 " "
y[1] (analytic) = -3.02894681403962 " "
y[1] (numeric) = -3.028946814039705 " "
absolute error = 8.48210390813619600000000000000E-14 " "
relative error = 2.800347589076302000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.869999999999957 " "
y[1] (analytic) = -3.026959287609937 " "
y[1] (numeric) = -3.0269592876100226 " "
absolute error = 8.57092175010620800000000000000E-14 " "
relative error = 2.8315285855310396000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.868999999999956 " "
y[1] (analytic) = -3.0249716042209798 " "
y[1] (numeric) = -3.024971604221066 " "
absolute error = 8.61533067109121500000000000000E-14 " "
relative error = 2.8480699319853350000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.867999999999956 " "
y[1] (analytic) = -3.022983764860431 " "
y[1] (numeric) = -3.022983764860518 " "
absolute error = 8.70414851306122700000000000000E-14 " "
relative error = 2.8793236054521426000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.866999999999956 " "
y[1] (analytic) = -3.020995770516131 " "
y[1] (numeric) = -3.020995770516218 " "
absolute error = 8.70414851306122700000000000000E-14 " "
relative error = 2.881218371111503000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.865999999999955 " "
y[1] (analytic) = -3.0190076221760727 " "
y[1] (numeric) = -3.0190076221761606 " "
absolute error = 8.7929663550312400000000000000E-14 " "
relative error = 2.9125353279808386000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.864999999999955 " "
y[1] (analytic) = -3.017019320828405 " "
y[1] (numeric) = -3.0170193208284934 " "
absolute error = 8.83737527601624600000000000000E-14 " "
relative error = 2.9291742399547194000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.863999999999955 " "
y[1] (analytic) = -3.0150308674614292 " "
y[1] (numeric) = -3.0150308674615185 " "
absolute error = 8.92619311798625900000000000000E-14 " "
relative error = 2.960564422181807000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.862999999999954 " "
y[1] (analytic) = -3.0130422630635985 " "
y[1] (numeric) = -3.0130422630636886 " "
absolute error = 9.01501095995627100000000000000E-14 " "
relative error = 2.991996186203507000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.861999999999954 " "
y[1] (analytic) = -3.011053508623517 " "
y[1] (numeric) = -3.011053508623608 " "
absolute error = 9.10382880192628400000000000000E-14 " "
relative error = 3.0234696181430660000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.860999999999954 " "
y[1] (analytic) = -3.00906460512994 " "
y[1] (numeric) = -3.0090646051300314 " "
absolute error = 9.1482377229112900000000000000E-14 " "
relative error = 3.0402264236251725000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.859999999999953 " "
y[1] (analytic) = -3.0070755535717697 " "
y[1] (numeric) = -3.007075553571862 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 3.071773688529254000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.858999999999953 " "
y[1] (analytic) = -3.0050863549380584 " "
y[1] (numeric) = -3.0050863549381512 " "
absolute error = 9.28146448586630900000000000000E-14 " "
relative error = 3.088584948853365000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.857999999999953 " "
y[1] (analytic) = -3.003097010218004 " "
y[1] (numeric) = -3.003097010218098 " "
absolute error = 9.37028232783632100000000000000E-14 " "
relative error = 3.120206338974079000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.856999999999952 " "
y[1] (analytic) = -3.001107520400952 " "
y[1] (numeric) = -3.001107520401046 " "
absolute error = 9.41469124882132700000000000000E-14 " "
relative error = 3.137072292419404000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.855999999999952 " "
y[1] (analytic) = -2.999117886476391 " "
y[1] (numeric) = -2.999117886476486 " "
absolute error = 9.5035090907913400000000000000E-14 " "
relative error = 3.168768101328901000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.854999999999952 " "
y[1] (analytic) = -2.9971281094339552 " "
y[1] (numeric) = -2.997128109434051 " "
absolute error = 9.59232693276135300000000000000E-14 " "
relative error = 3.2005061453889544000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.853999999999951 " "
y[1] (analytic) = -2.9951381902634227 " "
y[1] (numeric) = -2.995138190263519 " "
absolute error = 9.63673585374635900000000000000E-14 " "
relative error = 3.2174595099062214000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.852999999999951 " "
y[1] (analytic) = -2.993148129954711 " "
y[1] (numeric) = -2.9931481299548084 " "
absolute error = 9.72555369571637100000000000000E-14 " "
relative error = 3.249272429381411000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.851999999999950 " "
y[1] (analytic) = -2.9911579294978816 " "
y[1] (numeric) = -2.9911579294979793 " "
absolute error = 9.76996261670137800000000000000E-14 " "
relative error = 3.266281101493506700000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.85099999999995 " "
y[1] (analytic) = -2.989167589883134 " "
y[1] (numeric) = -2.989167589883232 " "
absolute error = 9.81437153768638400000000000000E-14 " "
relative error = 3.2833125753481396000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.84999999999995 " "
y[1] (analytic) = -2.9871771121008077 " "
y[1] (numeric) = -2.9871771121009068 " "
absolute error = 9.90318937965639600000000000000E-14 " "
relative error = 3.315233415367102000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.84899999999995 " "
y[1] (analytic) = -2.985186497141381 " "
y[1] (numeric) = -2.985186497141481 " "
absolute error = 9.99200722162640900000000000000E-14 " "
relative error = 3.3471969778755095000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.847999999999950 " "
y[1] (analytic) = -2.9831957459954688 " "
y[1] (numeric) = -2.983195745995569 " "
absolute error = 1.00364161426114150000000000000E-13 " "
relative error = 3.3643169933062310000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.846999999999949 " "
y[1] (analytic) = -2.981204859653822 " "
y[1] (numeric) = -2.9812048596539227 " "
absolute error = 1.00808250635964210000000000000E-13 " "
relative error = 3.381460026456219500000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.845999999999949 " "
y[1] (analytic) = -2.979213839107326 " "
y[1] (numeric) = -2.9792138391074277 " "
absolute error = 1.01696429055664340000000000000E-13 " "
relative error = 3.4135323796071000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.844999999999948 " "
y[1] (analytic) = -2.9772226853470025 " "
y[1] (numeric) = -2.9772226853471047 " "
absolute error = 1.0214051826551440000000000000E-13 " "
relative error = 3.4307315595914073000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.843999999999948 " "
y[1] (analytic) = -2.9752313993640045 " "
y[1] (numeric) = -2.9752313993641075 " "
absolute error = 1.03028696685214530000000000000E-13 " "
relative error = 3.462880121097078000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.842999999999948 " "
y[1] (analytic) = -2.973239982149618 " "
y[1] (numeric) = -2.973239982149722 " "
absolute error = 1.03916875104914650000000000000E-13 " "
relative error = 3.4950718989653823000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.841999999999947 " "
y[1] (analytic) = -2.9712484346952603 " "
y[1] (numeric) = -2.971248434695365 " "
absolute error = 1.04805053524614780000000000000E-13 " "
relative error = 3.5273069831794085000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.840999999999947 " "
y[1] (analytic) = -2.9692567579924787 " "
y[1] (numeric) = -2.9692567579925844 " "
absolute error = 1.0569323194431490000000000000E-13 " "
relative error = 3.5595854639318675000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.839999999999947 " "
y[1] (analytic) = -2.9672649530329496 " "
y[1] (numeric) = -2.967264953033056 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 3.591907431625689400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.838999999999946 " "
y[1] (analytic) = -2.9652730208084783 " "
y[1] (numeric) = -2.9652730208085853 " "
absolute error = 1.07025499573865090000000000000E-13 " "
relative error = 3.6092966422594275000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.837999999999946 " "
y[1] (analytic) = -2.963280962310997 " "
y[1] (numeric) = -2.9632809623111043 " "
absolute error = 1.07469588783715150000000000000E-13 " "
relative error = 3.626709385663586000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.836999999999946 " "
y[1] (analytic) = -2.9612887785325634 " "
y[1] (numeric) = -2.9612887785326714 " "
absolute error = 1.07913677993565220000000000000E-13 " "
relative error = 3.64414571033632000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.835999999999945 " "
y[1] (analytic) = -2.959296470465362 " "
y[1] (numeric) = -2.9592964704654703 " "
absolute error = 1.08357767203415280000000000000E-13 " "
relative error = 3.661605664888843000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.834999999999945 " "
y[1] (analytic) = -2.9573040391017 " "
y[1] (numeric) = -2.957304039101809 " "
absolute error = 1.0924594562311540000000000000E-13 " "
relative error = 3.694105989058182000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.833999999999945 " "
y[1] (analytic) = -2.955311485434009 " "
y[1] (numeric) = -2.955311485434119 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 3.7266502900164356000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.832999999999944 " "
y[1] (analytic) = -2.953318810454843 " "
y[1] (numeric) = -2.9533188104549537 " "
absolute error = 1.10578213252665590000000000000E-13 " "
relative error = 3.744201704916353400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.831999999999944 " "
y[1] (analytic) = -2.9513260151568765 " "
y[1] (numeric) = -2.951326015156988 " "
absolute error = 1.11466391672365720000000000000E-13 " "
relative error = 3.7768240817828036000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.830999999999944 " "
y[1] (analytic) = -2.949333100532905 " "
y[1] (numeric) = -2.949333100533017 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 3.794433421643525500000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.829999999999943 " "
y[1] (analytic) = -2.9473400675758423 " "
y[1] (numeric) = -2.947340067575955 " "
absolute error = 1.1279865930191590000000000000E-13 " "
relative error = 3.82713418593368050000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.828999999999943 " "
y[1] (analytic) = -2.945346917278722 " "
y[1] (numeric) = -2.945346917278836 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 3.85987935936097040000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.827999999999943 " "
y[1] (analytic) = -2.9433536506346942 " "
y[1] (numeric) = -2.943353650634809 " "
absolute error = 1.14575016141316150000000000000E-13 " "
relative error = 3.8926690347457776000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.826999999999942 " "
y[1] (analytic) = -2.9413602686370255 " "
y[1] (numeric) = -2.9413602686371405 " "
absolute error = 1.15019105351166220000000000000E-13 " "
relative error = 3.910405215491132300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.825999999999942 " "
y[1] (analytic) = -2.9393667722790973 " "
y[1] (numeric) = -2.939366772279213 " "
absolute error = 1.15907283770866340000000000000E-13 " "
relative error = 3.943273934507849400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.824999999999942 " "
y[1] (analytic) = -2.9373731625544064 " "
y[1] (numeric) = -2.937373162554523 " "
absolute error = 1.16795462190566470000000000000E-13 " "
relative error = 3.976187420770144000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.823999999999941 " "
y[1] (analytic) = -2.935379440456563 " "
y[1] (numeric) = -2.9353794404566798 " "
absolute error = 1.16795462190566470000000000000E-13 " "
relative error = 3.978888064038506000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.822999999999941 " "
y[1] (analytic) = -2.9333856069792876 " "
y[1] (numeric) = -2.9333856069794053 " "
absolute error = 1.1768364061026660000000000000E-13 " "
relative error = 4.01187079974302000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.821999999999940 " "
y[1] (analytic) = -2.9313916631164147 " "
y[1] (numeric) = -2.931391663116533 " "
absolute error = 1.18127729820116660000000000000E-13 " "
relative error = 4.029749122453768500000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.82099999999994 " "
y[1] (analytic) = -2.929397609861888 " "
y[1] (numeric) = -2.9293976098620065 " "
absolute error = 1.18571819029966720000000000000E-13 " "
relative error = 4.047651934677349300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.81999999999994 " "
y[1] (analytic) = -2.92740344820976 " "
y[1] (numeric) = -2.9274034482098794 " "
absolute error = 1.19459997449666840000000000000E-13 " "
relative error = 4.080749359051348000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8189999999999396 " "
y[1] (analytic) = -2.925409179154193 " "
y[1] (numeric) = -2.925409179154313 " "
absolute error = 1.1990408665951690000000000000E-13 " "
relative error = 4.098711643961686600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.817999999999940 " "
y[1] (analytic) = -2.9234148036894556 " "
y[1] (numeric) = -2.9234148036895764 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 4.131889355105297000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.816999999999939 " "
y[1] (analytic) = -2.9214203228099236 " "
y[1] (numeric) = -2.921420322810045 " "
absolute error = 1.2123635428906710000000000000E-13 " "
relative error = 4.149911375041635500000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8159999999999386 " "
y[1] (analytic) = -2.9194257375100774 " "
y[1] (numeric) = -2.919425737510199 " "
absolute error = 1.21680443498917160000000000000E-13 " "
relative error = 4.167958168468299000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.814999999999938 " "
y[1] (analytic) = -2.9174310487845023 " "
y[1] (numeric) = -2.9174310487846244 " "
absolute error = 1.22124532708767220000000000000E-13 " "
relative error = 4.186029786707326500000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.813999999999938 " "
y[1] (analytic) = -2.9154362576278867 " "
y[1] (numeric) = -2.9154362576280097 " "
absolute error = 1.23012711128467340000000000000E-13 " "
relative error = 4.219358622800256600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8129999999999376 " "
y[1] (analytic) = -2.9134413650350224 " "
y[1] (numeric) = -2.913441365035146 " "
absolute error = 1.2345680033831741000000000000E-13 " "
relative error = 4.237490475008524000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.811999999999937 " "
y[1] (analytic) = -2.9114463720008006 " "
y[1] (numeric) = -2.9114463720009254 " "
absolute error = 1.2478906796786760000000000000E-13 " "
relative error = 4.2861537539539224000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.810999999999937 " "
y[1] (analytic) = -2.9094512795202156 " "
y[1] (numeric) = -2.909451279520341 " "
absolute error = 1.25233157177717660000000000000E-13 " "
relative error = 4.304356565763468600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8099999999999365 " "
y[1] (analytic) = -2.9074560885883596 " "
y[1] (numeric) = -2.9074560885884853 " "
absolute error = 1.25677246387567720000000000000E-13 " "
relative error = 4.322584505432275300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.808999999999936 " "
y[1] (analytic) = -2.905460800200423 " "
y[1] (numeric) = -2.905460800200549 " "
absolute error = 1.26121335597417780000000000000E-13 " "
relative error = 4.340837625092644500000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.807999999999936 " "
y[1] (analytic) = -2.903465415351694 " "
y[1] (numeric) = -2.9034654153518207 " "
absolute error = 1.26565424807267850000000000000E-13 " "
relative error = 4.359115977000095000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8069999999999355 " "
y[1] (analytic) = -2.9014699350375572 " "
y[1] (numeric) = -2.901469935037685 " "
absolute error = 1.27897692436818030000000000000E-13 " "
relative error = 4.40803093950248000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.805999999999935 " "
y[1] (analytic) = -2.8994743602534943 " "
y[1] (numeric) = -2.899474360253622 " "
absolute error = 1.27897692436818030000000000000E-13 " "
relative error = 4.4110647843644407000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.804999999999935 " "
y[1] (analytic) = -2.897478691995078 " "
y[1] (numeric) = -2.897478691995207 " "
absolute error = 1.28785870856518160000000000000E-13 " "
relative error = 4.444756443328381500000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8039999999999345 " "
y[1] (analytic) = -2.8954829312579777 " "
y[1] (numeric) = -2.8954829312581074 " "
absolute error = 1.29674049276218280000000000000E-13 " "
relative error = 4.478494688272253700000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.802999999999934 " "
y[1] (analytic) = -2.893487079037954 " "
y[1] (numeric) = -2.893487079038084 " "
absolute error = 1.30118138486068350000000000000E-13 " "
relative error = 4.496931727420428500000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.801999999999934 " "
y[1] (analytic) = -2.8914911363308584 " "
y[1] (numeric) = -2.8914911363309894 " "
absolute error = 1.31006316905768470000000000000E-13 " "
relative error = 4.53075284443058060000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8009999999999335 " "
y[1] (analytic) = -2.889495104132634 " "
y[1] (numeric) = -2.8894951041327657 " "
absolute error = 1.31450406115618530000000000000E-13 " "
relative error = 4.549251733550771000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.799999999999933 " "
y[1] (analytic) = -2.887498983439313 " "
y[1] (numeric) = -2.8874989834394453 " "
absolute error = 1.32338584535318660000000000000E-13 " "
relative error = 4.583156056307579000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.798999999999933 " "
y[1] (analytic) = -2.885502775247016 " "
y[1] (numeric) = -2.885502775247149 " "
absolute error = 1.32782673745168720000000000000E-13 " "
relative error = 4.601717069352038000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7979999999999325 " "
y[1] (analytic) = -2.883506480551951 " "
y[1] (numeric) = -2.8835064805520845 " "
absolute error = 1.33670852164868850000000000000E-13 " "
relative error = 4.6357049330883430000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.796999999999932 " "
y[1] (analytic) = -2.881510100350412 " "
y[1] (numeric) = -2.8815101003505466 " "
absolute error = 1.34559030584568970000000000000E-13 " "
relative error = 4.669740028612277000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.795999999999932 " "
y[1] (analytic) = -2.87951363563878 " "
y[1] (numeric) = -2.8795136356389155 " "
absolute error = 1.3544720900426910000000000000E-13 " "
relative error = 4.703822455566251000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7949999999999315 " "
y[1] (analytic) = -2.8775170874135196 " "
y[1] (numeric) = -2.8775170874136555 " "
absolute error = 1.35891298214119160000000000000E-13 " "
relative error = 4.7225192444040776000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.793999999999931 " "
y[1] (analytic) = -2.8755204566711785 " "
y[1] (numeric) = -2.875520456671315 " "
absolute error = 1.36335387423969220000000000000E-13 " "
relative error = 4.741242132625852000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.792999999999930 " "
y[1] (analytic) = -2.8735237444083874 " "
y[1] (numeric) = -2.8735237444085246 " "
absolute error = 1.37223565843669350000000000000E-13 " "
relative error = 4.775445691398715000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7919999999999305 " "
y[1] (analytic) = -2.871526951621859 " "
y[1] (numeric) = -2.8715269516219966 " "
absolute error = 1.3766765505351940000000000000E-13 " "
relative error = 4.794231688327485000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.79099999999993 " "
y[1] (analytic) = -2.869530079308385 " "
y[1] (numeric) = -2.8695300793085234 " "
absolute error = 1.38555833473219540000000000000E-13 " "
relative error = 4.828519989120111000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.78999999999993 " "
y[1] (analytic) = -2.8675331284648387 " "
y[1] (numeric) = -2.8675331284649777 " "
absolute error = 1.3899992268306960000000000000E-13 " "
relative error = 4.847369374856518000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7889999999999295 " "
y[1] (analytic) = -2.8655361000881703 " "
y[1] (numeric) = -2.8655361000883097 " "
absolute error = 1.39444011892919660000000000000E-13 " "
relative error = 4.866245163989701000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.787999999999930 " "
y[1] (analytic) = -2.863538995175408 " "
y[1] (numeric) = -2.8635389951755483 " "
absolute error = 1.40332190312619800000000000000E-13 " "
relative error = 4.900655816074321000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.786999999999929 " "
y[1] (analytic) = -2.861541814723657 " "
y[1] (numeric) = -2.861541814723798 " "
absolute error = 1.4122036873231990000000000000E-13 " "
relative error = 4.935114629661903600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7859999999999285 " "
y[1] (analytic) = -2.8595445597300975 " "
y[1] (numeric) = -2.859544559730239 " "
absolute error = 1.41664457942169970000000000000E-13 " "
relative error = 4.954091638828709300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.784999999999928 " "
y[1] (analytic) = -2.857547231191984 " "
y[1] (numeric) = -2.8575472311921266 " "
absolute error = 1.4255263636187010000000000000E-13 " "
relative error = 4.988636226404781000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.783999999999928 " "
y[1] (analytic) = -2.8555498301066455 " "
y[1] (numeric) = -2.855549830106789 " "
absolute error = 1.43440814781570230000000000000E-13 " "
relative error = 5.023229266365601000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7829999999999275 " "
y[1] (analytic) = -2.853552357471483 " "
y[1] (numeric) = -2.853552357471627 " "
absolute error = 1.4388490399142030000000000000E-13 " "
relative error = 5.042308181754054000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.781999999999927 " "
y[1] (analytic) = -2.8515548142839693 " "
y[1] (numeric) = -2.8515548142841136 " "
absolute error = 1.44328993201270350000000000000E-13 " "
relative error = 5.061413951374861000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.780999999999927 " "
y[1] (analytic) = -2.8495572015416464 " "
y[1] (numeric) = -2.8495572015417916 " "
absolute error = 1.45217171620970480000000000000E-13 " "
relative error = 5.0961311302123070000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7799999999999265 " "
y[1] (analytic) = -2.847559520242128 " "
y[1] (numeric) = -2.8475595202422737 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 5.1153017099510870000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.778999999999926 " "
y[1] (analytic) = -2.845561771383095 " "
y[1] (numeric) = -2.8455617713832413 " "
absolute error = 1.4610535004067060000000000000E-13 " "
relative error = 5.134499328392916000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.777999999999926 " "
y[1] (analytic) = -2.8435639559622965 " "
y[1] (numeric) = -2.843563955962443 " "
absolute error = 1.46549439250520660000000000000E-13 " "
relative error = 5.153724042086001000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7769999999999255 " "
y[1] (analytic) = -2.841566074977547 " "
y[1] (numeric) = -2.8415660749776945 " "
absolute error = 1.4743761767022080000000000000E-13 " "
relative error = 5.188604233719456000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.775999999999925 " "
y[1] (analytic) = -2.839568129426728 " "
y[1] (numeric) = -2.839568129426876 " "
absolute error = 1.48325796089920900000000000000E-13 " "
relative error = 5.223533626568275000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.774999999999925 " "
y[1] (analytic) = -2.837570120307785 " "
y[1] (numeric) = -2.8375701203079338 " "
absolute error = 1.48769885299770980000000000000E-13 " "
relative error = 5.242861990794935000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7739999999999245 " "
y[1] (analytic) = -2.835572048618727 " "
y[1] (numeric) = -2.8355720486188765 " "
absolute error = 1.4965806371947110000000000000E-13 " "
relative error = 5.277879071786344000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.772999999999924 " "
y[1] (analytic) = -2.833573915357625 " "
y[1] (numeric) = -2.8335739153577757 " "
absolute error = 1.50546242139171230000000000000E-13 " "
relative error = 5.312945652246054000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.771999999999924 " "
y[1] (analytic) = -2.831575721522613 " "
y[1] (numeric) = -2.8315757215227646 " "
absolute error = 1.51434420558871350000000000000E-13 " "
relative error = 5.348061837365983000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7709999999999235 " "
y[1] (analytic) = -2.829577468111885 " "
y[1] (numeric) = -2.8295774681120367 " "
absolute error = 1.51878509768721410000000000000E-13 " "
relative error = 5.36753319109749000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.769999999999923 " "
y[1] (analytic) = -2.8275791561236927 " "
y[1] (numeric) = -2.8275791561238455 " "
absolute error = 1.52766688188421540000000000000E-13 " "
relative error = 5.402737810454377000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.768999999999923 " "
y[1] (analytic) = -2.82558078655635 " "
y[1] (numeric) = -2.825580786556503 " "
absolute error = 1.5321077739827160000000000000E-13 " "
relative error = 5.4222755947104170000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7679999999999225 " "
y[1] (analytic) = -2.823582360408225 " "
y[1] (numeric) = -2.8235823604083787 " "
absolute error = 1.53654866608121670000000000000E-13 " "
relative error = 5.441841143458154000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.766999999999922 " "
y[1] (analytic) = -2.8215838786777443 " "
y[1] (numeric) = -2.821583878677899 " "
absolute error = 1.5454304502782180000000000000E-13 " "
relative error = 5.477173519301649000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.765999999999922 " "
y[1] (analytic) = -2.819585342363389 " "
y[1] (numeric) = -2.8195853423635446 " "
absolute error = 1.55431223447521920000000000000E-13 " "
relative error = 5.512556088025297000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7649999999999215 " "
y[1] (analytic) = -2.817586752463697 " "
y[1] (numeric) = -2.8175867524638525 " "
absolute error = 1.55431223447521920000000000000E-13 " "
relative error = 5.516466292000163000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.763999999999921 " "
y[1] (analytic) = -2.8155881099772557 " "
y[1] (numeric) = -2.8155881099774125 " "
absolute error = 1.5676349107707210000000000000E-13 " "
relative error = 5.567699711529839000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.762999999999920 " "
y[1] (analytic) = -2.8135894159027095 " "
y[1] (numeric) = -2.8135894159028667 " "
absolute error = 1.57207580286922170000000000000E-13 " "
relative error = 5.587438572180008000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7619999999999205 " "
y[1] (analytic) = -2.8115906712387515 " "
y[1] (numeric) = -2.811590671238909 " "
absolute error = 1.57651669496772230000000000000E-13 " "
relative error = 5.607205597510141000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.76099999999992 " "
y[1] (analytic) = -2.809591876984126 " "
y[1] (numeric) = -2.8095918769842845 " "
absolute error = 1.58539847916472350000000000000E-13 " "
relative error = 5.642807028850480000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.75999999999992 " "
y[1] (analytic) = -2.8075930341376276 " "
y[1] (numeric) = -2.807593034137787 " "
absolute error = 1.59428026336172480000000000000E-13 " "
relative error = 5.678459249530870000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7589999999999195 " "
y[1] (analytic) = -2.8055941436980993 " "
y[1] (numeric) = -2.805594143698259 " "
absolute error = 1.59872115546022540000000000000E-13 " "
relative error = 5.698333663303577000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.757999999999920 " "
y[1] (analytic) = -2.803595206664431 " "
y[1] (numeric) = -2.8035952066645917 " "
absolute error = 1.60760293965722670000000000000E-13 " "
relative error = 5.734076502327408000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.756999999999919 " "
y[1] (analytic) = -2.8015962240355603 " "
y[1] (numeric) = -2.8015962240357215 " "
absolute error = 1.61204383175572730000000000000E-13 " "
relative error = 5.7540191478187320000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7559999999999185 " "
y[1] (analytic) = -2.7995971968104687 " "
y[1] (numeric) = -2.799597196810631 " "
absolute error = 1.62092561595272850000000000000E-13 " "
relative error = 5.789852975275944000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.754999999999918 " "
y[1] (analytic) = -2.797598125988184 " "
y[1] (numeric) = -2.797598125988347 " "
absolute error = 1.62980740014972980000000000000E-13 " "
relative error = 5.825738103731534000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.753999999999918 " "
y[1] (analytic) = -2.795599012567777 " "
y[1] (numeric) = -2.7955990125679406 " "
absolute error = 1.63424829224823040000000000000E-13 " "
relative error = 5.845789345687177000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7529999999999175 " "
y[1] (analytic) = -2.793599857548361 " "
y[1] (numeric) = -2.793599857548525 " "
absolute error = 1.6386891843467310000000000000E-13 " "
relative error = 5.865869372519336000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.751999999999917 " "
y[1] (analytic) = -2.791600661929091 " "
y[1] (numeric) = -2.7916006619292553 " "
absolute error = 1.64313007644523170000000000000E-13 " "
relative error = 5.885978244860326000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.750999999999917 " "
y[1] (analytic) = -2.789601426709162 " "
y[1] (numeric) = -2.789601426709327 " "
absolute error = 1.6520118606422330000000000000E-13 " "
relative error = 5.922035473688007000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7499999999999165 " "
y[1] (analytic) = -2.7876021528878097 " "
y[1] (numeric) = -2.7876021528879753 " "
absolute error = 1.65645275274073360000000000000E-13 " "
relative error = 5.942213636995277000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.748999999999916 " "
y[1] (analytic) = -2.7856028414643075 " "
y[1] (numeric) = -2.785602841464474 " "
absolute error = 1.66533453693773480000000000000E-13 " "
relative error = 5.9783631469241270000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.747999999999916 " "
y[1] (analytic) = -2.783603493437967 " "
y[1] (numeric) = -2.783603493438134 " "
absolute error = 1.66977542903623540000000000000E-13 " "
relative error = 5.998610911979898000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7469999999999155 " "
y[1] (analytic) = -2.7816041098081357 " "
y[1] (numeric) = -2.781604109808304 " "
absolute error = 1.68309810533173730000000000000E-13 " "
relative error = 6.0508183008394790000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.745999999999915 " "
y[1] (analytic) = -2.779604691574198 " "
y[1] (numeric) = -2.7796046915743666 " "
absolute error = 1.6875389974302380000000000000E-13 " "
relative error = 6.0711474640464770000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.744999999999915 " "
y[1] (analytic) = -2.7776052397355713 " "
y[1] (numeric) = -2.7776052397357405 " "
absolute error = 1.69197988952873860000000000000E-13 " "
relative error = 6.0915059682484450000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7439999999999145 " "
y[1] (analytic) = -2.7756057552917075 " "
y[1] (numeric) = -2.7756057552918776 " "
absolute error = 1.70086167372573980000000000000E-13 " "
relative error = 6.127893597579692000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.742999999999914 " "
y[1] (analytic) = -2.773606239242091 " "
y[1] (numeric) = -2.773606239242262 " "
absolute error = 1.7097434579227410000000000000E-13 " "
relative error = 6.1643337606204030000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.741999999999914 " "
y[1] (analytic) = -2.771606692586238 " "
y[1] (numeric) = -2.77160669258641 " "
absolute error = 1.71862524211974230000000000000E-13 " "
relative error = 6.2008265700789630000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7409999999999135 " "
y[1] (analytic) = -2.769607116323695 " "
y[1] (numeric) = -2.769607116323867 " "
absolute error = 1.7230661342182430000000000000E-13 " "
relative error = 6.2213377632615140000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.739999999999913 " "
y[1] (analytic) = -2.7676075114540377 " "
y[1] (numeric) = -2.7676075114542105 " "
absolute error = 1.72750702631674360000000000000E-13 " "
relative error = 6.241878659337613000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.738999999999913 " "
y[1] (analytic) = -2.7656078789768714 " "
y[1] (numeric) = -2.7656078789770446 " "
absolute error = 1.73194791841524420000000000000E-13 " "
relative error = 6.262449321109012000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7379999999999125 " "
y[1] (analytic) = -2.7636082198918284 " "
y[1] (numeric) = -2.7636082198920024 " "
absolute error = 1.74082970261224550000000000000E-13 " "
relative error = 6.2991189926348680000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.736999999999912 " "
y[1] (analytic) = -2.7616085351985675 " "
y[1] (numeric) = -2.7616085351987425 " "
absolute error = 1.74971148680924670000000000000E-13 " "
relative error = 6.335841827355293000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.735999999999912 " "
y[1] (analytic) = -2.7596088258967733 " "
y[1] (numeric) = -2.759608825896949 " "
absolute error = 1.7585932710062480000000000000E-13 " "
relative error = 6.372617939554417000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7349999999999115 " "
y[1] (analytic) = -2.7576090929861556 " "
y[1] (numeric) = -2.757609092986332 " "
absolute error = 1.76303416310474860000000000000E-13 " "
relative error = 6.393343304491343000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.733999999999911 " "
y[1] (analytic) = -2.7556093374664465 " "
y[1] (numeric) = -2.7556093374666237 " "
absolute error = 1.77191594730174980000000000000E-13 " "
relative error = 6.4302146287937870000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.732999999999910 " "
y[1] (analytic) = -2.7536095603374022 " "
y[1] (numeric) = -2.75360956033758 " "
absolute error = 1.77635683940025050000000000000E-13 " "
relative error = 6.4510120279455740000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7319999999999105 " "
y[1] (analytic) = -2.7516097625987985 " "
y[1] (numeric) = -2.751609762598977 " "
absolute error = 1.78523862359725170000000000000E-13 " "
relative error = 6.487978956402439000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.73099999999991 " "
y[1] (analytic) = -2.7496099452504343 " "
y[1] (numeric) = -2.7496099452506133 " "
absolute error = 1.78967951569575230000000000000E-13 " "
relative error = 6.508848714295541000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.72999999999991 " "
y[1] (analytic) = -2.7476101092921263 " "
y[1] (numeric) = -2.747610109292306 " "
absolute error = 1.79856129989275360000000000000E-13 " "
relative error = 6.545911640848204000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7289999999999095 " "
y[1] (analytic) = -2.7456102557237108 " "
y[1] (numeric) = -2.745610255723891 " "
absolute error = 1.80300219199125420000000000000E-13 " "
relative error = 6.566854083650718000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.727999999999910 " "
y[1] (analytic) = -2.7436103855450407 " "
y[1] (numeric) = -2.7436103855452214 " "
absolute error = 1.80744308408975480000000000000E-13 " "
relative error = 6.5878270967788720000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.726999999999909 " "
y[1] (analytic) = -2.7416104997559865 " "
y[1] (numeric) = -2.7416104997561677 " "
absolute error = 1.81188397618825550000000000000E-13 " "
relative error = 6.608830745102267000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7259999999999085 " "
y[1] (analytic) = -2.7396105993564337 " "
y[1] (numeric) = -2.7396105993566153 " "
absolute error = 1.8163248682867560000000000000E-13 " "
relative error = 6.629865093650287000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.724999999999908 " "
y[1] (analytic) = -2.737610685346282 " "
y[1] (numeric) = -2.737610685346465 " "
absolute error = 1.8296475445822580000000000000E-13 " "
relative error = 6.6833737696009340000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.723999999999908 " "
y[1] (analytic) = -2.735610758725447 " "
y[1] (numeric) = -2.73561075872563 " "
absolute error = 1.83408843668075860000000000000E-13 " "
relative error = 6.704493432886197000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7229999999999075 " "
y[1] (analytic) = -2.733610820493854 " "
y[1] (numeric) = -2.7336108204940377 " "
absolute error = 1.83852932877925920000000000000E-13 " "
relative error = 6.7256440272910200000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.721999999999907 " "
y[1] (analytic) = -2.7316108716514407 " "
y[1] (numeric) = -2.7316108716516254 " "
absolute error = 1.84741111297626050000000000000E-13 " "
relative error = 6.7630830296826930000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.720999999999907 " "
y[1] (analytic) = -2.729610913198157 " "
y[1] (numeric) = -2.7296109131983424 " "
absolute error = 1.8518520050747610000000000000E-13 " "
relative error = 6.784307595345276000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7199999999999065 " "
y[1] (analytic) = -2.727610946133961 " "
y[1] (numeric) = -2.727610946134147 " "
absolute error = 1.86073378927176240000000000000E-13 " "
relative error = 6.8218445592804000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.718999999999906 " "
y[1] (analytic) = -2.7256109714588197 " "
y[1] (numeric) = -2.7256109714590058 " "
absolute error = 1.86073378927176240000000000000E-13 " "
relative error = 6.826850231953124000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.717999999999906 " "
y[1] (analytic) = -2.7236109901727072 " "
y[1] (numeric) = -2.7236109901728938 " "
absolute error = 1.8651746813702630000000000000E-13 " "
relative error = 6.84816843558114000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7169999999999055 " "
y[1] (analytic) = -2.721611003275605 " "
y[1] (numeric) = -2.7216110032757923 " "
absolute error = 1.87405646556726420000000000000E-13 " "
relative error = 6.8858351296777420000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.715999999999905 " "
y[1] (analytic) = -2.7196110117674994 " "
y[1] (numeric) = -2.7196110117676877 " "
absolute error = 1.88293824976426550000000000000E-13 " "
relative error = 6.923557235269934000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.714999999999905 " "
y[1] (analytic) = -2.717611016648383 " "
y[1] (numeric) = -2.7176110166485716 " "
absolute error = 1.8873791418627660000000000000E-13 " "
relative error = 6.944993710654228000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7139999999999045 " "
y[1] (analytic) = -2.71561101891825 " "
y[1] (numeric) = -2.7156110189184393 " "
absolute error = 1.89182003396126670000000000000E-13 " "
relative error = 6.966461767837662000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.712999999999904 " "
y[1] (analytic) = -2.7136110195770984 " "
y[1] (numeric) = -2.713611019577288 " "
absolute error = 1.89626092605976740000000000000E-13 " "
relative error = 6.987961474136737000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.711999999999904 " "
y[1] (analytic) = -2.711611019624927 " "
y[1] (numeric) = -2.7116110196251175 " "
absolute error = 1.90514271025676860000000000000E-13 " "
relative error = 7.025870216887856000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7109999999999035 " "
y[1] (analytic) = -2.709611020061736 " "
y[1] (numeric) = -2.709611020061927 " "
absolute error = 1.90958360235526920000000000000E-13 " "
relative error = 7.0474455123516620000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.709999999999903 " "
y[1] (analytic) = -2.7076110218875247 " "
y[1] (numeric) = -2.7076110218877165 " "
absolute error = 1.91846538655227050000000000000E-13 " "
relative error = 7.085454192068082000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.708999999999903 " "
y[1] (analytic) = -2.7056110261022916 " "
y[1] (numeric) = -2.705611026102484 " "
absolute error = 1.92290627865077100000000000000E-13 " "
relative error = 7.107105419439814000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7079999999999025 " "
y[1] (analytic) = -2.7036110337060317 " "
y[1] (numeric) = -2.703611033706225 " "
absolute error = 1.93178806284777240000000000000E-13 " "
relative error = 7.145214451206516000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.706999999999902 " "
y[1] (analytic) = -2.7016110456987383 " "
y[1] (numeric) = -2.701611045698932 " "
absolute error = 1.9362289549462730000000000000E-13 " "
relative error = 7.1669419549826110000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.705999999999902 " "
y[1] (analytic) = -2.699611063080398 " "
y[1] (numeric) = -2.6996110630805927 " "
absolute error = 1.94511073914327430000000000000E-13 " "
relative error = 7.205151755911834000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7049999999999015 " "
y[1] (analytic) = -2.697611086850995 " "
y[1] (numeric) = -2.69761108685119 " "
absolute error = 1.9495516312417750000000000000E-13 " "
relative error = 7.2269558823527340000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.703999999999901 " "
y[1] (analytic) = -2.695611118010504 " "
y[1] (numeric) = -2.6956111180107 " "
absolute error = 1.95843341543877600000000000000E-13 " "
relative error = 7.265266871596071000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.702999999999900 " "
y[1] (analytic) = -2.693611157558894 " "
y[1] (numeric) = -2.693611157559091 " "
absolute error = 1.96731519963577740000000000000E-13 " "
relative error = 7.303634728847322000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7019999999999005 " "
y[1] (analytic) = -2.6916112064961264 " "
y[1] (numeric) = -2.6916112064963236 " "
absolute error = 1.9717560917342780000000000000E-13 " "
relative error = 7.325560567497644000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7009999999999 " "
y[1] (analytic) = -2.689611265822151 " "
y[1] (numeric) = -2.6896112658223488 " "
absolute error = 1.97619698383277860000000000000E-13 " "
relative error = 7.347518985159743000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6999999999999 " "
y[1] (analytic) = -2.687611336536909 " "
y[1] (numeric) = -2.6876113365371075 " "
absolute error = 1.985078768029780000000000000E-13 " "
relative error = 7.386033616704529000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6989999999998995 " "
y[1] (analytic) = -2.6856114196403293 " "
y[1] (numeric) = -2.6856114196405283 " "
absolute error = 1.98951966012828050000000000000E-13 " "
relative error = 7.40806970650551900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.697999999999900 " "
y[1] (analytic) = -2.683611516132329 " "
y[1] (numeric) = -2.6836115161325287 " "
absolute error = 1.99840144432528180000000000000E-13 " "
relative error = 7.44668679617762100000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.696999999999899 " "
y[1] (analytic) = -2.681611627012811 " "
y[1] (numeric) = -2.6816116270130115 " "
absolute error = 2.00284233642378240000000000000E-13 " "
relative error = 7.468800911543086000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6959999999998985 " "
y[1] (analytic) = -2.679611753281665 " "
y[1] (numeric) = -2.679611753281866 " "
absolute error = 2.01172412062078370000000000000E-13 " "
relative error = 7.507520886774238000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.694999999999898 " "
y[1] (analytic) = -2.6776118959387643 " "
y[1] (numeric) = -2.6776118959389663 " "
absolute error = 2.0206059048177850000000000000E-13 " "
relative error = 7.546298654717343000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.693999999999898 " "
y[1] (analytic) = -2.675612055983966 " "
y[1] (numeric) = -2.675612055984169 " "
absolute error = 2.02948768901478620000000000000E-13 " "
relative error = 7.585134341414957000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6929999999998975 " "
y[1] (analytic) = -2.6736122344171105 " "
y[1] (numeric) = -2.673612234417314 " "
absolute error = 2.03392858111328680000000000000E-13 " "
relative error = 7.607417990278292000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.691999999999897 " "
y[1] (analytic) = -2.671612432238019 " "
y[1] (numeric) = -2.671612432238223 " "
absolute error = 2.0428103653102880000000000000E-13 " "
relative error = 7.646357460610478000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.690999999999897 " "
y[1] (analytic) = -2.6696126504464934 " "
y[1] (numeric) = -2.669612650446698 " "
absolute error = 2.04725125740878870000000000000E-13 " "
relative error = 7.668720243239728000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6899999999998965 " "
y[1] (analytic) = -2.6676128900423155 " "
y[1] (numeric) = -2.667612890042521 " "
absolute error = 2.056133041605790000000000000E-13 " "
relative error = 7.707763931119609000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.688999999999896 " "
y[1] (analytic) = -2.6656131520252457 " "
y[1] (numeric) = -2.6656131520254522 " "
absolute error = 2.06501482580279120000000000000E-13 " "
relative error = 7.746866135597584000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.687999999999896 " "
y[1] (analytic) = -2.663613437395022 " "
y[1] (numeric) = -2.663613437395229 " "
absolute error = 2.06945571790129180000000000000E-13 " "
relative error = 7.769354549904928000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6869999999998955 " "
y[1] (analytic) = -2.661613747151359 " "
y[1] (numeric) = -2.661613747151567 " "
absolute error = 2.0783375020982930000000000000E-13 " "
relative error = 7.808561645440372000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.685999999999895 " "
y[1] (analytic) = -2.6596140822939467 " "
y[1] (numeric) = -2.659614082294155 " "
absolute error = 2.08277839419679370000000000000E-13 " "
relative error = 7.83113011794694100000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.684999999999895 " "
y[1] (analytic) = -2.6576144438224496 " "
y[1] (numeric) = -2.6576144438226588 " "
absolute error = 2.0916601783937950000000000000E-13 " "
relative error = 7.87044254389797100000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6839999999998945 " "
y[1] (analytic) = -2.655614832736507 " "
y[1] (numeric) = -2.6556148327367164 " "
absolute error = 2.09610107049229550000000000000E-13 " "
relative error = 7.89309144026863900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.682999999999894 " "
y[1] (analytic) = -2.6536152500357284 " "
y[1] (numeric) = -2.653615250035939 " "
absolute error = 2.10498285468929680000000000000E-13 " "
relative error = 7.932509638166102000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.681999999999894 " "
y[1] (analytic) = -2.651615696719698 " "
y[1] (numeric) = -2.651615696719909 " "
absolute error = 2.10942374678779740000000000000E-13 " "
relative error = 7.955239325960229000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6809999999998935 " "
y[1] (analytic) = -2.649616173787968 " "
y[1] (numeric) = -2.64961617378818 " "
absolute error = 2.11830553098479870000000000000E-13 " "
relative error = 7.994763739520836000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.679999999999893 " "
y[1] (analytic) = -2.647616682240062 " "
y[1] (numeric) = -2.6476166822402742 " "
absolute error = 2.12274642308329930000000000000E-13 " "
relative error = 8.017574588204034000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.678999999999893 " "
y[1] (analytic) = -2.6456172230754706 " "
y[1] (numeric) = -2.645617223075684 " "
absolute error = 2.13162820728030060000000000000E-13 " "
relative error = 8.057205663343583000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6779999999998925 " "
y[1] (analytic) = -2.6436177972936536 " "
y[1] (numeric) = -2.6436177972938673 " "
absolute error = 2.13606909937880120000000000000E-13 " "
relative error = 8.08009804429958000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.676999999999892 " "
y[1] (analytic) = -2.6416184058940364 " "
y[1] (numeric) = -2.641618405894251 " "
absolute error = 2.14495088357580240000000000000E-13 " "
relative error = 8.119836229146273000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.675999999999892 " "
y[1] (analytic) = -2.6396190498760106 " "
y[1] (numeric) = -2.6396190498762255 " "
absolute error = 2.1493917756743030000000000000E-13 " "
relative error = 8.142810515688865000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6749999999998915 " "
y[1] (analytic) = -2.6376197302389315 " "
y[1] (numeric) = -2.6376197302391473 " "
absolute error = 2.15827355987130430000000000000E-13 " "
relative error = 8.182656260596728000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.673999999999891 " "
y[1] (analytic) = -2.6356204479821193 " "
y[1] (numeric) = -2.6356204479823355 " "
absolute error = 2.1627144519698050000000000000E-13 " "
relative error = 8.205712827981813000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.672999999999890 " "
y[1] (analytic) = -2.633621204104856 " "
y[1] (numeric) = -2.6336212041050726 " "
absolute error = 2.16715534406830560000000000000E-13 " "
relative error = 8.22880428168827000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6719999999998905 " "
y[1] (analytic) = -2.6316219996063848 " "
y[1] (numeric) = -2.6316219996066024 " "
absolute error = 2.17603712826530680000000000000E-13 " "
relative error = 8.268805810981895000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.67099999999989 " "
y[1] (analytic) = -2.629622835485911 " "
y[1] (numeric) = -2.629622835486129 " "
absolute error = 2.18047802036380740000000000000E-13 " "
relative error = 8.291980092882373000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.66999999999989 " "
y[1] (analytic) = -2.627623712742598 " "
y[1] (numeric) = -2.627623712742817 " "
absolute error = 2.18935980456080870000000000000E-13 " "
relative error = 8.332090298711954000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6689999999998895 " "
y[1] (analytic) = -2.6256246323755694 " "
y[1] (numeric) = -2.625624632375789 " "
absolute error = 2.19380069665930930000000000000E-13 " "
relative error = 8.355347788897144000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.667999999999890 " "
y[1] (analytic) = -2.623625595383904 " "
y[1] (numeric) = -2.6236255953841243 " "
absolute error = 2.20268248085631060000000000000E-13 " "
relative error = 8.395567129440211000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.666999999999889 " "
y[1] (analytic) = -2.62162660276664 " "
y[1] (numeric) = -2.621626602766861 " "
absolute error = 2.20712337295481120000000000000E-13 " "
relative error = 8.418908209985367000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6659999999998885 " "
y[1] (analytic) = -2.6196276555227693 " "
y[1] (numeric) = -2.619627655522991 " "
absolute error = 2.21600515715181250000000000000E-13 " "
relative error = 8.459237145706456000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.664999999999888 " "
y[1] (analytic) = -2.6176287546512396 " "
y[1] (numeric) = -2.6176287546514616 " "
absolute error = 2.2204460492503130000000000000E-13 " "
relative error = 8.48266220068381900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.663999999999888 " "
y[1] (analytic) = -2.615629901150951 " "
y[1] (numeric) = -2.6156299011511734 " "
absolute error = 2.22488694134881370000000000000E-13 " "
relative error = 8.506122905116662000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6629999999998875 " "
y[1] (analytic) = -2.613631096020757 " "
y[1] (numeric) = -2.6136310960209803 " "
absolute error = 2.2337687255458150000000000000E-13 " "
relative error = 8.546610609839771000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.661999999999887 " "
y[1] (analytic) = -2.611632340259463 " "
y[1] (numeric) = -2.611632340259687 " "
absolute error = 2.23820961764431560000000000000E-13 " "
relative error = 8.570155849050145000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.660999999999887 " "
y[1] (analytic) = -2.6096336348658244 " "
y[1] (numeric) = -2.609633634866049 " "
absolute error = 2.24709140184131680000000000000E-13 " "
relative error = 8.610754290637628000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6599999999998865 " "
y[1] (analytic) = -2.607634980838547 " "
y[1] (numeric) = -2.6076349808387724 " "
absolute error = 2.2559731860383180000000000000E-13 " "
relative error = 8.651414797759985000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.658999999999886 " "
y[1] (analytic) = -2.605636379176284 " "
y[1] (numeric) = -2.6056363791765103 " "
absolute error = 2.26041407813681870000000000000E-13 " "
relative error = 8.675094100625813000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.657999999999886 " "
y[1] (analytic) = -2.603637830877638 " "
y[1] (numeric) = -2.6036378308778647 " "
absolute error = 2.269295862333820000000000000E-13 " "
relative error = 8.715866067934965000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6569999999998855 " "
y[1] (analytic) = -2.601639336941156 " "
y[1] (numeric) = -2.6016393369413837 " "
absolute error = 2.2781776465308212000000000000E-13 " "
relative error = 8.75670049334878000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.655999999999885 " "
y[1] (analytic) = -2.5996408983653327 " "
y[1] (numeric) = -2.599640898365561 " "
absolute error = 2.2826185386293218000000000000E-13 " "
relative error = 8.780514801350617000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.654999999999885 " "
y[1] (analytic) = -2.597642516148606 " "
y[1] (numeric) = -2.5976425161488352 " "
absolute error = 2.2915003228263230000000000000E-13 " "
relative error = 8.821461415806419000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6539999999998845 " "
y[1] (analytic) = -2.595644191289359 " "
y[1] (numeric) = -2.5956441912895887 " "
absolute error = 2.29594121492482370000000000000E-13 " "
relative error = 8.845361866736977000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.652999999999884 " "
y[1] (analytic) = -2.5936459247859154 " "
y[1] (numeric) = -2.593645924786146 " "
absolute error = 2.3048229991218250000000000000E-13 " "
relative error = 8.886421145986106000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.651999999999884 " "
y[1] (analytic) = -2.5916477176365422 " "
y[1] (numeric) = -2.591647717636773 " "
absolute error = 2.30926389122032560000000000000E-13 " "
relative error = 8.910408137284426000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6509999999998834 " "
y[1] (analytic) = -2.5896495708394465 " "
y[1] (numeric) = -2.589649570839678 " "
absolute error = 2.3137047833188262000000000000E-13 " "
relative error = 8.934431937711281000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.649999999999883 " "
y[1] (analytic) = -2.5876514853927746 " "
y[1] (numeric) = -2.587651485393007 " "
absolute error = 2.32258656751582750000000000000E-13 " "
relative error = 8.975654490671439000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.648999999999883 " "
y[1] (analytic) = -2.585653462294612 " "
y[1] (numeric) = -2.5856534622948453 " "
absolute error = 2.33146835171282870000000000000E-13 " "
relative error = 9.016940536353973000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6479999999998824 " "
y[1] (analytic) = -2.583655502542982 " "
y[1] (numeric) = -2.5836555025432157 " "
absolute error = 2.33590924381132940000000000000E-13 " "
relative error = 9.041101809092557000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.646999999999882 " "
y[1] (analytic) = -2.581657607135844 " "
y[1] (numeric) = -2.5816576071360786 " "
absolute error = 2.34479102800833060000000000000E-13 " "
relative error = 9.082501961248458000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.645999999999882 " "
y[1] (analytic) = -2.5796597770710936 " "
y[1] (numeric) = -2.579659777071329 " "
absolute error = 2.3536728122053320000000000000E-13 " "
relative error = 9.123966009493143000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6449999999998814 " "
y[1] (analytic) = -2.5776620133465604 " "
y[1] (numeric) = -2.5776620133467967 " "
absolute error = 2.3625545964023330000000000000E-13 " "
relative error = 9.16549409569428000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.643999999999881 " "
y[1] (analytic) = -2.5756643169600086 " "
y[1] (numeric) = -2.5756643169602453 " "
absolute error = 2.36699548850083370000000000000E-13 " "
relative error = 9.189844627325268000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.642999999999880 " "
y[1] (analytic) = -2.5736666889091335 " "
y[1] (numeric) = -2.573666688909371 " "
absolute error = 2.3758772726978350000000000000E-13 " "
relative error = 9.231487833822285000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.64199999999988 " "
y[1] (analytic) = -2.571669130191564 " "
y[1] (numeric) = -2.571669130191802 " "
absolute error = 2.38031816479633560000000000000E-13 " "
relative error = 9.255926965297536000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.64099999999988 " "
y[1] (analytic) = -2.569671641804859 " "
y[1] (numeric) = -2.5696716418050976 " "
absolute error = 2.3847590568948362000000000000E-13 " "
relative error = 9.280403838756045000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.63999999999988 " "
y[1] (analytic) = -2.5676742247465056 " "
y[1] (numeric) = -2.567674224746745 " "
absolute error = 2.39364084109183750000000000000E-13 " "
relative error = 9.322213924268957000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.638999999999880 " "
y[1] (analytic) = -2.5656768800139216 " "
y[1] (numeric) = -2.565676880014162 " "
absolute error = 2.4025226252888388000000000000E-13 " "
relative error = 9.364088845341282000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.637999999999879 " "
y[1] (analytic) = -2.5636796086044518 " "
y[1] (numeric) = -2.5636796086046925 " "
absolute error = 2.40696351738733940000000000000E-13 " "
relative error = 9.38870640975912900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.636999999999879 " "
y[1] (analytic) = -2.561682411515367 " "
y[1] (numeric) = -2.561682411515608 " "
absolute error = 2.411404409485840000000000000E-13 " "
relative error = 9.413362088313555000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.635999999999878 " "
y[1] (analytic) = -2.559685289743864 " "
y[1] (numeric) = -2.559685289744106 " "
absolute error = 2.42028619368284130000000000000E-13 " "
relative error = 9.455405331977464000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.634999999999878 " "
y[1] (analytic) = -2.5576882442870654 " "
y[1] (numeric) = -2.557688244287308 " "
absolute error = 2.4247270857813420000000000000E-13 " "
relative error = 9.480151035597439000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.633999999999878 " "
y[1] (analytic) = -2.555691276142016 " "
y[1] (numeric) = -2.555691276142259 " "
absolute error = 2.4336088699783430000000000000E-13 " "
relative error = 9.522311605852627000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.632999999999877 " "
y[1] (analytic) = -2.5536943863056836 " "
y[1] (numeric) = -2.553694386305928 " "
absolute error = 2.44249065417534440000000000000E-13 " "
relative error = 9.56453782125741100000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.631999999999877 " "
y[1] (analytic) = -2.5516975757749583 " "
y[1] (numeric) = -2.5516975757752034 " "
absolute error = 2.45137243837234560000000000000E-13 " "
relative error = 9.606829828287377000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.630999999999877 " "
y[1] (analytic) = -2.549700845546651 " "
y[1] (numeric) = -2.5497008455468966 " "
absolute error = 2.45581333047084630000000000000E-13 " "
relative error = 9.631770467348003000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.629999999999876 " "
y[1] (analytic) = -2.547704196617491 " "
y[1] (numeric) = -2.547704196617737 " "
absolute error = 2.4602542225693470000000000000E-13 " "
relative error = 9.65674989206263000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.628999999999876 " "
y[1] (analytic) = -2.5457076299841277 " "
y[1] (numeric) = -2.5457076299843746 " "
absolute error = 2.4691360067663481000000000000E-13 " "
relative error = 9.699212814873572000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.627999999999876 " "
y[1] (analytic) = -2.5437111466431275 " "
y[1] (numeric) = -2.543711146643375 " "
absolute error = 2.4735768988648488000000000000E-13 " "
relative error = 9.724283758119182000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.626999999999875 " "
y[1] (analytic) = -2.5417147475909734 " "
y[1] (numeric) = -2.5417147475912216 " "
absolute error = 2.482458683061850000000000000E-13 " "
relative error = 9.76686579567874000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.625999999999875 " "
y[1] (analytic) = -2.539718433824065 " "
y[1] (numeric) = -2.5397184338243135 " "
absolute error = 2.48689957516035070000000000000E-13 " "
relative error = 9.792028683336427000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.624999999999875 " "
y[1] (analytic) = -2.537722206338715 " "
y[1] (numeric) = -2.5377222063389646 " "
absolute error = 2.4957813593573520000000000000E-13 " "
relative error = 9.834730346463442000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.623999999999874 " "
y[1] (analytic) = -2.5357260661311516 " "
y[1] (numeric) = -2.535726066131402 " "
absolute error = 2.5046631435543530000000000000E-13 " "
relative error = 9.877498902615328000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.622999999999874 " "
y[1] (analytic) = -2.533730014197515 " "
y[1] (numeric) = -2.533730014197766 " "
absolute error = 2.5091040356528540000000000000E-13 " "
relative error = 9.9028074088136000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.621999999999874 " "
y[1] (analytic) = -2.5317340515338564 " "
y[1] (numeric) = -2.5317340515341082 " "
absolute error = 2.5179858198498550000000000000E-13 " "
relative error = 9.945696382778942000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.620999999999873 " "
y[1] (analytic) = -2.5297381791361393 " "
y[1] (numeric) = -2.5297381791363915 " "
absolute error = 2.52242671194835570000000000000E-13 " "
relative error = 9.971097929232028000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.619999999999873 " "
y[1] (analytic) = -2.527742398000235 " "
y[1] (numeric) = -2.527742398000488 " "
absolute error = 2.5313084961453570000000000000E-13 " "
relative error = 1.001410783847255700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.618999999999873 " "
y[1] (analytic) = -2.525746709121925 " "
y[1] (numeric) = -2.525746709122179 " "
absolute error = 2.5401902803423580000000000000E-13 " "
relative error = 1.005718535104200700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.617999999999872 " "
y[1] (analytic) = -2.5237511134968984 " "
y[1] (numeric) = -2.523751113497153 " "
absolute error = 2.5446311724408590000000000000E-13 " "
relative error = 1.008273422380002000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.616999999999872 " "
y[1] (analytic) = -2.5217556121207503 " "
y[1] (numeric) = -2.521755612121005 " "
absolute error = 2.54907206453935940000000000000E-13 " "
relative error = 1.010832315505639700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.615999999999872 " "
y[1] (analytic) = -2.519760205988982 " "
y[1] (numeric) = -2.5197602059892374 " "
absolute error = 2.553512956637860000000000000E-13 " "
relative error = 1.013395223310795300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.614999999999871 " "
y[1] (analytic) = -2.517764896097 " "
y[1] (numeric) = -2.517764896097256 " "
absolute error = 2.56239474083486130000000000000E-13 " "
relative error = 1.017725977833373600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.613999999999871 " "
y[1] (analytic) = -2.5157696834401135 " "
y[1] (numeric) = -2.51576968344037 " "
absolute error = 2.5668356329333620000000000000E-13 " "
relative error = 1.020298340436084600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.612999999999870 " "
y[1] (analytic) = -2.513774569013535 " "
y[1] (numeric) = -2.5137745690137927 " "
absolute error = 2.5757174171303630000000000000E-13 " "
relative error = 1.024641369548557300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.61199999999987 " "
y[1] (analytic) = -2.51177955381238 " "
y[1] (numeric) = -2.511779553812638 " "
absolute error = 2.5801583092288640000000000000E-13 " "
relative error = 1.027223231160034900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.61099999999987 " "
y[1] (analytic) = -2.5097846388316625 " "
y[1] (numeric) = -2.5097846388319214 " "
absolute error = 2.5890400934258650000000000000E-13 " "
relative error = 1.031578587807078600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.60999999999987 " "
y[1] (analytic) = -2.5077898250662978 " "
y[1] (numeric) = -2.507789825066557 " "
absolute error = 2.59348098552436570000000000000E-13 " "
relative error = 1.034169992876417500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.608999999999870 " "
y[1] (analytic) = -2.5057951135110996 " "
y[1] (numeric) = -2.5057951135113594 " "
absolute error = 2.59792187762286630000000000000E-13 " "
relative error = 1.036765481589067100000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.607999999999869 " "
y[1] (analytic) = -2.503800505160779 " "
y[1] (numeric) = -2.5038005051610397 " "
absolute error = 2.60680366181986760000000000000E-13 " "
relative error = 1.041138723491260900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.606999999999869 " "
y[1] (analytic) = -2.5018060010099448 " "
y[1] (numeric) = -2.501806001010206 " "
absolute error = 2.6112445539183680000000000000E-13 " "
relative error = 1.043743820609689400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.605999999999868 " "
y[1] (analytic) = -2.499811602053101 " "
y[1] (numeric) = -2.4998116020533625 " "
absolute error = 2.6156854460168690000000000000E-13 " "
relative error = 1.046353030711834600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.604999999999868 " "
y[1] (analytic) = -2.497817309284646 " "
y[1] (numeric) = -2.4978173092849083 " "
absolute error = 2.624567230213870000000000000E-13 " "
relative error = 1.050744271992223600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.603999999999868 " "
y[1] (analytic) = -2.4958231236988726 " "
y[1] (numeric) = -2.495823123699136 " "
absolute error = 2.63344901441087130000000000000E-13 " "
relative error = 1.055142485621350400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.602999999999867 " "
y[1] (analytic) = -2.493829046289967 " "
y[1] (numeric) = -2.4938290462902306 " "
absolute error = 2.6378899065093720000000000000E-13 " "
relative error = 1.057766934920307500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.601999999999867 " "
y[1] (analytic) = -2.4918350780520053 " "
y[1] (numeric) = -2.49183507805227 " "
absolute error = 2.6467716907063730000000000000E-13 " "
relative error = 1.062177715539460900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.600999999999867 " "
y[1] (analytic) = -2.489841219978957 " "
y[1] (numeric) = -2.489841219979222 " "
absolute error = 2.6512125828048740000000000000E-13 " "
relative error = 1.064811909101288200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.599999999999866 " "
y[1] (analytic) = -2.4878474730646793 " "
y[1] (numeric) = -2.487847473064945 " "
absolute error = 2.65565347490337440000000000000E-13 " "
relative error = 1.067450277259956600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.598999999999866 " "
y[1] (analytic) = -2.485853838302919 " "
y[1] (numeric) = -2.4858538383031856 " "
absolute error = 2.66453525910037570000000000000E-13 " "
relative error = 1.071879294769575700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.597999999999866 " "
y[1] (analytic) = -2.483860316687311 " "
y[1] (numeric) = -2.4838603166875783 " "
absolute error = 2.6734170432973770000000000000E-13 " "
relative error = 1.076315373025031700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.596999999999865 " "
y[1] (analytic) = -2.481866909211377 " "
y[1] (numeric) = -2.4818669092116448 " "
absolute error = 2.67785793539587760000000000000E-13 " "
relative error = 1.078969192690021200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.595999999999865 " "
y[1] (analytic) = -2.4798736168685243 " "
y[1] (numeric) = -2.4798736168687925 " "
absolute error = 2.6822988274943780000000000000E-13 " "
relative error = 1.081627228601055700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.594999999999865 " "
y[1] (analytic) = -2.4778804406520445 " "
y[1] (numeric) = -2.4778804406523136 " "
absolute error = 2.69118061169137950000000000000E-13 " "
relative error = 1.086081704161321700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.593999999999864 " "
y[1] (analytic) = -2.475887381555115 " "
y[1] (numeric) = -2.4758873815553843 " "
absolute error = 2.695621503789880000000000000E-13 " "
relative error = 1.088749643409365900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.592999999999864 " "
y[1] (analytic) = -2.4738944405707937 " "
y[1] (numeric) = -2.4738944405710637 " "
absolute error = 2.70006239588838070000000000000E-13 " "
relative error = 1.091421829326478500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.591999999999864 " "
y[1] (analytic) = -2.471901618692022 " "
y[1] (numeric) = -2.4719016186922924 " "
absolute error = 2.70450328798688130000000000000E-13 " "
relative error = 1.094098271361599700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.590999999999863 " "
y[1] (analytic) = -2.4699089169116215 " "
y[1] (numeric) = -2.469908916911893 " "
absolute error = 2.71338507218388260000000000000E-13 " "
relative error = 1.098576977314897900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.589999999999863 " "
y[1] (analytic) = -2.467916336222294 " "
y[1] (numeric) = -2.467916336222566 " "
absolute error = 2.7222668563808840000000000000E-13 " "
relative error = 1.103062861745115500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.588999999999863 " "
y[1] (analytic) = -2.46592387761662 " "
y[1] (numeric) = -2.465923877616893 " "
absolute error = 2.7311486405778850000000000000E-13 " "
relative error = 1.107555940947216900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.587999999999862 " "
y[1] (analytic) = -2.4639315420870584 " "
y[1] (numeric) = -2.463931542087332 " "
absolute error = 2.73558953267638570000000000000E-13 " "
relative error = 1.11025387107923500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.586999999999862 " "
y[1] (analytic) = -2.461939330625944 " "
y[1] (numeric) = -2.4619393306262185 " "
absolute error = 2.7444713168733870000000000000E-13 " "
relative error = 1.114759930406412500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.585999999999862 " "
y[1] (analytic) = -2.459947244225489 " "
y[1] (numeric) = -2.459947244225764 " "
absolute error = 2.7533531010703880000000000000E-13 " "
relative error = 1.119273231380731500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.584999999999861 " "
y[1] (analytic) = -2.457955283877779 " "
y[1] (numeric) = -2.457955283878055 " "
absolute error = 2.7577939931688890000000000000E-13 " "
relative error = 1.12198704803859200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.583999999999861 " "
y[1] (analytic) = -2.4559634505747745 " "
y[1] (numeric) = -2.455963450575051 " "
absolute error = 2.766675777365890000000000000E-13 " "
relative error = 1.126513416442903000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.582999999999860 " "
y[1] (analytic) = -2.453971745308309 " "
y[1] (numeric) = -2.453971745308586 " "
absolute error = 2.77111666946439100000000000000E-13 " "
relative error = 1.129237398418471400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.58199999999986 " "
y[1] (analytic) = -2.4519801690700875 " "
y[1] (numeric) = -2.451980169070365 " "
absolute error = 2.77555756156289140000000000000E-13 " "
relative error = 1.131965746124089000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.58099999999986 " "
y[1] (analytic) = -2.449988722851686 " "
y[1] (numeric) = -2.4499887228519643 " "
absolute error = 2.78443934575989260000000000000E-13 " "
relative error = 1.136511086679174600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.57999999999986 " "
y[1] (analytic) = -2.4479974076445505 " "
y[1] (numeric) = -2.4479974076448294 " "
absolute error = 2.7888802378583930000000000000E-13 " "
relative error = 1.139249669607223200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.578999999999860 " "
y[1] (analytic) = -2.4460062244399965 " "
y[1] (numeric) = -2.4460062244402763 " "
absolute error = 2.79776202205539450000000000000E-13 " "
relative error = 1.143808218515850600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.577999999999859 " "
y[1] (analytic) = -2.444015174229207 " "
y[1] (numeric) = -2.4440151742294876 " "
absolute error = 2.80664380625239600000000000000E-13 " "
relative error = 1.148374132798727400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.576999999999859 " "
y[1] (analytic) = -2.442024258003232 " "
y[1] (numeric) = -2.442024258003513 " "
absolute error = 2.81108469835089640000000000000E-13 " "
relative error = 1.151128900189318200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.575999999999858 " "
y[1] (analytic) = -2.440033476752988 " "
y[1] (numeric) = -2.44003347675327 " "
absolute error = 2.81996648254789760000000000000E-13 " "
relative error = 1.155708111964306300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.574999999999858 " "
y[1] (analytic) = -2.4380428314692555 " "
y[1] (numeric) = -2.4380428314695384 " "
absolute error = 2.8288482667448990000000000000E-13 " "
relative error = 1.160294737332456700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.573999999999858 " "
y[1] (analytic) = -2.4360523231426803 " "
y[1] (numeric) = -2.436052323142964 " "
absolute error = 2.83773005094190000000000000E-13 " "
relative error = 1.164888793226340500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.572999999999857 " "
y[1] (analytic) = -2.4340619527637704 " "
y[1] (numeric) = -2.434061952764055 " "
absolute error = 2.84661183513890140000000000000E-13 " "
relative error = 1.169490296624003000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.571999999999857 " "
y[1] (analytic) = -2.432071721322896 " "
y[1] (numeric) = -2.4320717213231817 " "
absolute error = 2.85549361933590260000000000000E-13 " "
relative error = 1.174099264549110900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.570999999999857 " "
y[1] (analytic) = -2.430081629810289 " "
y[1] (numeric) = -2.430081629810575 " "
absolute error = 2.8599345114344030000000000000E-13 " "
relative error = 1.176888247847736600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.569999999999856 " "
y[1] (analytic) = -2.4280916792160405 " "
y[1] (numeric) = -2.428091679216327 " "
absolute error = 2.8643754035329040000000000000E-13 " "
relative error = 1.179681734446586700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.568999999999856 " "
y[1] (analytic) = -2.426101870530101 " "
y[1] (numeric) = -2.426101870530388 " "
absolute error = 2.86881629563140450000000000000E-13 " "
relative error = 1.182479734457552200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.567999999999856 " "
y[1] (analytic) = -2.4241122047422787 " "
y[1] (numeric) = -2.4241122047425665 " "
absolute error = 2.8776980798284060000000000000E-13 " "
relative error = 1.187114224415346500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.566999999999855 " "
y[1] (analytic) = -2.42212268284224 " "
y[1] (numeric) = -2.422122682842528 " "
absolute error = 2.88213897192690640000000000000E-13 " "
relative error = 1.189922786464664300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.565999999999855 " "
y[1] (analytic) = -2.420133305819506 " "
y[1] (numeric) = -2.420133305819795 " "
absolute error = 2.89102075612390760000000000000E-13 " "
relative error = 1.194570873088724200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.564999999999855 " "
y[1] (analytic) = -2.4181440746634544 " "
y[1] (numeric) = -2.418144074663744 " "
absolute error = 2.89546164822240800000000000000E-13 " "
relative error = 1.197390047416998800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.563999999999854 " "
y[1] (analytic) = -2.4161549903633155 " "
y[1] (numeric) = -2.416154990363606 " "
absolute error = 2.90434343241940950000000000000E-13 " "
relative error = 1.202051790552842600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.562999999999854 " "
y[1] (analytic) = -2.414166053908174 " "
y[1] (numeric) = -2.414166053908465 " "
absolute error = 2.908784324517910000000000000E-13 " "
relative error = 1.204881627678022800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.561999999999854 " "
y[1] (analytic) = -2.4121772662869665 " "
y[1] (numeric) = -2.4121772662872583 " "
absolute error = 2.91766610871491140000000000000E-13 " "
relative error = 1.209557087488034200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.560999999999853 " "
y[1] (analytic) = -2.41018862848848 " "
y[1] (numeric) = -2.4101886284887724 " "
absolute error = 2.9221070008134120000000000000E-13 " "
relative error = 1.212397638207253100000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.559999999999853 " "
y[1] (analytic) = -2.4082001415013528 " "
y[1] (numeric) = -2.4082001415016454 " "
absolute error = 2.92654789291191260000000000000E-13 " "
relative error = 1.215242804149743300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.558999999999853 " "
y[1] (analytic) = -2.406211806314071 " "
y[1] (numeric) = -2.4062118063143645 " "
absolute error = 2.9354296771089140000000000000E-13 " "
relative error = 1.21993819056416290000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.557999999999852 " "
y[1] (analytic) = -2.4042236239149704 " "
y[1] (numeric) = -2.4042236239152643 " "
absolute error = 2.93987056920741450000000000000E-13 " "
relative error = 1.222794144423309400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.556999999999852 " "
y[1] (analytic) = -2.402235595292233 " "
y[1] (numeric) = -2.4022355952925274 " "
absolute error = 2.9443114613059150000000000000E-13 " "
relative error = 1.225654747217971600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.555999999999852 " "
y[1] (analytic) = -2.400247721433887 " "
y[1] (numeric) = -2.4002477214341824 " "
absolute error = 2.95319324550291640000000000000E-13 " "
relative error = 1.230370190181330300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.554999999999851 " "
y[1] (analytic) = -2.3982600033278074 " "
y[1] (numeric) = -2.398260003328103 " "
absolute error = 2.9576341376014170000000000000E-13 " "
relative error = 1.233241655824400400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.553999999999851 " "
y[1] (analytic) = -2.396272441961711 " "
y[1] (numeric) = -2.3962724419620076 " "
absolute error = 2.96651592179841800000000000000E-13 " "
relative error = 1.237971054480715300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.552999999999850 " "
y[1] (analytic) = -2.3942850383231593 " "
y[1] (numeric) = -2.394285038323457 " "
absolute error = 2.97539770599541950000000000000E-13 " "
relative error = 1.242708223277894800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.55199999999985 " "
y[1] (analytic) = -2.3922977933995564 " "
y[1] (numeric) = -2.3922977933998544 " "
absolute error = 2.979838598093920000000000000E-13 " "
relative error = 1.245596850992134900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.55099999999985 " "
y[1] (analytic) = -2.3903107081781463 " "
y[1] (numeric) = -2.390310708178445 " "
absolute error = 2.98872038229092140000000000000E-13 " "
relative error = 1.250348070677754200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.54999999999985 " "
y[1] (analytic) = -2.388323783646015 " "
y[1] (numeric) = -2.3883237836463143 " "
absolute error = 2.9931612743894220000000000000E-13 " "
relative error = 1.253247694004061000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.548999999999850 " "
y[1] (analytic) = -2.3863370207900867 " "
y[1] (numeric) = -2.3863370207903865 " "
absolute error = 2.99760216648792270000000000000E-13 " "
relative error = 1.256152060824775600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.547999999999849 " "
y[1] (analytic) = -2.3843504205971238 " "
y[1] (numeric) = -2.3843504205974244 " "
absolute error = 3.0064839506849240000000000000E-13 " "
relative error = 1.26092369842684300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.546999999999849 " "
y[1] (analytic) = -2.3823639840537267 " "
y[1] (numeric) = -2.382363984054028 " "
absolute error = 3.01092484278342450000000000000E-13 " "
relative error = 1.26383913748568580000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.545999999999848 " "
y[1] (analytic) = -2.380377712146332 " "
y[1] (numeric) = -2.380377712146634 " "
absolute error = 3.0198066269804260000000000000E-13 " "
relative error = 1.268624979796813500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.544999999999848 " "
y[1] (analytic) = -2.378391605861211 " "
y[1] (numeric) = -2.3783916058615135 " "
absolute error = 3.02424751907892640000000000000E-13 " "
relative error = 1.2715515441721600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.543999999999848 " "
y[1] (analytic) = -2.376405666184471 " "
y[1] (numeric) = -2.3764056661847737 " "
absolute error = 3.0286884111774270000000000000E-13 " "
relative error = 1.274482911009151800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.542999999999847 " "
y[1] (analytic) = -2.37441989410205 " "
y[1] (numeric) = -2.3744198941023535 " "
absolute error = 3.03757019537442830000000000000E-13 " "
relative error = 1.279289397346953500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.541999999999847 " "
y[1] (analytic) = -2.3724342905997213 " "
y[1] (numeric) = -2.3724342906000255 " "
absolute error = 3.0420110874729290000000000000E-13 " "
relative error = 1.282231967193471500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.540999999999847 " "
y[1] (analytic) = -2.3704488566630877 " "
y[1] (numeric) = -2.370448856663393 " "
absolute error = 3.050892871669930000000000000E-13 " "
relative error = 1.287052814109102000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.539999999999846 " "
y[1] (analytic) = -2.3684635932775833 " "
y[1] (numeric) = -2.368463593277889 " "
absolute error = 3.0553337637684310000000000000E-13 " "
relative error = 1.290006640777757000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.538999999999846 " "
y[1] (analytic) = -2.366478501428471 " "
y[1] (numeric) = -2.3664785014287775 " "
absolute error = 3.0642155479654320000000000000E-13 " "
relative error = 1.294841912198140800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.537999999999846 " "
y[1] (analytic) = -2.3644935821008435 " "
y[1] (numeric) = -2.3644935821011503 " "
absolute error = 3.06865644006393270000000000000E-13 " "
relative error = 1.297807049802792400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.536999999999845 " "
y[1] (analytic) = -2.362508836279619 " "
y[1] (numeric) = -2.3625088362799267 " "
absolute error = 3.0775382242609340000000000000E-13 " "
relative error = 1.302656809998355000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.535999999999845 " "
y[1] (analytic) = -2.360524264949544 " "
y[1] (numeric) = -2.360524264949852 " "
absolute error = 3.08197911635943460000000000000E-13 " "
relative error = 1.305633312956141800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.534999999999845 " "
y[1] (analytic) = -2.358539869095189 " "
y[1] (numeric) = -2.358539869095498 " "
absolute error = 3.0908609005564360000000000000E-13 " "
relative error = 1.310497626543064800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.533999999999844 " "
y[1] (analytic) = -2.3565556497009505 " "
y[1] (numeric) = -2.35655564970126 " "
absolute error = 3.09530179265493640000000000000E-13 " "
relative error = 1.313485549576447800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.532999999999844 " "
y[1] (analytic) = -2.3545716077510477 " "
y[1] (numeric) = -2.3545716077513577 " "
absolute error = 3.0997426847534370000000000000E-13 " "
relative error = 1.31647840929931800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.531999999999844 " "
y[1] (analytic) = -2.3525877442295218 " "
y[1] (numeric) = -2.3525877442298326 " "
absolute error = 3.10862446895043830000000000000E-13 " "
relative error = 1.321363879657768400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.530999999999843 " "
y[1] (analytic) = -2.350604060120237 " "
y[1] (numeric) = -2.3506040601205487 " "
absolute error = 3.11750625314743960000000000000E-13 " "
relative error = 1.326257495270375000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.529999999999843 " "
y[1] (analytic) = -2.348620556406877 " "
y[1] (numeric) = -2.348620556407189 " "
absolute error = 3.121947145245940000000000000E-13 " "
relative error = 1.32926842385394320000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.528999999999843 " "
y[1] (analytic) = -2.3466372340729453 " "
y[1] (numeric) = -2.3466372340732584 " "
absolute error = 3.13082892944294140000000000000E-13 " "
relative error = 1.33417678880382900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.527999999999842 " "
y[1] (analytic) = -2.344654094101765 " "
y[1] (numeric) = -2.3446540941020784 " "
absolute error = 3.1352698215414420000000000000E-13 " "
relative error = 1.33719930348299900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.526999999999842 " "
y[1] (analytic) = -2.342671137476475 " "
y[1] (numeric) = -2.342671137476789 " "
absolute error = 3.13971071363994270000000000000E-13 " "
relative error = 1.34022683056659800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.525999999999842 " "
y[1] (analytic) = -2.3406883651800316 " "
y[1] (numeric) = -2.3406883651803465 " "
absolute error = 3.1485924978369440000000000000E-13 " "
relative error = 1.34515664053158700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.524999999999841 " "
y[1] (analytic) = -2.338705778195208 " "
y[1] (numeric) = -2.3387057781955236 " "
absolute error = 3.1574742820339450000000000000E-13 " "
relative error = 1.350094702579725800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.523999999999841 " "
y[1] (analytic) = -2.336723377504591 " "
y[1] (numeric) = -2.336723377504907 " "
absolute error = 3.1619151741324460000000000000E-13 " "
relative error = 1.353140557659454300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.522999999999840 " "
y[1] (analytic) = -2.33474116409058 " "
y[1] (numeric) = -2.334741164090897 " "
absolute error = 3.1707969583294470000000000000E-13 " "
relative error = 1.358093568185544400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.52199999999984 " "
y[1] (analytic) = -2.33275913893539 " "
y[1] (numeric) = -2.3327591389357076 " "
absolute error = 3.17523785042794770000000000000E-13 " "
relative error = 1.361151178203954000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.52099999999984 " "
y[1] (analytic) = -2.330777303021045 " "
y[1] (numeric) = -2.3307773030213634 " "
absolute error = 3.1841196346249490000000000000E-13 " "
relative error = 1.366119204309155200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.51999999999984 " "
y[1] (analytic) = -2.328795657329381 " "
y[1] (numeric) = -2.3287956573297004 " "
absolute error = 3.193001418821950000000000000E-13 " "
relative error = 1.371095574131920000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.518999999999840 " "
y[1] (analytic) = -2.326814202842044 " "
y[1] (numeric) = -2.326814202842364 " "
absolute error = 3.1974423109204510000000000000E-13 " "
relative error = 1.374171735334516200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.517999999999839 " "
y[1] (analytic) = -2.324832940540488 " "
y[1] (numeric) = -2.3248329405408086 " "
absolute error = 3.2063240951174520000000000000E-13 " "
relative error = 1.379163224679718600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.516999999999839 " "
y[1] (analytic) = -2.3228518714059754 " "
y[1] (numeric) = -2.3228518714062965 " "
absolute error = 3.21076498721595270000000000000E-13 " "
relative error = 1.382251286334733600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.515999999999838 " "
y[1] (analytic) = -2.3208709964195755 " "
y[1] (numeric) = -2.320870996419897 " "
absolute error = 3.21520587931445330000000000000E-13 " "
relative error = 1.385344503970524500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.514999999999838 " "
y[1] (analytic) = -2.3188903165621624 " "
y[1] (numeric) = -2.318890316562485 " "
absolute error = 3.22408766351145460000000000000E-13 " "
relative error = 1.390357983076698200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.513999999999838 " "
y[1] (analytic) = -2.316909832814417 " "
y[1] (numeric) = -2.3169098328147397 " "
absolute error = 3.2285285556099550000000000000E-13 " "
relative error = 1.393463185266976500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.512999999999837 " "
y[1] (analytic) = -2.314929546156822 " "
y[1] (numeric) = -2.3149295461571455 " "
absolute error = 3.23741033980695650000000000000E-13 " "
relative error = 1.398491952025758300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.511999999999837 " "
y[1] (analytic) = -2.312949457569664 " "
y[1] (numeric) = -2.3129494575699887 " "
absolute error = 3.24629212400395800000000000000E-13 " "
relative error = 1.403529209589822000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.510999999999837 " "
y[1] (analytic) = -2.310969568033032 " "
y[1] (numeric) = -2.3109695680333577 " "
absolute error = 3.2551739082009590000000000000E-13 " "
relative error = 1.4085749778918900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.509999999999836 " "
y[1] (analytic) = -2.308989878526816 " "
y[1] (numeric) = -2.308989878527142 " "
absolute error = 3.25961480029945960000000000000E-13 " "
relative error = 1.411705971781549000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.508999999999836 " "
y[1] (analytic) = -2.307010390030704 " "
y[1] (numeric) = -2.307010390031031 " "
absolute error = 3.2684965844964610000000000000E-13 " "
relative error = 1.41676717132295180000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.507999999999836 " "
y[1] (analytic) = -2.3050311035241853 " "
y[1] (numeric) = -2.305031103524513 " "
absolute error = 3.2773783686934620000000000000E-13 " "
relative error = 1.421836939068911200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.506999999999835 " "
y[1] (analytic) = -2.3030520199865463 " "
y[1] (numeric) = -2.3030520199868745 " "
absolute error = 3.28181926079196300000000000000E-13 " "
relative error = 1.424987031257389500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.505999999999835 " "
y[1] (analytic) = -2.3010731403968703 " "
y[1] (numeric) = -2.301073140397199 " "
absolute error = 3.28626015289046340000000000000E-13 " "
relative error = 1.428142415466062000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.504999999999835 " "
y[1] (analytic) = -2.299094465734037 " "
y[1] (numeric) = -2.299094465734366 " "
absolute error = 3.2907010449889640000000000000E-13 " "
relative error = 1.431303103910667200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.503999999999834 " "
y[1] (analytic) = -2.2971159969767205 " "
y[1] (numeric) = -2.29711599697705 " "
absolute error = 3.29514193708746460000000000000E-13 " "
relative error = 1.434469108840940300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.502999999999834 " "
y[1] (analytic) = -2.2951377351033897 " "
y[1] (numeric) = -2.29513773510372 " "
absolute error = 3.3040237212844660000000000000E-13 " "
relative error = 1.439575355653166800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.501999999999834 " "
y[1] (analytic) = -2.2931596810923067 " "
y[1] (numeric) = -2.2931596810926376 " "
absolute error = 3.30846461338296650000000000000E-13 " "
relative error = 1.442753699475056400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.500999999999833 " "
y[1] (analytic) = -2.2911818359215252 " "
y[1] (numeric) = -2.2911818359218565 " "
absolute error = 3.3129055054814670000000000000E-13 " "
relative error = 1.445937399442152600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.499999999999833 " "
y[1] (analytic) = -2.28920420056889 " "
y[1] (numeric) = -2.2892042005692224 " "
absolute error = 3.32178728967846840000000000000E-13 " "
relative error = 1.45106639628433810000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.498999999999833 " "
y[1] (analytic) = -2.287226776012037 " "
y[1] (numeric) = -2.28722677601237 " "
absolute error = 3.33066907387546960000000000000E-13 " "
relative error = 1.4562041284261100000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.497999999999832 " "
y[1] (analytic) = -2.28524956322839 " "
y[1] (numeric) = -2.285249563228724 " "
absolute error = 3.3395508580724710000000000000E-13 " "
relative error = 1.46135061649663400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.496999999999832 " "
y[1] (analytic) = -2.2832725631951627 " "
y[1] (numeric) = -2.283272563195497 " "
absolute error = 3.34399175017097150000000000000E-13 " "
relative error = 1.464560913170813400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.495999999999832 " "
y[1] (analytic) = -2.281295776889354 " "
y[1] (numeric) = -2.281295776889689 " "
absolute error = 3.3528735343679730000000000000E-13 " "
relative error = 1.46972328986632400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.494999999999831 " "
y[1] (analytic) = -2.2793192052877504 " "
y[1] (numeric) = -2.279319205288086 " "
absolute error = 3.35731442646647340000000000000E-13 " "
relative error = 1.472946140530866400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.493999999999831 " "
y[1] (analytic) = -2.2773428493669234 " "
y[1] (numeric) = -2.27734284936726 " "
absolute error = 3.36619621066347460000000000000E-13 " "
relative error = 1.47812447809482900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.492999999999830 " "
y[1] (analytic) = -2.275366710103229 " "
y[1] (numeric) = -2.2753667101035666 " "
absolute error = 3.3750779948604760000000000000E-13 " "
relative error = 1.48331167010321400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.49199999999983 " "
y[1] (analytic) = -2.2733907884728066 " "
y[1] (numeric) = -2.273390788473145 " "
absolute error = 3.3839597790574770000000000000E-13 " "
relative error = 1.488507737523963600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.49099999999983 " "
y[1] (analytic) = -2.2714150854515776 " "
y[1] (numeric) = -2.2714150854519164 " "
absolute error = 3.3884006711559780000000000000E-13 " "
relative error = 1.491757580047212400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.48999999999983 " "
y[1] (analytic) = -2.269439602015245 " "
y[1] (numeric) = -2.2694396020155843 " "
absolute error = 3.39284156325447840000000000000E-13 " "
relative error = 1.495012936339729400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.488999999999830 " "
y[1] (analytic) = -2.2674643391392917 " "
y[1] (numeric) = -2.267464339139632 " "
absolute error = 3.40172334745147960000000000000E-13 " "
relative error = 1.50023234709073420000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.487999999999829 " "
y[1] (analytic) = -2.2654892977989807 " "
y[1] (numeric) = -2.2654892977993217 " "
absolute error = 3.4106051316484810000000000000E-13 " "
relative error = 1.50546071215698500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.486999999999829 " "
y[1] (analytic) = -2.2635144789693533 " "
y[1] (numeric) = -2.2635144789696953 " "
absolute error = 3.4194869158454820000000000000E-13 " "
relative error = 1.51069805279199200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = 1.0 + sin(x);"
Iterations = 514
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Expected Time Remaining "= 0 Years 0 Days 0 Hours 55 Minutes 28 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 55 Minutes 16 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 58 Minutes 17 Seconds
"Time to Timeout " Unknown
Percent Done = 5.15000000000172 "%"
(%o57) true
(%o57) diffeq.max