(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp1
1
array_tmp2 : ----------------, array_tmp3 : array_tmp2 + array_const_0D0 ,
1 array_const_2D0 1 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_tmp1_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
array_tmp1
2
array_tmp2 : ----------------, array_tmp3 : array_tmp2 ,
2 array_const_2D0 2 2
1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
array_tmp1
3
array_tmp2 : ----------------, array_tmp3 : array_tmp2 ,
3 array_const_2D0 3 3
1
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
array_tmp1
4
array_tmp2 : ----------------, array_tmp3 : array_tmp2 ,
4 array_const_2D0 4 4
1
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
array_tmp1
5
array_tmp2 : ----------------, array_tmp3 : array_tmp2 ,
5 array_const_2D0 5 5
1
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
array_tmp1_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------,
kkk kkk - 1
array_tmp1
kkk
array_tmp2 : ----------------, array_tmp3 : array_tmp2 , order_d : 1,
kkk array_const_2D0 kkk kkk
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 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp1
1
array_tmp2 : ----------------, array_tmp3 : array_tmp2 + array_const_0D0 ,
1 array_const_2D0 1 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_tmp1_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
array_tmp1
2
array_tmp2 : ----------------, array_tmp3 : array_tmp2 ,
2 array_const_2D0 2 2
1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
array_tmp1
3
array_tmp2 : ----------------, array_tmp3 : array_tmp2 ,
3 array_const_2D0 3 3
1
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
array_tmp1
4
array_tmp2 : ----------------, array_tmp3 : array_tmp2 ,
4 array_const_2D0 4 4
1
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
array_tmp1
5
array_tmp2 : ----------------, array_tmp3 : array_tmp2 ,
5 array_const_2D0 5 5
1
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
array_tmp1_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------,
kkk kkk - 1
array_tmp1
kkk
array_tmp2 : ----------------, array_tmp3 : array_tmp2 , order_d : 1,
kkk array_const_2D0 kkk kkk
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)
- cos(x)
(%i55) exact_soln_y(x) := block(--------)
2.0
- cos(x)
(%o55) exact_soln_y(x) := block(--------)
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/div_sin_cpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x) / 2.0;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS,
"glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "glob_display_interval:0.1,"),
omniout_str(ALWAYS, "glob_max_minutes:10,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (-cos(x)/2.0) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 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_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 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_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_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_look_poles : true, glob_max_iter : 1000000,
glob_display_interval : 0.1, glob_max_minutes : 10,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = sin(x) / 2.0;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-12T22:23:57-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "div_sin_c"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x) / 2.0;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 156 | "), logitem_str(html_log_file, "div_sin_c diffeq.max"),
logitem_str(html_log_file,
"div_sin_c maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%o56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/div_sin_cpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x) / 2.0;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS,
"glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "glob_display_interval:0.1,"),
omniout_str(ALWAYS, "glob_max_minutes:10,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (-cos(x)/2.0) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 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_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 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_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_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_look_poles : true, glob_max_iter : 1000000,
glob_display_interval : 0.1, glob_max_minutes : 10,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = sin(x) / 2.0;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-12T22:23:57-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "div_sin_c"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x) / 2.0;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 156 | "), logitem_str(html_log_file, "div_sin_c diffeq.max"),
logitem_str(html_log_file,
"div_sin_c maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i57) main()
"##############ECHO OF PROBLEM#################"
"##############temp/div_sin_cpostode.ode#################"
"diff ( y , x , 1 ) = sin(x) / 2.0;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:-5.0,"
"x_end:5.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.05,"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"glob_display_interval:0.1,"
"glob_max_minutes:10,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (-cos(x)/2.0) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 10. ""
estimated_steps = 10000. ""
step_error = 1.00000000000000E-14 ""
est_needed_step_err = 1.00000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 3.5166183127224690000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 ""
max_value3 = 3.5166183127224690000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 ""
value3 = 3.5166183127224690000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = -5. " "
y[1] (analytic) = -0.14183109273161312 " "
y[1] (numeric) = -0.14183109273161312 " "
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) = -0.14183109273161312 " "
y[1] (numeric) = -0.14183109273161312 " "
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) = -0.1413515597586513 " "
y[1] (numeric) = -0.14135155975865146 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 1.17815080341609720000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.998000000000000 " "
y[1] (analytic) = -0.14087188543414148 " "
y[1] (numeric) = -0.1408718854341418 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 2.36432490671290070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.996999999999999 " "
y[1] (analytic) = -0.140392070237758 " "
y[1] (numeric) = -0.14039207023775846 " "
absolute error = 4.7184478546569153000000000000000E-16 " "
relative error = 3.36090766855000330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.995999999999999 " "
y[1] (analytic) = -0.13991211464931594 " "
y[1] (numeric) = -0.13991211464931658 " "
absolute error = 6.383782391594650000000000000000E-16 " "
relative error = 4.5627088173138847000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.994999999999998 " "
y[1] (analytic) = -0.1394320191487709 " "
y[1] (numeric) = -0.1394320191487717 " "
absolute error = 8.0491169285323850000000000000000E-16 " "
relative error = 5.7727894766726100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.993999999999998 " "
y[1] (analytic) = -0.13895178421621834 " "
y[1] (numeric) = -0.13895178421621932 " "
absolute error = 9.714451465470120000000000000000E-16 " "
relative error = 6.9912390979836410000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.992999999999998 " "
y[1] (analytic) = -0.1384714103318931 " "
y[1] (numeric) = -0.13847141033189428 " "
absolute error = 1.1657341758564144000000000000000E-15 " "
relative error = 8.4185910511226970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.991999999999997 " "
y[1] (analytic) = -0.13799089797616912 " "
y[1] (numeric) = -0.13799089797617045 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 9.654750053009070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.990999999999997 " "
y[1] (analytic) = -0.13751024762955866 " "
y[1] (numeric) = -0.13751024762956013 " "
absolute error = 1.4710455076283324000000000000000E-15 " "
relative error = 1.0697715501110931000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.989999999999997 " "
y[1] (analytic) = -0.13702945977271203 " "
y[1] (numeric) = -0.13702945977271364 " "
absolute error = 1.609823385706477000000000000000E-15 " "
relative error = 1.1748009430794358000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.988999999999996 " "
y[1] (analytic) = -0.13654853488641702 " "
y[1] (numeric) = -0.1365485348864188 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.3008977656756615000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.987999999999996 " "
y[1] (analytic) = -0.1360674734515985 " "
y[1] (numeric) = -0.13606747345160045 " "
absolute error = 1.942890293094024000000000000000E-15 " "
relative error = 1.4278873883736387000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.986999999999996 " "
y[1] (analytic) = -0.1355862759493179 " "
y[1] (numeric) = -0.13558627594932 " "
absolute error = 2.0816681711721685000000000000000E-15 " "
relative error = 1.5353089068913545000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.985999999999995 " "
y[1] (analytic) = -0.13510494286077263 " "
y[1] (numeric) = -0.13510494286077487 " "
absolute error = 2.248201624865942000000000000000E-15 " "
relative error = 1.6640409871478518000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.984999999999995 " "
y[1] (analytic) = -0.13462347466729577 " "
y[1] (numeric) = -0.13462347466729815 " "
absolute error = 2.3869795029440866000000000000000E-15 " "
relative error = 1.773078215997019000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.983999999999995 " "
y[1] (analytic) = -0.13414187185035545 " "
y[1] (numeric) = -0.134141871850358 " "
absolute error = 2.55351295663786000000000000000E-15 " "
relative error = 1.9035912660339796000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.982999999999994 " "
y[1] (analytic) = -0.13366013489155446 " "
y[1] (numeric) = -0.13366013489155718 " "
absolute error = 2.7200464103316335000000000000000E-15 " "
relative error = 2.0350468840530134000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.981999999999994 " "
y[1] (analytic) = -0.13317826427262972 " "
y[1] (numeric) = -0.1331782642726326 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.167455687901351800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.980999999999994 " "
y[1] (analytic) = -0.1326962604754518 " "
y[1] (numeric) = -0.13269626047545485 " "
absolute error = 3.0531133177191805000000000000000E-15 " "
relative error = 2.3008284534770237000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.979999999999993 " "
y[1] (analytic) = -0.13221412398202445 " "
y[1] (numeric) = -0.13221412398202767 " "
absolute error = 3.219646771412954000000000000000E-15 " "
relative error = 2.43517611768217000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.978999999999993 " "
y[1] (analytic) = -0.13173185527448417 " "
y[1] (numeric) = -0.13173185527448752 " "
absolute error = 3.3584246494910985000000000000000E-15 " "
relative error = 2.549440029135921000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.977999999999993 " "
y[1] (analytic) = -0.13124945483509956 " "
y[1] (numeric) = -0.13124945483510309 " "
absolute error = 3.524958103184872000000000000000E-15 " "
relative error = 2.6856935197282095000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.976999999999992 " "
y[1] (analytic) = -0.13076692314627106 " "
y[1] (numeric) = -0.13076692314627475 " "
absolute error = 3.6914915568786455000000000000000E-15 " "
relative error = 2.8229551235594025000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.975999999999992 " "
y[1] (analytic) = -0.1302842606905303 " "
y[1] (numeric) = -0.13028426069053417 " "
absolute error = 3.858025010572419000000000000000E-15 " "
relative error = 2.9612364456951157000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.974999999999992 " "
y[1] (analytic) = -0.12980146795053973 " "
y[1] (numeric) = -0.12980146795054376 " "
absolute error = 4.0245584642661925000000000000000E-15 " "
relative error = 3.100549267901756000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.973999999999991 " "
y[1] (analytic) = -0.12931854540909204 " "
y[1] (numeric) = -0.1293185454090962 " "
absolute error = 4.163336342344337000000000000000E-15 " "
relative error = 3.219442601348363000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.972999999999991 " "
y[1] (analytic) = -0.1288354935491097 " "
y[1] (numeric) = -0.12883549354911403 " "
absolute error = 4.3298697960381105000000000000000E-15 " "
relative error = 3.3607740202335196000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.971999999999990 " "
y[1] (analytic) = -0.12835231285364454 " "
y[1] (numeric) = -0.12835231285364904 " "
absolute error = 4.496403249731884000000000000000E-15 " "
relative error = 3.5031727514399900000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.97099999999999 " "
y[1] (analytic) = -0.1278690038058772 " "
y[1] (numeric) = -0.12786900380588187 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.646651310824818300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96999999999999 " "
y[1] (analytic) = -0.12738556688911676 " "
y[1] (numeric) = -0.12738556688912156 " "
absolute error = 4.801714581503802000000000000000E-15 " "
relative error = 3.7694337739874980000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96899999999999 " "
y[1] (analytic) = -0.1269020025868 " "
y[1] (numeric) = -0.12690200258680498 " "
absolute error = 4.9682480351975755000000000000000E-15 " "
relative error = 3.915027291865888000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.967999999999990 " "
y[1] (analytic) = -0.12641831138249127 " "
y[1] (numeric) = -0.1264183113824964 " "
absolute error = 5.134781488891349000000000000000E-15 " "
relative error = 4.061738709161803000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.966999999999989 " "
y[1] (analytic) = -0.12593449375988167 " "
y[1] (numeric) = -0.12593449375988697 " "
absolute error = 5.3013149425851220000000000000000E-15 " "
relative error = 4.209581334160201000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.965999999999989 " "
y[1] (analytic) = -0.1254505502027888 " "
y[1] (numeric) = -0.12545055020279428 " "
absolute error = 5.467848396278896000000000000000E-15 " "
relative error = 4.358568684984009000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.964999999999988 " "
y[1] (analytic) = -0.12496648119515619 " "
y[1] (numeric) = -0.12496648119516182 " "
absolute error = 5.6343818499726690000000000000000E-15 " "
relative error = 4.508714493747834600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.963999999999988 " "
y[1] (analytic) = -0.1244822872210528 " "
y[1] (numeric) = -0.12448228722105859 " "
absolute error = 5.7870375158586280000000000000000E-15 " "
relative error = 4.648884307196364000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.962999999999988 " "
y[1] (analytic) = -0.12399796876467256 " "
y[1] (numeric) = -0.1239979687646785 " "
absolute error = 5.9396931817445870000000000000000E-15 " "
relative error = 4.790153613739539000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.961999999999987 " "
y[1] (analytic) = -0.12351352631033388 " "
y[1] (numeric) = -0.12351352631033999 " "
absolute error = 6.106226635438361000000000000000E-15 " "
relative error = 4.9437715996353004000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.960999999999987 " "
y[1] (analytic) = -0.12302896034247919 " "
y[1] (numeric) = -0.12302896034248546 " "
absolute error = 6.2727600891321340000000000000000E-15 " "
relative error = 5.098604484399832000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.959999999999987 " "
y[1] (analytic) = -0.12254427134567442 " "
y[1] (numeric) = -0.12254427134568084 " "
absolute error = 6.4254157550180930000000000000000E-15 " "
relative error = 5.243342413692436000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.958999999999986 " "
y[1] (analytic) = -0.1220594598046085 " "
y[1] (numeric) = -0.12205945980461509 " "
absolute error = 6.591949208711867000000000000000E-15 " "
relative error = 5.4006049340740890000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.957999999999986 " "
y[1] (analytic) = -0.12157452620409295 " "
y[1] (numeric) = -0.12157452620409971 " "
absolute error = 6.7584826624056400000000000000000E-15 " "
relative error = 5.559127288770884000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.956999999999986 " "
y[1] (analytic) = -0.12108947102906134 " "
y[1] (numeric) = -0.12108947102906825 " "
absolute error = 6.9111383282916000000000000000000E-15 " "
relative error = 5.707464298554028000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.955999999999985 " "
y[1] (analytic) = -0.12060429476456877 " "
y[1] (numeric) = -0.12060429476457586 " "
absolute error = 7.0915495697931870000000000000000E-15 " "
relative error = 5.880014126890404000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.954999999999985 " "
y[1] (analytic) = -0.1201189978957915 " "
y[1] (numeric) = -0.12011899789579875 " "
absolute error = 7.244205235679146000000000000000E-15 " "
relative error = 6.030857202092056000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.953999999999985 " "
y[1] (analytic) = -0.11963358090802635 " "
y[1] (numeric) = -0.11963358090803375 " "
absolute error = 7.396860901565105000000000000000E-15 " "
relative error = 6.182930282135224000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.952999999999984 " "
y[1] (analytic) = -0.11914804428669025 " "
y[1] (numeric) = -0.11914804428669781 " "
absolute error = 7.563394355258879000000000000000E-15 " "
relative error = 6.347896350745027000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.951999999999984 " "
y[1] (analytic) = -0.11866238851731979 " "
y[1] (numeric) = -0.11866238851732752 " "
absolute error = 7.729927808952652000000000000000E-15 " "
relative error = 6.514218958119491000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.950999999999984 " "
y[1] (analytic) = -0.11817661408557072 " "
y[1] (numeric) = -0.1181766140855786 " "
absolute error = 7.882583474838611000000000000000E-15 " "
relative error = 6.670172043625228000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.949999999999983 " "
y[1] (analytic) = -0.11769072147721739 " "
y[1] (numeric) = -0.11769072147722544 " "
absolute error = 8.049116928532385000000000000000E-15 " "
relative error = 6.839211135340466000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.948999999999983 " "
y[1] (analytic) = -0.1172047111781524 " "
y[1] (numeric) = -0.11720471117816061 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 7.0096588265451920000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.947999999999983 " "
y[1] (analytic) = -0.11671858367438599 " "
y[1] (numeric) = -0.11671858367439437 " "
absolute error = 8.382183835919932000000000000000E-15 " "
relative error = 7.181533198949716000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.946999999999982 " "
y[1] (analytic) = -0.11623233945204564 " "
y[1] (numeric) = -0.11623233945205419 " "
absolute error = 8.548717289613705000000000000000E-15 " "
relative error = 7.354852642487401000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.945999999999982 " "
y[1] (analytic) = -0.11574597899737553 " "
y[1] (numeric) = -0.11574597899738423 " "
absolute error = 8.701372955499664000000000000000E-15 " "
relative error = 7.517645995889812000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.944999999999982 " "
y[1] (analytic) = -0.11525950279673607 " "
y[1] (numeric) = -0.11525950279674492 " "
absolute error = 8.854028621385623000000000000000E-15 " "
relative error = 7.681820940178785000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.943999999999981 " "
y[1] (analytic) = -0.1147729113366034 " "
y[1] (numeric) = -0.11477291133661242 " "
absolute error = 9.020562075079397000000000000000E-15 " "
relative error = 7.859487025317408000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.942999999999981 " "
y[1] (analytic) = -0.11428620510356896 " "
y[1] (numeric) = -0.11428620510357815 " "
absolute error = 9.18709552877317000000000000000E-15 " "
relative error = 8.038674064334885000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.941999999999980 " "
y[1] (analytic) = -0.11379938458433896 " "
y[1] (numeric) = -0.1137993845843483 " "
absolute error = 9.33975119465912900000000000000E-15 " "
relative error = 8.207207120471953000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.94099999999998 " "
y[1] (analytic) = -0.11331245026573385 " "
y[1] (numeric) = -0.11331245026574334 " "
absolute error = 9.492406860545088000000000000000E-15 " "
relative error = 8.377196714292243000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93999999999998 " "
y[1] (analytic) = -0.1128254026346879 " "
y[1] (numeric) = -0.11282540263469756 " "
absolute error = 9.658940314238862000000000000000E-15 " "
relative error = 8.560962415098214000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93899999999998 " "
y[1] (analytic) = -0.11233824217824874 " "
y[1] (numeric) = -0.11233824217825855 " "
absolute error = 9.811595980124821000000000000000E-15 " "
relative error = 8.73397677396145900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.937999999999980 " "
y[1] (analytic) = -0.11185096938357675 " "
y[1] (numeric) = -0.11185096938358673 " "
absolute error = 9.978129433818594000000000000000E-15 " "
relative error = 8.920914578397654000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.936999999999979 " "
y[1] (analytic) = -0.1113635847379447 " "
y[1] (numeric) = -0.11136358473795484 " "
absolute error = 1.013078509970455300000000000000E-14 " "
relative error = 9.0970357352844000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.935999999999979 " "
y[1] (analytic) = -0.1108760887287372 " "
y[1] (numeric) = -0.11087608872874749 " "
absolute error = 1.029731855339832700000000000000E-14 " "
relative error = 9.287231062588372000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.934999999999978 " "
y[1] (analytic) = -0.1103884818434502 " "
y[1] (numeric) = -0.11038848184346066 " "
absolute error = 1.0463852007092100000000000000E-14 " "
relative error = 9.479115784862082000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.933999999999978 " "
y[1] (analytic) = -0.10990076456969056 " "
y[1] (numeric) = -0.10990076456970119 " "
absolute error = 1.063038546078587400000000000000E-14 " "
relative error = 9.672712926437291000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.932999999999978 " "
y[1] (analytic) = -0.1094129373951755 " "
y[1] (numeric) = -0.1094129373951863 " "
absolute error = 1.079691891447964700000000000000E-14 " "
relative error = 9.86804592905091900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.931999999999977 " "
y[1] (analytic) = -0.10892500080773218 " "
y[1] (numeric) = -0.10892500080774313 " "
absolute error = 1.094957458036560600000000000000E-14 " "
relative error = 1.005239797949887800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.930999999999977 " "
y[1] (analytic) = -0.10843695529529712 " "
y[1] (numeric) = -0.10843695529530824 " "
absolute error = 1.11161080340593800000000000000E-14 " "
relative error = 1.025121740442437700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.929999999999977 " "
y[1] (analytic) = -0.1079488013459158 " "
y[1] (numeric) = -0.10794880134592708 " "
absolute error = 1.126876369994533900000000000000E-14 " "
relative error = 1.043898918695282700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.928999999999976 " "
y[1] (analytic) = -0.10746053944774213 " "
y[1] (numeric) = -0.10746053944775356 " "
absolute error = 1.143529715363911200000000000000E-14 " "
relative error = 1.064139191223777300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.927999999999976 " "
y[1] (analytic) = -0.10697217008903798 " "
y[1] (numeric) = -0.10697217008904956 " "
absolute error = 1.158795281952507100000000000000E-14 " "
relative error = 1.083267994832662800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.926999999999976 " "
y[1] (analytic) = -0.10648369375817264 " "
y[1] (numeric) = -0.1064836937581844 " "
absolute error = 1.175448627321884500000000000000E-14 " "
relative error = 1.103876646119508300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.925999999999975 " "
y[1] (analytic) = -0.10599511094362242 " "
y[1] (numeric) = -0.10599511094363434 " "
absolute error = 1.192101972691261800000000000000E-14 " "
relative error = 1.124676376182414000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.924999999999975 " "
y[1] (analytic) = -0.10550642213397009 " "
y[1] (numeric) = -0.10550642213398218 " "
absolute error = 1.208755318060639200000000000000E-14 " "
relative error = 1.145669897255907600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.923999999999975 " "
y[1] (analytic) = -0.10501762781790441 " "
y[1] (numeric) = -0.10501762781791667 " "
absolute error = 1.225408663430016500000000000000E-14 " "
relative error = 1.166859972836957300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.922999999999974 " "
y[1] (analytic) = -0.10452872848421967 " "
y[1] (numeric) = -0.10452872848423209 " "
absolute error = 1.242062008799393900000000000000E-14 " "
relative error = 1.188249418902004200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.921999999999974 " "
y[1] (analytic) = -0.10403972462181516 " "
y[1] (numeric) = -0.10403972462182774 " "
absolute error = 1.258715354168771200000000000000E-14 " "
relative error = 1.209841105158829400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.920999999999974 " "
y[1] (analytic) = -0.10355061671969469 " "
y[1] (numeric) = -0.10355061671970744 " "
absolute error = 1.275368699538148600000000000000E-14 " "
relative error = 1.231637956334432300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.919999999999973 " "
y[1] (analytic) = -0.10306140526696614 " "
y[1] (numeric) = -0.10306140526697906 " "
absolute error = 1.29202204490752600000000000000E-14 " "
relative error = 1.253642953500123400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.918999999999973 " "
y[1] (analytic) = -0.1025720907528409 " "
y[1] (numeric) = -0.10257209075285399 " "
absolute error = 1.308675390276903300000000000000E-14 " "
relative error = 1.275859135435101200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.917999999999973 " "
y[1] (analytic) = -0.10208267366663346 " "
y[1] (numeric) = -0.10208267366664672 " "
absolute error = 1.32671651442706200000000000000E-14 " "
relative error = 1.299649065579588000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.916999999999972 " "
y[1] (analytic) = -0.10159315449776087 " "
y[1] (numeric) = -0.10159315449777429 " "
absolute error = 1.34198208101565800000000000000E-14 " "
relative error = 1.320937505730502300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.915999999999972 " "
y[1] (analytic) = -0.10110353373574223 " "
y[1] (numeric) = -0.10110353373575581 " "
absolute error = 1.358635426385035300000000000000E-14 " "
relative error = 1.34380607302623800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.914999999999972 " "
y[1] (analytic) = -0.10061381187019829 " "
y[1] (numeric) = -0.10061381187021204 " "
absolute error = 1.375288771754412700000000000000E-14 " "
relative error = 1.366898585980094400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.913999999999971 " "
y[1] (analytic) = -0.10012398939085086 " "
y[1] (numeric) = -0.10012398939086478 " "
absolute error = 1.3919421171237900000000000000E-14 " "
relative error = 1.390218393805813500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.912999999999971 " "
y[1] (analytic) = -9.96340667875223900E-2 " "
y[1] (numeric) = -9.96340667875364800E-2 " "
absolute error = 1.408595462493167400000000000000E-14 " "
relative error = 1.41376891249165800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.911999999999970 " "
y[1] (analytic) = -9.91440445501354200E-2 " "
y[1] (numeric) = -9.91440445501496800E-2 " "
absolute error = 1.425248807862544700000000000000E-14 " "
relative error = 1.437553626473066800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.91099999999997 " "
y[1] (analytic) = -9.86539231687121800E-2 " "
y[1] (numeric) = -9.86539231687265900E-2 " "
absolute error = 1.44190215323192200000000000000E-14 " "
relative error = 1.461576090355844700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90999999999997 " "
y[1] (analytic) = -9.81637031333739800E-2 " "
y[1] (numeric) = -9.81637031333885600E-2 " "
absolute error = 1.45716771982051800000000000000E-14 " "
relative error = 1.484426191461705200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90899999999997 " "
y[1] (analytic) = -9.76733849343408300E-2 " "
y[1] (numeric) = -9.76733849343555700E-2 " "
absolute error = 1.473821065189895300000000000000E-14 " "
relative error = 1.50892801163863100000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.907999999999970 " "
y[1] (analytic) = -9.71829690619308900E-2 " "
y[1] (numeric) = -9.71829690619457900E-2 " "
absolute error = 1.490474410559272700000000000000E-14 " "
relative error = 1.533678611536813400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.906999999999969 " "
y[1] (analytic) = -9.66924560065599800E-2 " "
y[1] (numeric) = -9.66924560065750400E-2 " "
absolute error = 1.505739977147868600000000000000E-14 " "
relative error = 1.557246593307872200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.905999999999969 " "
y[1] (analytic) = -9.62018462587411200E-2 " "
y[1] (numeric) = -9.62018462587563400E-2 " "
absolute error = 1.52239332251724600000000000000E-14 " "
relative error = 1.582499070155753700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.904999999999968 " "
y[1] (analytic) = -9.57111403090840200E-2 " "
y[1] (numeric) = -9.57111403090994200E-2 " "
absolute error = 1.539046667886623300000000000000E-14 " "
relative error = 1.608012048458011300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.903999999999968 " "
y[1] (analytic) = -9.5220338648294600E-2 " "
y[1] (numeric) = -9.52203386483101400E-2 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.632332185055778700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.902999999999968 " "
y[1] (analytic) = -9.47294417671744500E-2 " "
y[1] (numeric) = -9.47294417671901600E-2 " "
absolute error = 1.570965579844596500000000000000E-14 " "
relative error = 1.658370988510317600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.901999999999967 " "
y[1] (analytic) = -9.42384501566204500E-2 " "
y[1] (numeric) = -9.4238450156636300E-2 " "
absolute error = 1.586231146433192400000000000000E-14 " "
relative error = 1.683210137472487300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.900999999999967 " "
y[1] (analytic) = -9.37473643076241100E-2 " "
y[1] (numeric) = -9.37473643076401500E-2 " "
absolute error = 1.602884491802569800000000000000E-14 " "
relative error = 1.70979152709065900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.899999999999967 " "
y[1] (analytic) = -9.3256184711271300E-2 " "
y[1] (numeric) = -9.3256184711287490E-2 " "
absolute error = 1.61953783717194700000000000000E-14 " "
relative error = 1.736654616727209600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.898999999999966 " "
y[1] (analytic) = -9.27649118587415400E-2 " "
y[1] (numeric) = -9.2764911858757900E-2 " "
absolute error = 1.636191182541324500000000000000E-14 " "
relative error = 1.763803953193904500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.897999999999966 " "
y[1] (analytic) = -9.22735462413076600E-2 " "
y[1] (numeric) = -9.22735462413241800E-2 " "
absolute error = 1.652844527910701800000000000000E-14 " "
relative error = 1.791244181282783400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.896999999999966 " "
y[1] (analytic) = -9.17820883503352100E-2 " "
y[1] (numeric) = -9.17820883503519100E-2 " "
absolute error = 1.66949787328007910000000000000E-14 " "
relative error = 1.81898004641989800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.895999999999965 " "
y[1] (analytic) = -9.12905386772820800E-2 " "
y[1] (numeric) = -9.12905386772989500E-2 " "
absolute error = 1.686151218649456500000000000000E-14 " "
relative error = 1.8470163974057700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.894999999999965 " "
y[1] (analytic) = -9.07988977136978700E-2 " "
y[1] (numeric) = -9.0798897713714900E-2 " "
absolute error = 1.70280456401883380000000000000E-14 " "
relative error = 1.875358189245891800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.893999999999965 " "
y[1] (analytic) = -9.03071659512235100E-2 " "
y[1] (numeric) = -9.0307165951240710E-2 " "
absolute error = 1.719457909388211200000000000000E-14 " "
relative error = 1.90401048607473800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.892999999999964 " "
y[1] (analytic) = -8.98153438815907400E-2 " "
y[1] (numeric) = -8.98153438816080800E-2 " "
absolute error = 1.73472347597680700000000000000E-14 " "
relative error = 1.93143331752289820000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.891999999999964 " "
y[1] (analytic) = -8.93234319966215600E-2 " "
y[1] (numeric) = -8.93234319966390700E-2 " "
absolute error = 1.751376821346184400000000000000E-14 " "
relative error = 1.960713759198623200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.890999999999964 " "
y[1] (analytic) = -8.88314307882278200E-2 " "
y[1] (numeric) = -8.8831430788245500E-2 " "
absolute error = 1.768030166715561800000000000000E-14 " "
relative error = 1.990320487948130700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.889999999999963 " "
y[1] (analytic) = -8.83393407484107100E-2 " "
y[1] (numeric) = -8.83393407484285400E-2 " "
absolute error = 1.783295733304157700000000000000E-14 " "
relative error = 2.018688070565254300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.888999999999963 " "
y[1] (analytic) = -8.7847162369260200E-2 " "
y[1] (numeric) = -8.7847162369278200E-2 " "
absolute error = 1.79994907867353500000000000000E-14 " "
relative error = 2.048955287943802500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.887999999999963 " "
y[1] (analytic) = -8.73548961429546500E-2 " "
y[1] (numeric) = -8.73548961429728200E-2 " "
absolute error = 1.816602424042912400000000000000E-14 " "
relative error = 2.079565661746167700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.886999999999962 " "
y[1] (analytic) = -8.68625425617602400E-2 " "
y[1] (numeric) = -8.68625425617785700E-2 " "
absolute error = 1.833255769412289700000000000000E-14 " "
relative error = 2.1105251070780300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.885999999999962 " "
y[1] (analytic) = -8.63701021180304900E-2 " "
y[1] (numeric) = -8.63701021180489900E-2 " "
absolute error = 1.84990911478166700000000000000E-14 " "
relative error = 2.141839675323809500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.884999999999962 " "
y[1] (analytic) = -8.58775753042058300E-2 " "
y[1] (numeric) = -8.58775753042244800E-2 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 2.171899561396811500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.883999999999961 " "
y[1] (analytic) = -8.53849626128130300E-2 " "
y[1] (numeric) = -8.53849626128318500E-2 " "
absolute error = 1.881828026739640300000000000000E-14 " "
relative error = 2.20393377142177220000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.882999999999961 " "
y[1] (analytic) = -8.48922645364647200E-2 " "
y[1] (numeric) = -8.48922645364837100E-2 " "
absolute error = 1.898481372109017700000000000000E-14 " "
relative error = 2.23634200651290400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.881999999999960 " "
y[1] (analytic) = -8.43994815678589500E-2 " "
y[1] (numeric) = -8.4399481567878110E-2 " "
absolute error = 1.91513471747839500000000000000E-14 " "
relative error = 2.269130902111746700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.88099999999996 " "
y[1] (analytic) = -8.39066141997786500E-2 " "
y[1] (numeric) = -8.39066141997979600E-2 " "
absolute error = 1.93040028406699100000000000000E-14 " "
relative error = 2.30065329471020800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87999999999996 " "
y[1] (analytic) = -8.34136629250911400E-2 " "
y[1] (numeric) = -8.34136629251106100E-2 " "
absolute error = 1.947053629436368300000000000000E-14 " "
relative error = 2.334214277563738400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87899999999996 " "
y[1] (analytic) = -8.29206282367476600E-2 " "
y[1] (numeric) = -8.2920628236767290E-2 " "
absolute error = 1.963706974805745600000000000000E-14 " "
relative error = 2.368176672756437400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.877999999999960 " "
y[1] (analytic) = -8.24275106277828500E-2 " "
y[1] (numeric) = -8.24275106278026500E-2 " "
absolute error = 1.98036032017512300000000000000E-14 " "
relative error = 2.402547772087668400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.876999999999959 " "
y[1] (analytic) = -8.19343105913142900E-2 " "
y[1] (numeric) = -8.19343105913342500E-2 " "
absolute error = 1.99562588676371900000000000000E-14 " "
relative error = 2.435641274530076800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.875999999999959 " "
y[1] (analytic) = -8.14410286205419400E-2 " "
y[1] (numeric) = -8.14410286205620700E-2 " "
absolute error = 2.012279232133096200000000000000E-14 " "
relative error = 2.47084211265172700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.874999999999958 " "
y[1] (analytic) = -8.09476652087477900E-2 " "
y[1] (numeric) = -8.09476652087680700E-2 " "
absolute error = 2.028932577502473600000000000000E-14 " "
relative error = 2.50647448851089600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.873999999999958 " "
y[1] (analytic) = -8.04542208492951500E-2 " "
y[1] (numeric) = -8.04542208493156200E-2 " "
absolute error = 2.04558592287185100000000000000E-14 " "
relative error = 2.542546433584375600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.872999999999958 " "
y[1] (analytic) = -7.99606960356283800E-2 " "
y[1] (numeric) = -7.996069603564899E-2 " "
absolute error = 2.062239268241228300000000000000E-14 " "
relative error = 2.57906617936685900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.871999999999957 " "
y[1] (analytic) = -7.94670912612722300E-2 " "
y[1] (numeric) = -7.94670912612930200E-2 " "
absolute error = 2.078892613610605600000000000000E-14 " "
relative error = 2.616042163636786400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.870999999999957 " "
y[1] (analytic) = -7.89734070198314500E-2 " "
y[1] (numeric) = -7.89734070198523900E-2 " "
absolute error = 2.094158180199201500000000000000E-14 " "
relative error = 2.651725763424801500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.869999999999957 " "
y[1] (analytic) = -7.84796438049902200E-2 " "
y[1] (numeric) = -7.84796438050113300E-2 " "
absolute error = 2.112199304349360300000000000000E-14 " "
relative error = 2.691397669436229000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.868999999999956 " "
y[1] (analytic) = -7.79858021105117400E-2 " "
y[1] (numeric) = -7.798580211053301E-2 " "
absolute error = 2.127464870937956200000000000000E-14 " "
relative error = 2.728015630233794300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.867999999999956 " "
y[1] (analytic) = -7.74918824302376400E-2 " "
y[1] (numeric) = -7.74918824302590700E-2 " "
absolute error = 2.144118216307333600000000000000E-14 " "
relative error = 2.766893962393524600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.866999999999956 " "
y[1] (analytic) = -7.69978852580875500E-2 " "
y[1] (numeric) = -7.69978852581091600E-2 " "
absolute error = 2.16077156167671100000000000000E-14 " "
relative error = 2.806273905359955600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.865999999999955 " "
y[1] (analytic) = -7.65038110880586400E-2 " "
y[1] (numeric) = -7.65038110880804100E-2 " "
absolute error = 2.177424907046088300000000000000E-14 " "
relative error = 2.846165277360881000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.864999999999955 " "
y[1] (analytic) = -7.60096604142250100E-2 " "
y[1] (numeric) = -7.60096604142469500E-2 " "
absolute error = 2.194078252415465600000000000000E-14 " "
relative error = 2.886578153959032400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.863999999999955 " "
y[1] (analytic) = -7.5515433730737300E-2 " "
y[1] (numeric) = -7.5515433730759410E-2 " "
absolute error = 2.21073159778484300000000000000E-14 " "
relative error = 2.927522876538814500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.862999999999954 " "
y[1] (analytic) = -7.50211315318221600E-2 " "
y[1] (numeric) = -7.50211315318444200E-2 " "
absolute error = 2.22599716437343900000000000000E-14 " "
relative error = 2.96716021062575500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.861999999999954 " "
y[1] (analytic) = -7.45267543117817300E-2 " "
y[1] (numeric) = -7.45267543118041600E-2 " "
absolute error = 2.242650509742816200000000000000E-14 " "
relative error = 3.009188486004256700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.860999999999954 " "
y[1] (analytic) = -7.4032302564993200E-2 " "
y[1] (numeric) = -7.40323025650158000E-2 " "
absolute error = 2.259303855112193600000000000000E-14 " "
relative error = 3.051781150706130400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.859999999999953 " "
y[1] (analytic) = -7.35377767859082800E-2 " "
y[1] (numeric) = -7.35377767859310300E-2 " "
absolute error = 2.274569421700789500000000000000E-14 " "
relative error = 3.09306253345512500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.858999999999953 " "
y[1] (analytic) = -7.3043177469052700E-2 " "
y[1] (numeric) = -7.30431774690756200E-2 " "
absolute error = 2.291222767070166800000000000000E-14 " "
relative error = 3.136805991279505400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.857999999999953 " "
y[1] (analytic) = -7.25485051090257300E-2 " "
y[1] (numeric) = -7.25485051090488100E-2 " "
absolute error = 2.307876112439544200000000000000E-14 " "
relative error = 3.181149093246336500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.856999999999952 " "
y[1] (analytic) = -7.20537602004997100E-2 " "
y[1] (numeric) = -7.20537602005229500E-2 " "
absolute error = 2.324529457808921500000000000000E-14 " "
relative error = 3.226104302316203400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.855999999999952 " "
y[1] (analytic) = -7.15589432382194900E-2 " "
y[1] (numeric) = -7.1558943238242900E-2 " "
absolute error = 2.34118280317829890000000000000E-14 " "
relative error = 3.27168442857590700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.854999999999952 " "
y[1] (analytic) = -7.10640547170019900E-2 " "
y[1] (numeric) = -7.10640547170255700E-2 " "
absolute error = 2.357836148547676200000000000000E-14 " "
relative error = 3.31790264140890200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.853999999999951 " "
y[1] (analytic) = -7.05690951317356900E-2 " "
y[1] (numeric) = -7.05690951317594400E-2 " "
absolute error = 2.374489493917053600000000000000E-14 " "
relative error = 3.36477248218139600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.852999999999951 " "
y[1] (analytic) = -7.00740649773801300E-2 " "
y[1] (numeric) = -7.00740649774040500E-2 " "
absolute error = 2.39114283928643100000000000000E-14 " "
relative error = 3.41230787746977460000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.851999999999950 " "
y[1] (analytic) = -6.95789647489654700E-2 " "
y[1] (numeric) = -6.95789647489895200E-2 " "
absolute error = 2.406408405875026800000000000000E-14 " "
relative error = 3.45852861501623100000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.85099999999995 " "
y[1] (analytic) = -6.90837949415918400E-2 " "
y[1] (numeric) = -6.90837949416160700E-2 " "
absolute error = 2.42306175124440410000000000000E-14 " "
relative error = 3.50742421329492100000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.84999999999995 " "
y[1] (analytic) = -6.85885560504290200E-2 " "
y[1] (numeric) = -6.85885560504534200E-2 " "
absolute error = 2.439715096613781500000000000000E-14 " "
relative error = 3.55702938959672250000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.84899999999995 " "
y[1] (analytic) = -6.80932485707158600E-2 " "
y[1] (numeric) = -6.80932485707404200E-2 " "
absolute error = 2.45636844198315880000000000000E-14 " "
relative error = 3.60735975084546470000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.847999999999950 " "
y[1] (analytic) = -6.75978729977598100E-2 " "
y[1] (numeric) = -6.75978729977845400E-2 " "
absolute error = 2.473021787352536200000000000000E-14 " "
relative error = 3.65843136430415800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.846999999999949 " "
y[1] (analytic) = -6.7102429826936390E-2 " "
y[1] (numeric) = -6.7102429826961300E-2 " "
absolute error = 2.489675132721913500000000000000E-14 " "
relative error = 3.71026077467391900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.845999999999949 " "
y[1] (analytic) = -6.66069195536887500E-2 " "
y[1] (numeric) = -6.66069195537138100E-2 " "
absolute error = 2.50632847809129100000000000000E-14 " "
relative error = 3.76286502196075300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.844999999999948 " "
y[1] (analytic) = -6.6111342673527100E-2 " "
y[1] (numeric) = -6.61113426735523300E-2 " "
absolute error = 2.522981823460668000000000000000E-14 " "
relative error = 3.81626166015070700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.843999999999948 " "
y[1] (analytic) = -6.56156996820282800E-2 " "
y[1] (numeric) = -6.56156996820536700E-2 " "
absolute error = 2.539635168830045600000000000000E-14 " "
relative error = 3.87046877673642400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.842999999999948 " "
y[1] (analytic) = -6.51199910748352500E-2 " "
y[1] (numeric) = -6.51199910748608200E-2 " "
absolute error = 2.55628851419942300000000000000E-14 " "
relative error = 3.925505013140682700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.841999999999947 " "
y[1] (analytic) = -6.46242173476565800E-2 " "
y[1] (numeric) = -6.4624217347682300E-2 " "
absolute error = 2.571554080788019000000000000000E-14 " "
relative error = 3.979242126761739500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.840999999999947 " "
y[1] (analytic) = -6.41283789962659300E-2 " "
y[1] (numeric) = -6.41283789962918200E-2 " "
absolute error = 2.589595204938177600000000000000E-14 " "
relative error = 4.038142309957600000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.839999999999947 " "
y[1] (analytic) = -6.36324765165016300E-2 " "
y[1] (numeric) = -6.3632476516527700E-2 " "
absolute error = 2.60624855030755500000000000000E-14 " "
relative error = 4.09578362022682500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.838999999999946 " "
y[1] (analytic) = -6.31365104042661400E-2 " "
y[1] (numeric) = -6.31365104042923600E-2 " "
absolute error = 2.62151411689615100000000000000E-14 " "
relative error = 4.152136537338647600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.837999999999946 " "
y[1] (analytic) = -6.26404811555254700E-2 " "
y[1] (numeric) = -6.26404811555518700E-2 " "
absolute error = 2.639555241046309700000000000000E-14 " "
relative error = 4.21381699558269760000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.836999999999946 " "
y[1] (analytic) = -6.2144389266308900E-2 " "
y[1] (numeric) = -6.214438926633545000E-2 " "
absolute error = 2.655514697025296300000000000000E-14 " "
relative error = 4.27313668760272600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.835999999999945 " "
y[1] (analytic) = -6.16482352327082300E-2 " "
y[1] (numeric) = -6.164823523273495000E-2 " "
absolute error = 2.67147415300428300000000000000E-14 " "
relative error = 4.33341545450582400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.834999999999945 " "
y[1] (analytic) = -6.115201955087747000E-2 " "
y[1] (numeric) = -6.115201955090435000E-2 " "
absolute error = 2.688127498373660000000000000000E-14 " "
relative error = 4.395811484422330600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.833999999999945 " "
y[1] (analytic) = -6.06557427170322300E-2 " "
y[1] (numeric) = -6.065574271705929000E-2 " "
absolute error = 2.704780843743037600000000000000E-14 " "
relative error = 4.459232914451693500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.832999999999944 " "
y[1] (analytic) = -6.01594052274493500E-2 " "
y[1] (numeric) = -6.015940522747656000E-2 " "
absolute error = 2.72143418911241500000000000000E-14 " "
relative error = 4.52370527737645800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.831999999999944 " "
y[1] (analytic) = -5.96630075784662500E-2 " "
y[1] (numeric) = -5.96630075784936300E-2 " "
absolute error = 2.738087534481792300000000000000E-14 " "
relative error = 4.589254959835500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.830999999999944 " "
y[1] (analytic) = -5.916655026648054000E-2 " "
y[1] (numeric) = -5.91665502665080900E-2 " "
absolute error = 2.754740879851169700000000000000E-14 " "
relative error = 4.65590923831806560000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.829999999999943 " "
y[1] (analytic) = -5.8670033787949500E-2 " "
y[1] (numeric) = -5.867003378797722000E-2 " "
absolute error = 2.77139422522054700000000000000E-14 " "
relative error = 4.7236963169940700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.828999999999943 " "
y[1] (analytic) = -5.81734586393895600E-2 " "
y[1] (numeric) = -5.81734586394174400E-2 " "
absolute error = 2.788047570589924400000000000000E-14 " "
relative error = 4.792645367490876000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.827999999999943 " "
y[1] (analytic) = -5.76768253173758200E-2 " "
y[1] (numeric) = -5.767682531740388000E-2 " "
absolute error = 2.804700915959301700000000000000E-14 " "
relative error = 4.8627865707344200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.826999999999942 " "
y[1] (analytic) = -5.71801343185415900E-2 " "
y[1] (numeric) = -5.718013431856980000E-2 " "
absolute error = 2.820660371938288300000000000000E-14 " "
relative error = 4.932937646184652500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.825999999999942 " "
y[1] (analytic) = -5.66833861395777800E-2 " "
y[1] (numeric) = -5.66833861396061600E-2 " "
absolute error = 2.837313717307665700000000000000E-14 " "
relative error = 5.00554732266882100000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.824999999999942 " "
y[1] (analytic) = -5.618658127723257000E-2 " "
y[1] (numeric) = -5.618658127726112000E-2 " "
absolute error = 2.85396706267704300000000000000E-14 " "
relative error = 5.079446013266342000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.823999999999941 " "
y[1] (analytic) = -5.568972022831077000E-2 " "
y[1] (numeric) = -5.56897202283394700E-2 " "
absolute error = 2.870620408046420400000000000000E-14 " "
relative error = 5.15466839531202100000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.822999999999941 " "
y[1] (analytic) = -5.51928034896733700E-2 " "
y[1] (numeric) = -5.51928034897022500E-2 " "
absolute error = 2.88727375341579800000000000000E-14 " "
relative error = 5.231250400164960000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.821999999999940 " "
y[1] (analytic) = -5.46958315582370800E-2 " "
y[1] (numeric) = -5.46958315582661200E-2 " "
absolute error = 2.903233209394784400000000000000E-14 " "
relative error = 5.30796063737248900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.82099999999994 " "
y[1] (analytic) = -5.4198804930973800E-2 " "
y[1] (numeric) = -5.419880493100300E-2 " "
absolute error = 2.91988655476416170000000000000E-14 " "
relative error = 5.387363353274770000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.81999999999994 " "
y[1] (analytic) = -5.3701724104910100E-2 " "
y[1] (numeric) = -5.370172410493946000E-2 " "
absolute error = 2.93653990013353900000000000000E-14 " "
relative error = 5.468241381592892000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8189999999999396 " "
y[1] (analytic) = -5.32045895771267700E-2 " "
y[1] (numeric) = -5.3204589577156300E-2 " "
absolute error = 2.953193245502916400000000000000E-14 " "
relative error = 5.55063626836532500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.817999999999940 " "
y[1] (analytic) = -5.27074018447583000E-2 " "
y[1] (numeric) = -5.27074018447879900E-2 " "
absolute error = 2.96984659087229400000000000000E-14 " "
relative error = 5.63459113317618900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.816999999999939 " "
y[1] (analytic) = -5.221016140499236000E-2 " "
y[1] (numeric) = -5.22101614050222300E-2 " "
absolute error = 2.98649993624167100000000000000E-14 " "
relative error = 5.72015074436467900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8159999999999386 " "
y[1] (analytic) = -5.171286875506939000E-2 " "
y[1] (numeric) = -5.171286875509942000E-2 " "
absolute error = 3.003153281611048400000000000000E-14 " "
relative error = 5.807361598589812000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.814999999999938 " "
y[1] (analytic) = -5.12155243922819600E-2 " "
y[1] (numeric) = -5.12155243923121500E-2 " "
absolute error = 3.01911273759003500000000000000E-14 " "
relative error = 5.89491716313463600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.813999999999938 " "
y[1] (analytic) = -5.07181288139744100E-2 " "
y[1] (numeric) = -5.07181288140047700E-2 " "
absolute error = 3.035766082959412400000000000000E-14 " "
relative error = 5.98556404573617700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8129999999999376 " "
y[1] (analytic) = -5.02206825175422700E-2 " "
y[1] (numeric) = -5.02206825175727900E-2 " "
absolute error = 3.0524194283287900000000000000E-14 " "
relative error = 6.07801263406280600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.811999999999937 " "
y[1] (analytic) = -4.972318600043179600E-2 " "
y[1] (numeric) = -4.97231860004624900E-2 " "
absolute error = 3.06907277369816700000000000000E-14 " "
relative error = 6.17231722374249200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.810999999999937 " "
y[1] (analytic) = -4.922563976013947000E-2 " "
y[1] (numeric) = -4.922563976017032500E-2 " "
absolute error = 3.08503222967715400000000000000E-14 " "
relative error = 6.26712470312120200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8099999999999365 " "
y[1] (analytic) = -4.87280442942114870E-2 " "
y[1] (numeric) = -4.872804429424250000E-2 " "
absolute error = 3.10168557504653100000000000000E-14 " "
relative error = 6.36529871036705600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.808999999999936 " "
y[1] (analytic) = -4.823040010024326500E-2 " "
y[1] (numeric) = -4.82304001002744500E-2 " "
absolute error = 3.118338920415908400000000000000E-14 " "
relative error = 6.46550498012596900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.807999999999936 " "
y[1] (analytic) = -4.77327076758789600E-2 " "
y[1] (numeric) = -4.77327076759103130E-2 " "
absolute error = 3.13499226578528600000000000000E-14 " "
relative error = 6.56780731374580900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8069999999999355 " "
y[1] (analytic) = -4.72349675188109660E-2 " "
y[1] (numeric) = -4.72349675188424800E-2 " "
absolute error = 3.150951721764272400000000000000E-14 " "
relative error = 6.67080319364976800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.805999999999935 " "
y[1] (analytic) = -4.67371801267793900E-2 " "
y[1] (numeric) = -4.673718012681106000E-2 " "
absolute error = 3.1676050671336500000000000000E-14 " "
relative error = 6.77748434659771200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.804999999999935 " "
y[1] (analytic) = -4.623934599757157400E-2 " "
y[1] (numeric) = -4.62393459976034200E-2 " "
absolute error = 3.18425841250302700000000000000E-14 " "
relative error = 6.88646939917848300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8039999999999345 " "
y[1] (analytic) = -4.574146562902161600E-2 " "
y[1] (numeric) = -4.574146562905362400E-2 " "
absolute error = 3.200911757872404500000000000000E-14 " "
relative error = 6.99783383381908900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.802999999999934 " "
y[1] (analytic) = -4.52435395190098400E-2 " "
y[1] (numeric) = -4.52435395190420200E-2 " "
absolute error = 3.21756510324178200000000000000E-14 " "
relative error = 7.11165646509567900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.801999999999934 " "
y[1] (analytic) = -4.47455681654623200E-2 " "
y[1] (numeric) = -4.47455681654946600E-2 " "
absolute error = 3.23421844861115900000000000000E-14 " "
relative error = 7.2280196256565800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8009999999999335 " "
y[1] (analytic) = -4.42475520663503600E-2 " "
y[1] (numeric) = -4.42475520663828670E-2 " "
absolute error = 3.250871793980536500000000000000E-14 " "
relative error = 7.34700936473450500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.799999999999933 " "
y[1] (analytic) = -4.37494917196900150E-2 " "
y[1] (numeric) = -4.37494917197226940E-2 " "
absolute error = 3.26752513934991400000000000000E-14 " "
relative error = 7.46871566025376900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.798999999999933 " "
y[1] (analytic) = -4.3251387623541604E-2 " "
y[1] (numeric) = -4.325138762357444400E-2 " "
absolute error = 3.28417848471929100000000000000E-14 " "
relative error = 7.59323264563128700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7979999999999325 " "
y[1] (analytic) = -4.27532402760091750E-2 " "
y[1] (numeric) = -4.27532402760421800E-2 " "
absolute error = 3.300831830088668500000000000000E-14 " "
relative error = 7.720658852472800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.796999999999932 " "
y[1] (analytic) = -4.225505017524003000E-2 " "
y[1] (numeric) = -4.2255050175273200E-2 " "
absolute error = 3.31748517545804600000000000000E-14 " "
relative error = 7.8510974704793400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.795999999999932 " "
y[1] (analytic) = -4.175681781942422500E-2 " "
y[1] (numeric) = -4.175681781945756500E-2 " "
absolute error = 3.33413852082742300000000000000E-14 " "
relative error = 7.98465662600483200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7949999999999315 " "
y[1] (analytic) = -4.12585437067940800E-2 " "
y[1] (numeric) = -4.12585437068275900E-2 " "
absolute error = 3.350791866196800600000000000000E-14 " "
relative error = 8.12144968084518900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.793999999999931 " "
y[1] (analytic) = -4.07602283356236770E-2 " "
y[1] (numeric) = -4.07602283356573500E-2 " "
absolute error = 3.36744521156617800000000000000E-14 " "
relative error = 8.26159555299422600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.792999999999930 " "
y[1] (analytic) = -4.02618722042283330E-2 " "
y[1] (numeric) = -4.026187220426217000E-2 " "
absolute error = 3.38409855693555530000000000000E-14 " "
relative error = 8.40521906127394300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7919999999999305 " "
y[1] (analytic) = -3.976347581096413300E-2 " "
y[1] (numeric) = -3.97634758109981450E-2 " "
absolute error = 3.400751902304932600000000000000E-14 " "
relative error = 8.55245129593834500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.79099999999993 " "
y[1] (analytic) = -3.92650396542274400E-2 " "
y[1] (numeric) = -3.92650396542616200E-2 " "
absolute error = 3.41809913706470070000000000000E-14 " "
relative error = 8.70519721147586800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.78999999999993 " "
y[1] (analytic) = -3.876656423245436500E-2 " "
y[1] (numeric) = -3.87665642324887100E-2 " "
absolute error = 3.43475248243407800000000000000E-14 " "
relative error = 8.86009000394879500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7889999999999295 " "
y[1] (analytic) = -3.82680500441202900E-2 " "
y[1] (numeric) = -3.8268050044154800E-2 " "
absolute error = 3.451405827803455400000000000000E-14 " "
relative error = 9.01902716188631200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.787999999999930 " "
y[1] (analytic) = -3.776949758773935400E-2 " "
y[1] (numeric) = -3.77694975877740370E-2 " "
absolute error = 3.46805917317283300000000000000E-14 " "
relative error = 9.18216919649634400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.786999999999929 " "
y[1] (analytic) = -3.72709073618639800E-2 " "
y[1] (numeric) = -3.72709073618988300E-2 " "
absolute error = 3.4847125185422100000000000000E-14 " "
relative error = 9.34968522421272600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7859999999999285 " "
y[1] (analytic) = -3.67722798650843500E-2 " "
y[1] (numeric) = -3.67722798651193700E-2 " "
absolute error = 3.50205975330197800000000000000E-14 " "
relative error = 9.5236405416005210000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.784999999999928 " "
y[1] (analytic) = -3.627361559602792500E-2 " "
y[1] (numeric) = -3.627361559606310000E-2 " "
absolute error = 3.51801920928096500000000000000E-14 " "
relative error = 9.69856230616889300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.783999999999928 " "
y[1] (analytic) = -3.57749150533589200E-2 " "
y[1] (numeric) = -3.577491505339426300E-2 " "
absolute error = 3.53467255465034200000000000000E-14 " "
relative error = 9.88031012618287300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7829999999999275 " "
y[1] (analytic) = -3.52761787357778470E-2 " "
y[1] (numeric) = -3.52761787358133570E-2 " "
absolute error = 3.551325900019719500000000000000E-14 " "
relative error = 1.00672069007800140000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.781999999999927 " "
y[1] (analytic) = -3.477740714202098000E-2 " "
y[1] (numeric) = -3.477740714205665400E-2 " "
absolute error = 3.56797924538909700000000000000E-14 " "
relative error = 1.02594745802022880000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.780999999999927 " "
y[1] (analytic) = -3.427860077085986000E-2 " "
y[1] (numeric) = -3.42786007708957060E-2 " "
absolute error = 3.58532648014886500000000000000E-14 " "
relative error = 1.04593723183612010000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7799999999999265 " "
y[1] (analytic) = -3.37797601211008300E-2 " "
y[1] (numeric) = -3.37797601211368400E-2 " "
absolute error = 3.601285936127851500000000000000E-14 " "
relative error = 1.06610761095318630000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.778999999999926 " "
y[1] (analytic) = -3.328088569158449400E-2 " "
y[1] (numeric) = -3.328088569162067600E-2 " "
absolute error = 3.61793928149722900000000000000E-14 " "
relative error = 1.08709224719102720000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.777999999999926 " "
y[1] (analytic) = -3.278197798118523400E-2 " "
y[1] (numeric) = -3.27819779812215900E-2 " "
absolute error = 3.63528651625699700000000000000E-14 " "
relative error = 1.10892836251168840000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7769999999999255 " "
y[1] (analytic) = -3.228303748881073400E-2 " "
y[1] (numeric) = -3.22830374888472500E-2 " "
absolute error = 3.651245972235983600000000000000E-14 " "
relative error = 1.13101066574094880000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.775999999999925 " "
y[1] (analytic) = -3.17840647134014300E-2 " "
y[1] (numeric) = -3.178406471343811500E-2 " "
absolute error = 3.668593206995751600000000000000E-14 " "
relative error = 1.15422405537984150000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.774999999999925 " "
y[1] (analytic) = -3.12850601539300670E-2 " "
y[1] (numeric) = -3.12850601539669150E-2 " "
absolute error = 3.68455266297473800000000000000E-14 " "
relative error = 1.1777355213145979000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7739999999999245 " "
y[1] (analytic) = -3.078602430940115000E-2 " "
y[1] (numeric) = -3.078602430943816500E-2 " "
absolute error = 3.701206008344115600000000000000E-14 " "
relative error = 1.20223578437631360000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.772999999999924 " "
y[1] (analytic) = -3.028695767885049000E-2 " "
y[1] (numeric) = -3.028695767888767700E-2 " "
absolute error = 3.718206298408688300000000000000E-14 " "
relative error = 1.2276592247510972000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.771999999999924 " "
y[1] (analytic) = -2.97878607613446800E-2 " "
y[1] (numeric) = -2.97878607613820300E-2 " "
absolute error = 3.734859643778065700000000000000E-14 " "
relative error = 1.25381935738894830000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7709999999999235 " "
y[1] (analytic) = -2.92887340559805860E-2 " "
y[1] (numeric) = -2.928873405601810600E-2 " "
absolute error = 3.75151298914744300000000000000E-14 " "
relative error = 1.28087235930957080000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.769999999999923 " "
y[1] (analytic) = -2.878957806188488000E-2 " "
y[1] (numeric) = -2.878957806192256600E-2 " "
absolute error = 3.768166334516820400000000000000E-14 " "
relative error = 1.30886473098595860000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.768999999999923 " "
y[1] (analytic) = -2.829039327821351600E-2 " "
y[1] (numeric) = -2.82903932782513600E-2 " "
absolute error = 3.784472735191002400000000000000E-14 " "
relative error = 1.33772362157490100000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7679999999999225 " "
y[1] (analytic) = -2.779118020415122000E-2 " "
y[1] (numeric) = -2.779118020418923600E-2 " "
absolute error = 3.80147302525557500000000000000E-14 " "
relative error = 1.3678703089722480000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.766999999999922 " "
y[1] (analytic) = -2.729193933891105000E-2 " "
y[1] (numeric) = -2.729193933894922000E-2 " "
absolute error = 3.81777942592975700000000000000E-14 " "
relative error = 1.3988670348855050000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.765999999999922 " "
y[1] (analytic) = -2.679267118173380000E-2 " "
y[1] (numeric) = -2.679267118177215000E-2 " "
absolute error = 3.834432771299134400000000000000E-14 " "
relative error = 1.43114986381548300000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7649999999999215 " "
y[1] (analytic) = -2.62933762318876100E-2 " "
y[1] (numeric) = -2.62933762319261200E-2 " "
absolute error = 3.85108611666851200000000000000E-14 " "
relative error = 1.46466018007914120000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.763999999999921 " "
y[1] (analytic) = -2.579405498866737500E-2 " "
y[1] (numeric) = -2.579405498870605600E-2 " "
absolute error = 3.86773946203788900000000000000E-14 " "
relative error = 1.49946934041087420000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.762999999999920 " "
y[1] (analytic) = -2.529470795139430000E-2 " "
y[1] (numeric) = -2.52947079514331500E-2 " "
absolute error = 3.88473975210246200000000000000E-14 " "
relative error = 1.53579150214633170000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7619999999999205 " "
y[1] (analytic) = -2.47953356194153870E-2 " "
y[1] (numeric) = -2.479533561945440300E-2 " "
absolute error = 3.90139309747183900000000000000E-14 " "
relative error = 1.57343831007350720000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.76099999999992 " "
y[1] (analytic) = -2.42959384921029200E-2 " "
y[1] (numeric) = -2.4295938492142100E-2 " "
absolute error = 3.918046442841216500000000000000E-14 " "
relative error = 1.6126343273855120000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.75999999999992 " "
y[1] (analytic) = -2.379651706885398400E-2 " "
y[1] (numeric) = -2.37965170688933300E-2 " "
absolute error = 3.93469978821059400000000000000E-14 " "
relative error = 1.65347717770031000000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7589999999999195 " "
y[1] (analytic) = -2.32970718490899620E-2 " "
y[1] (numeric) = -2.329707184912947800E-2 " "
absolute error = 3.951700078275166600000000000000E-14 " "
relative error = 1.69622178438254220000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.757999999999920 " "
y[1] (analytic) = -2.27976033322560300E-2 " "
y[1] (numeric) = -2.279760333229571600E-2 " "
absolute error = 3.96835342364454400000000000000E-14 " "
relative error = 1.74068886356565950000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.756999999999919 " "
y[1] (analytic) = -2.22981120178206700E-2 " "
y[1] (numeric) = -2.22981120178605220E-2 " "
absolute error = 3.98500676901392100000000000000E-14 " "
relative error = 1.78714985637757150000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7559999999999185 " "
y[1] (analytic) = -2.17985984052751500E-2 " "
y[1] (numeric) = -2.179859840531516700E-2 " "
absolute error = 4.001660114383298600000000000000E-14 " "
relative error = 1.83574193165323750000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.754999999999918 " "
y[1] (analytic) = -2.129906299413303600E-2 " "
y[1] (numeric) = -2.129906299417322300E-2 " "
absolute error = 4.01866040444787130000000000000E-14 " "
relative error = 1.8867780265990280000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.753999999999918 " "
y[1] (analytic) = -2.07995062839297080E-2 " "
y[1] (numeric) = -2.07995062839700620E-2 " "
absolute error = 4.035313749817248700000000000000E-14 " "
relative error = 1.94010073832139330000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7529999999999175 " "
y[1] (analytic) = -2.029992877422182600E-2 " "
y[1] (numeric) = -2.029992877426234600E-2 " "
absolute error = 4.05196709518662600000000000000E-14 " "
relative error = 1.99604990749133960000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.751999999999917 " "
y[1] (analytic) = -1.980033096458686200E-2 " "
y[1] (numeric) = -1.98003309646275500E-2 " "
absolute error = 4.068620440556003400000000000000E-14 " "
relative error = 2.0548244611833920000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.750999999999917 " "
y[1] (analytic) = -1.930071335462258400E-2 " "
y[1] (numeric) = -1.930071335466343700E-2 " "
absolute error = 4.08527378592538070000000000000E-14 " "
relative error = 2.11664393479370740000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7499999999999165 " "
y[1] (analytic) = -1.880107644394656300E-2 " "
y[1] (numeric) = -1.880107644398758300E-2 " "
absolute error = 4.10192713129475800000000000000E-14 " "
relative error = 2.18175121170546970000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.748999999999916 " "
y[1] (analytic) = -1.83014207321956600E-2 " "
y[1] (numeric) = -1.83014207322368500E-2 " "
absolute error = 4.11892742135933100000000000000E-14 " "
relative error = 2.2506052844921260000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.747999999999916 " "
y[1] (analytic) = -1.780174671902555500E-2 " "
y[1] (numeric) = -1.780174671906690800E-2 " "
absolute error = 4.13523382203351300000000000000E-14 " "
relative error = 2.32293711808291060000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7469999999999155 " "
y[1] (analytic) = -1.73020549041102120E-2 " "
y[1] (numeric) = -1.73020549041517300E-2 " "
absolute error = 4.1518871674028900000000000000E-14 " "
relative error = 2.3996497470462790000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.745999999999915 " "
y[1] (analytic) = -1.680234578714140400E-2 " "
y[1] (numeric) = -1.68023457871830900E-2 " "
absolute error = 4.168540512772267400000000000000E-14 " "
relative error = 2.4809277023464140000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.744999999999915 " "
y[1] (analytic) = -1.63026198678282100E-2 " "
y[1] (numeric) = -1.630261986787006600E-2 " "
absolute error = 4.1855408028368400000000000000E-14 " "
relative error = 2.56740378955693960000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7439999999999145 " "
y[1] (analytic) = -1.58028776458965100E-2 " "
y[1] (numeric) = -1.580287764593853000E-2 " "
absolute error = 4.20184720351102200000000000000E-14 " "
relative error = 2.6589126978415250000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.742999999999914 " "
y[1] (analytic) = -1.530311962108847600E-2 " "
y[1] (numeric) = -1.530311962113066500E-2 " "
absolute error = 4.21884749357559500000000000000E-14 " "
relative error = 2.75685454863844160000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.741999999999914 " "
y[1] (analytic) = -1.480334629316209800E-2 " "
y[1] (numeric) = -1.480334629320445300E-2 " "
absolute error = 4.23550083894497200000000000000E-14 " "
relative error = 2.8611779762940610000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7409999999999135 " "
y[1] (analytic) = -1.430355816189066400E-2 " "
y[1] (numeric) = -1.430355816193318600E-2 " "
absolute error = 4.252154184314349500000000000000E-14 " "
relative error = 2.9727946963878350000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.739999999999913 " "
y[1] (analytic) = -1.380375572706225600E-2 " "
y[1] (numeric) = -1.380375572710494400E-2 " "
absolute error = 4.26880752968372700000000000000E-14 " "
relative error = 3.092497153738190000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.738999999999913 " "
y[1] (analytic) = -1.330393948847927400E-2 " "
y[1] (numeric) = -1.330393948852213000E-2 " "
absolute error = 4.28546087505310400000000000000E-14 " "
relative error = 3.2211969084526860000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7379999999999125 " "
y[1] (analytic) = -1.28041099459579100E-2 " "
y[1] (numeric) = -1.280410994600093000E-2 " "
absolute error = 4.302114220422481600000000000000E-14 " "
relative error = 3.35994789062288750000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.736999999999912 " "
y[1] (analytic) = -1.230426759932766700E-2 " "
y[1] (numeric) = -1.230426759937085500E-2 " "
absolute error = 4.31876756579185900000000000000E-14 " "
relative error = 3.5099753243564420000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.735999999999912 " "
y[1] (analytic) = -1.180441294843085100E-2 " "
y[1] (numeric) = -1.180441294847420500E-2 " "
absolute error = 4.33542091116123630000000000000E-14 " "
relative error = 3.6727120019446110000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7349999999999115 " "
y[1] (analytic) = -1.130454649312207100E-2 " "
y[1] (numeric) = -1.130454649316559200E-2 " "
absolute error = 4.352074256530613600000000000000E-14 " "
relative error = 3.84984418364638400000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.733999999999911 " "
y[1] (analytic) = -1.08046687332677400E-2 " "
y[1] (numeric) = -1.080466873331142700E-2 " "
absolute error = 4.36872760189999100000000000000E-14 " "
relative error = 4.04337024091133150000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.732999999999910 " "
y[1] (analytic) = -1.030478016874557400E-2 " "
y[1] (numeric) = -1.03047801687894290E-2 " "
absolute error = 4.38555441961696600000000000000E-14 " "
relative error = 4.2558447126493430000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7319999999999105 " "
y[1] (analytic) = -9.8048812994440990E-3 " "
y[1] (numeric) = -9.804881299488122000E-3 " "
absolute error = 4.402207764986343400000000000000E-14 " "
relative error = 4.4898124011311920000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.73099999999991 " "
y[1] (analytic) = -9.304972625262142000E-3 " "
y[1] (numeric) = -9.304972625306331000E-3 " "
absolute error = 4.41886111035572070000000000000E-14 " "
relative error = 4.7489243529410510000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.72999999999991 " "
y[1] (analytic) = -8.805054646108335000E-3 " "
y[1] (numeric) = -8.80505464615269000E-3 " "
absolute error = 4.43551445572509800000000000000E-14 " "
relative error = 5.0374638591090530000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7289999999999095 " "
y[1] (analytic) = -8.305127861900616000E-3 " "
y[1] (numeric) = -8.305127861945137000E-3 " "
absolute error = 4.452167801094475400000000000000E-14 " "
relative error = 5.3607456442887360000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.727999999999910 " "
y[1] (analytic) = -7.8051927725657270000E-3 " "
y[1] (numeric) = -7.805192772610415000E-3 " "
absolute error = 4.468907882637651600000000000000E-14 " "
relative error = 5.7255573473409940000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.726999999999909 " "
y[1] (analytic) = -7.305249878038715000E-3 " "
y[1] (numeric) = -7.305249878083571000E-3 " "
absolute error = 4.48556122800702900000000000000E-14 " "
relative error = 6.1401886354246040000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7259999999999085 " "
y[1] (analytic) = -6.805299678262434000E-3 " "
y[1] (numeric) = -6.805299678307457000E-3 " "
absolute error = 4.50230130955020500000000000000E-14 " "
relative error = 6.6158751596663810000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.724999999999908 " "
y[1] (analytic) = -6.305342673187043000E-3 " "
y[1] (numeric) = -6.305342673232233000E-3 " "
absolute error = 4.518954654919582500000000000000E-14 " "
relative error = 7.1668660834819810000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.723999999999908 " "
y[1] (analytic) = -5.805379362769503000E-3 " "
y[1] (numeric) = -5.80537936281486000E-3 " "
absolute error = 4.535694736462758700000000000000E-14 " "
relative error = 7.8129170430284670000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7229999999999075 " "
y[1] (analytic) = -5.305410246973085000E-3 " "
y[1] (numeric) = -5.305410247018608000E-3 " "
absolute error = 4.55243481800593500000000000000E-14 " "
relative error = 8.5807404254991460000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.721999999999907 " "
y[1] (analytic) = -4.8054358257668606000E-3 " "
y[1] (numeric) = -4.805435825812552400E-3 " "
absolute error = 4.56917489954911100000000000000E-14 " "
relative error = 9.5083465167697930000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.720999999999907 " "
y[1] (analytic) = -4.305456599125212000E-3 " "
y[1] (numeric) = -4.3054565991710700000E-3 " "
absolute error = 4.585828244918488400000000000000E-14 " "
relative error = 1.0651200724797093000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7199999999999065 " "
y[1] (analytic) = -3.805473067027323000E-3 " "
y[1] (numeric) = -3.8054730670733483000E-3 " "
absolute error = 4.60252495837476500000000000000E-14 " "
relative error = 1.2094488325915459000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.718999999999906 " "
y[1] (analytic) = -3.3054857294566840000E-3 " "
y[1] (numeric) = -3.3054857295028767000E-3 " "
absolute error = 4.61922167183104200000000000000E-14 " "
relative error = 1.397441117554089000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.717999999999906 " "
y[1] (analytic) = -2.805495086400591000E-3 " "
y[1] (numeric) = -2.80549508644695000E-3 " "
absolute error = 4.63591838528731870000000000000E-14 " "
relative error = 1.6524421688562407000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7169999999999055 " "
y[1] (analytic) = -2.3055016378496457000E-3 " "
y[1] (numeric) = -2.3055016378961712000E-3 " "
absolute error = 4.65257173065669600000000000000E-14 " "
relative error = 2.0180301129589204000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.715999999999905 " "
y[1] (analytic) = -1.8055058837972543000E-3 " "
y[1] (numeric) = -1.805505883843947000E-3 " "
absolute error = 4.66926844411297300000000000000E-14 " "
relative error = 2.5861275147399626000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.714999999999905 " "
y[1] (analytic) = -1.3055083242391297000E-3 " "
y[1] (numeric) = -1.3055083242859894000E-3 " "
absolute error = 4.685965157569249600000000000000E-14 " "
relative error = 3.5893797615578610000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7139999999999045 " "
y[1] (analytic) = -8.0550945917278940000E-4 " "
y[1] (numeric) = -8.0550945921981620000E-4 " "
absolute error = 4.70268355506897600000000000000E-14 " "
relative error = 5.838148145272377000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.712999999999904 " "
y[1] (analytic) = -3.0550978859705730000E-4 " "
y[1] (numeric) = -3.05509788644251050000E-4 " "
absolute error = 4.719374847514390400000000000000E-14 " "
relative error = 1.544754054914706200000000E-8 "%"
Correct digits = 10
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.711999999999904 " "
y[1] (analytic) = 1.944901874884380200E-4 " "
y[1] (numeric) = 1.94490187441077270000E-4 " "
absolute error = 4.736074271476098400000000000000E-14 " "
relative error = 2.435122477198315000000000E-8 "%"
Correct digits = 10
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7109999999999035 " "
y[1] (analytic) = 6.9448996908376200000E-4 " "
y[1] (numeric) = 6.9448996903623440000E-4 " "
absolute error = 4.752773695437806400000000000000E-14 " "
relative error = 6.843545489516749000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.709999999999903 " "
y[1] (analytic) = 1.194489056189175100E-3 " "
y[1] (numeric) = 1.1944890561414803000E-3 " "
absolute error = 4.76947040889408300000000000000E-14 " "
relative error = 3.992895861357081000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.708999999999903 " "
y[1] (analytic) = 1.6944869488056308000E-3 " "
y[1] (numeric) = 1.6944869487577696000E-3 " "
absolute error = 4.786123754263460500000000000000E-14 " "
relative error = 2.8245267735092255000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7079999999999025 " "
y[1] (analytic) = 2.1944831469352796000E-3 " "
y[1] (numeric) = 2.194483146887251000E-3 " "
absolute error = 4.80284215176318700000000000000E-14 " "
relative error = 2.188598330532011000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.706999999999902 " "
y[1] (analytic) = 2.6944771505819640000E-3 " "
y[1] (numeric) = 2.694477150533769000E-3 " "
absolute error = 4.81953886521946400000000000000E-14 " "
relative error = 1.7886731250174157000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.705999999999902 " "
y[1] (analytic) = 3.1944684597517226000E-3 " "
y[1] (numeric) = 3.1944684597033600000E-3 " "
absolute error = 4.836235578675740500000000000000E-14 " "
relative error = 1.5139406256813120000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7049999999999015 " "
y[1] (analytic) = 3.6944565744532876000E-3 " "
y[1] (numeric) = 3.694456574404758000E-3 " "
absolute error = 4.85293229213201700000000000000E-14 " "
relative error = 1.3135713451578906000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.703999999999901 " "
y[1] (analytic) = 4.1944409946985856000E-3 " "
y[1] (numeric) = 4.194440994649889000E-3 " "
absolute error = 4.86962900558829400000000000000E-14 " "
relative error = 1.1609721084986267000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.702999999999900 " "
y[1] (analytic) = 4.694421220503239000E-3 " "
y[1] (numeric) = 4.694421220454375000E-3 " "
absolute error = 4.8863690871314700000000000000E-14 " "
relative error = 1.0408885052303966000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7019999999999005 " "
y[1] (analytic) = 5.194396751887063000E-3 " "
y[1] (numeric) = 5.1943967518380320000E-3 " "
absolute error = 4.903109168674646400000000000000E-14 " "
relative error = 9.4392273114166820000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7009999999999 " "
y[1] (analytic) = 5.694367088874568000E-3 " "
y[1] (numeric) = 5.6943670888253700000E-3 " "
absolute error = 4.919849250217822600000000000000E-14 " "
relative error = 8.6398526358267840000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6999999999999 " "
y[1] (analytic) = 6.194331731495458000E-3 " "
y[1] (numeric) = 6.194331731446093000E-3 " "
absolute error = 4.936502595587200000000000000E-14 " "
relative error = 7.9693868678153780000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6989999999998995 " "
y[1] (analytic) = 6.694290179785133000E-3 " "
y[1] (numeric) = 6.694290179735601000E-3 " "
absolute error = 4.95324267713037600000000000000E-14 " "
relative error = 7.3992052093704740000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.697999999999900 " "
y[1] (analytic) = 7.194241933785187000E-3 " "
y[1] (numeric) = 7.194241933735487000E-3 " "
absolute error = 4.969982758673552300000000000000E-14 " "
relative error = 6.9082785989359120000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.696999999999899 " "
y[1] (analytic) = 7.694186493543905000E-3 " "
y[1] (numeric) = 7.6941864934940400000E-3 " "
absolute error = 4.98654936786913100000000000000E-14 " "
relative error = 6.4809312486164480000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6959999999998985 " "
y[1] (analytic) = 8.194123359116772000E-3 " "
y[1] (numeric) = 8.19412335906674000E-3 " "
absolute error = 5.00328944941230700000000000000E-14 " "
relative error = 6.1059484097779090000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.694999999999898 " "
y[1] (analytic) = 8.694052030566963000E-3 " "
y[1] (numeric) = 8.694052030516763000E-3 " "
absolute error = 5.019942794781684000000000000000E-14 " "
relative error = 5.7739967245794370000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.693999999999898 " "
y[1] (analytic) = 9.193972007965847000E-3 " "
y[1] (numeric) = 9.19397200791548100E-3 " "
absolute error = 5.03659614015106200000000000000E-14 " "
relative error = 5.4781503965720700000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6929999999998975 " "
y[1] (analytic) = 9.69388279139349000E-3 " "
y[1] (numeric) = 9.693882791342956000E-3 " "
absolute error = 5.05342295786803700000000000000E-14 " "
relative error = 5.2130019174098250000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.691999999999897 " "
y[1] (analytic) = 1.019378388093914700E-2 " "
y[1] (numeric) = 1.019378388088844600E-2 " "
absolute error = 5.07007630323741400000000000000E-14 " "
relative error = 4.9736941281614766000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.690999999999897 " "
y[1] (analytic) = 1.069367477670177500E-2 " "
y[1] (numeric) = 1.069367477665090800E-2 " "
absolute error = 5.08690312095438900000000000000E-14 " "
relative error = 4.7569270874378790000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6899999999998965 " "
y[1] (analytic) = 1.119355497879051700E-2 " "
y[1] (numeric) = 1.119355497873948100E-2 " "
absolute error = 5.103556466323766000000000000000E-14 " "
relative error = 4.5593705270523577000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.688999999999896 " "
y[1] (analytic) = 1.169342398732521300E-2 " "
y[1] (numeric) = 1.16934239872740100E-2 " "
absolute error = 5.12020981169314400000000000000E-14 " "
relative error = 4.3787087659209690000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.687999999999896 " "
y[1] (analytic) = 1.219328130243689500E-2 " "
y[1] (numeric) = 1.219328130238552700E-2 " "
absolute error = 5.13686315706252100000000000000E-14 " "
relative error = 4.21286364978382840000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6869999999998955 " "
y[1] (analytic) = 1.269312642426829200E-2 " "
y[1] (numeric) = 1.269312642421675500E-2 " "
absolute error = 5.15368997477949600000000000000E-14 " "
relative error = 4.06022110118278900000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.685999999999895 " "
y[1] (analytic) = 1.319295885297432400E-2 " "
y[1] (numeric) = 1.319295885292262000E-2 " "
absolute error = 5.170343320148874000000000000000E-14 " "
relative error = 3.9190172407634180000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.684999999999895 " "
y[1] (analytic) = 1.3692778088722599E-2 " "
y[1] (numeric) = 1.369277808867073000E-2 " "
absolute error = 5.187170137865849000000000000000E-14 " "
relative error = 3.78825254032124640000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6839999999998945 " "
y[1] (analytic) = 1.419258363169392800E-2 " "
y[1] (numeric) = 1.41925836316418900E-2 " "
absolute error = 5.20382348323522600000000000000E-14 " "
relative error = 3.66657940391796940000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.682999999999894 " "
y[1] (analytic) = 1.469237498208281000E-2 " "
y[1] (numeric) = 1.469237498203060000E-2 " "
absolute error = 5.22065030095220100000000000000E-14 " "
relative error = 3.55330592046468160000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.681999999999894 " "
y[1] (analytic) = 1.51921516400979300E-2 " "
y[1] (numeric) = 1.519215164004555600E-2 " "
absolute error = 5.23730364632157800000000000000E-14 " "
relative error = 3.44737451968180730000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6809999999998935 " "
y[1] (analytic) = 1.569191310596268000E-2 " "
y[1] (numeric) = 1.56919131059101400E-2 " "
absolute error = 5.25378351934335800000000000000E-14 " "
relative error = 3.3480834897989610000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.679999999999893 " "
y[1] (analytic) = 1.619165887991562700E-2 " "
y[1] (numeric) = 1.619165887986292500E-2 " "
absolute error = 5.27043686471273500000000000000E-14 " "
relative error = 3.25503205310869240000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.678999999999893 " "
y[1] (analytic) = 1.66913884622110500E-2 " "
y[1] (numeric) = 1.669138846215817400E-2 " "
absolute error = 5.28743715477730800000000000000E-14 " "
relative error = 3.1677635247348980000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6779999999998925 " "
y[1] (analytic) = 1.719110135311939500E-2 " "
y[1] (numeric) = 1.719110135306635400E-2 " "
absolute error = 5.304090500146685000000000000000E-14 " "
relative error = 3.0853698033629690000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.676999999999892 " "
y[1] (analytic) = 1.769079705292782300E-2 " "
y[1] (numeric) = 1.769079705287461600E-2 " "
absolute error = 5.32074384551606300000000000000E-14 " "
relative error = 3.00763375985678400000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.675999999999892 " "
y[1] (analytic) = 1.819047506194067200E-2 " "
y[1] (numeric) = 1.8190475061887298E-2 " "
absolute error = 5.3373971908854400000000000000E-14 " "
relative error = 2.93417141262720450000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6749999999998915 " "
y[1] (analytic) = 1.869013488047997500E-2 " "
y[1] (numeric) = 1.869013488042643400E-2 " "
absolute error = 5.354050536254817000000000000000E-14 " "
relative error = 2.8646398597404460000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.673999999999891 " "
y[1] (analytic) = 1.918977600888595300E-2 " "
y[1] (numeric) = 1.918977600883224600E-2 " "
absolute error = 5.37070388162419500000000000000E-14 " "
relative error = 2.798731928469230000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.672999999999890 " "
y[1] (analytic) = 1.968939794751752300E-2 " "
y[1] (numeric) = 1.96893979474636500E-2 " "
absolute error = 5.38735722699357200000000000000E-14 " "
relative error = 2.73617163986104530000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6719999999998905 " "
y[1] (analytic) = 2.018900019675278800E-2 " "
y[1] (numeric) = 2.018900019669874800E-2 " "
absolute error = 5.404010572362950000000000000000E-14 " "
relative error = 2.67671034706916060000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.67099999999989 " "
y[1] (analytic) = 2.068858225698953500E-2 " "
y[1] (numeric) = 2.068858225693532800E-2 " "
absolute error = 5.42066391773232700000000000000E-14 " "
relative error = 2.6201234334948120000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.66999999999989 " "
y[1] (analytic) = 2.11881436286457500E-2 " "
y[1] (numeric) = 2.118814362859137700E-2 " "
absolute error = 5.43731726310170400000000000000E-14 " "
relative error = 2.5662074782948940000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6689999999998895 " "
y[1] (analytic) = 2.168768381216010200E-2 " "
y[1] (numeric) = 2.168768381210556300E-2 " "
absolute error = 5.453970608471082000000000000000E-14 " "
relative error = 2.51477781385446350000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.667999999999890 " "
y[1] (analytic) = 2.21872023079924500E-2 " "
y[1] (numeric) = 2.218720230793774500E-2 " "
absolute error = 5.47062395384045900000000000000E-14 " "
relative error = 2.4656664134124680000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.666999999999889 " "
y[1] (analytic) = 2.26866986166243400E-2 " "
y[1] (numeric) = 2.268669861656946700E-2 " "
absolute error = 5.48727729920983600000000000000E-14 " "
relative error = 2.41872005792366530000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6659999999998885 " "
y[1] (analytic) = 2.318617223855950500E-2 " "
y[1] (numeric) = 2.318617223850446600E-2 " "
absolute error = 5.503930644579214000000000000000E-14 " "
relative error = 2.37379874002055570000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.664999999999888 " "
y[1] (analytic) = 2.36856226743243600E-2 " "
y[1] (numeric) = 2.368562267426915500E-2 " "
absolute error = 5.52058398994859100000000000000E-14 " "
relative error = 2.3307742700524410000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.663999999999888 " "
y[1] (analytic) = 2.418504942446851600E-2 " "
y[1] (numeric) = 2.418504942441314400E-2 " "
absolute error = 5.53723733531796800000000000000E-14 " "
relative error = 2.28952905496890600000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6629999999998875 " "
y[1] (analytic) = 2.468445198956526200E-2 " "
y[1] (numeric) = 2.468445198950972300E-2 " "
absolute error = 5.553890680687346000000000000000E-14 " "
relative error = 2.24995502555013770000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.661999999999887 " "
y[1] (analytic) = 2.518382987021207000E-2 " "
y[1] (numeric) = 2.518382987015637000E-2 " "
absolute error = 5.570197081361528000000000000000E-14 " "
relative error = 2.2118149265096750000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.660999999999887 " "
y[1] (analytic) = 2.56831825670311200E-2 " "
y[1] (numeric) = 2.568318256697525000E-2 " "
absolute error = 5.587197371426100000000000000E-14 " "
relative error = 2.17543030613279620000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6599999999998865 " "
y[1] (analytic) = 2.618250958066973000E-2 " "
y[1] (numeric) = 2.618250958061369400E-2 " "
absolute error = 5.603850716795478000000000000000E-14 " "
relative error = 2.14030312851780290000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.658999999999886 " "
y[1] (analytic) = 2.66818104118009500E-2 " "
y[1] (numeric) = 2.668181041174474400E-2 " "
absolute error = 5.62050406216485500000000000000E-14 " "
relative error = 2.10649276620262340000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.657999999999886 " "
y[1] (analytic) = 2.71810845611239800E-2 " "
y[1] (numeric) = 2.718108456106761000E-2 " "
absolute error = 5.637157407534232000000000000000E-14 " "
relative error = 2.0739265921702160000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6569999999998855 " "
y[1] (analytic) = 2.76803315293647100E-2 " "
y[1] (numeric) = 2.768033152930817000E-2 " "
absolute error = 5.653810752903610000000000000000E-14 " "
relative error = 2.0425372242762910000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.655999999999885 " "
y[1] (analytic) = 2.817955081727622000E-2 " "
y[1] (numeric) = 2.817955081721952000E-2 " "
absolute error = 5.670811042968182000000000000000E-14 " "
relative error = 2.0123851795009950000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.654999999999885 " "
y[1] (analytic) = 2.867874192563926000E-2 " "
y[1] (numeric) = 2.86787419255823900E-2 " "
absolute error = 5.6874643883375600000000000000E-14 " "
relative error = 1.98316383720196400000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6539999999998845 " "
y[1] (analytic) = 2.917790435526277000E-2 " "
y[1] (numeric) = 2.917790435520572500E-2 " "
absolute error = 5.70411773370693700000000000000E-14 " "
relative error = 1.95494428395372230000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.652999999999884 " "
y[1] (analytic) = 2.967703760698434700E-2 " "
y[1] (numeric) = 2.96770376069271400E-2 " "
absolute error = 5.72077107907631400000000000000E-14 " "
relative error = 1.92767592063500250000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.651999999999884 " "
y[1] (analytic) = 3.017614118167079600E-2 " "
y[1] (numeric) = 3.017614118161342500E-2 " "
absolute error = 5.73742442444569200000000000000E-14 " "
relative error = 1.90131149967267650000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6509999999998834 " "
y[1] (analytic) = 3.067521458021858000E-2 " "
y[1] (numeric) = 3.067521458016103700E-2 " "
absolute error = 5.75407776981506900000000000000E-14 " "
relative error = 1.87580685206540730000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.649999999999883 " "
y[1] (analytic) = 3.117425730355433700E-2 " "
y[1] (numeric) = 3.117425730349663000E-2 " "
absolute error = 5.77073111518444600000000000000E-14 " "
relative error = 1.8511206406596561000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.648999999999883 " "
y[1] (analytic) = 3.16732688526353830E-2 " "
y[1] (numeric) = 3.16732688525775130E-2 " "
absolute error = 5.78703751585862800000000000000E-14 " "
relative error = 1.8271045981340558000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6479999999998824 " "
y[1] (analytic) = 3.217224872845022600E-2 " "
y[1] (numeric) = 3.21722487283921830E-2 " "
absolute error = 5.80438475061839700000000000000E-14 " "
relative error = 1.80415885740853540000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.646999999999882 " "
y[1] (analytic) = 3.26711964320190100E-2 " "
y[1] (numeric) = 3.26711964319608100E-2 " "
absolute error = 5.82034420659738300000000000000E-14 " "
relative error = 1.78149098968816000000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.645999999999882 " "
y[1] (analytic) = 3.317011146439409000E-2 " "
y[1] (numeric) = 3.31701114643357160E-2 " "
absolute error = 5.83769144135715100000000000000E-14 " "
relative error = 1.75992518072286970000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6449999999998814 " "
y[1] (analytic) = 3.36689933266604700E-2 " "
y[1] (numeric) = 3.366899332660193700E-2 " "
absolute error = 5.85365089733613800000000000000E-14 " "
relative error = 1.7385880357465220000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.643999999999881 " "
y[1] (analytic) = 3.416784151993634000E-2 " "
y[1] (numeric) = 3.416784151987762300E-2 " "
absolute error = 5.87099813209590600000000000000E-14 " "
relative error = 1.71828183195894380000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.642999999999880 " "
y[1] (analytic) = 3.46666555453735200E-2 " "
y[1] (numeric) = 3.466665554531464500E-2 " "
absolute error = 5.88765147746528300000000000000E-14 " "
relative error = 1.69836154796046550000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.64199999999988 " "
y[1] (analytic) = 3.51654349041580500E-2 " "
y[1] (numeric) = 3.516543490409901000E-2 " "
absolute error = 5.9043048228346610000000000000E-14 " "
relative error = 1.6790080483652772000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.64099999999988 " "
y[1] (analytic) = 3.56641790975106070E-2 " "
y[1] (numeric) = 3.5664179097451400E-2 " "
absolute error = 5.92095816820403800000000000000E-14 " "
relative error = 1.66019751976215440000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.63999999999988 " "
y[1] (analytic) = 3.61628876266870400E-2 " "
y[1] (numeric) = 3.616288762662766600E-2 " "
absolute error = 5.93761151357341500000000000000E-14 " "
relative error = 1.64190746459960540000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.638999999999880 " "
y[1] (analytic) = 3.666155999297885400E-2 " "
y[1] (numeric) = 3.66615599929193100E-2 " "
absolute error = 5.95426485894279300000000000000E-14 " "
relative error = 1.62411661153620000000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.637999999999879 " "
y[1] (analytic) = 3.716019569771373000E-2 " "
y[1] (numeric) = 3.716019569765402500E-2 " "
absolute error = 5.9709182043121700000000000000E-14 " "
relative error = 1.60680483302178320000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.636999999999879 " "
y[1] (analytic) = 3.765879424225601600E-2 " "
y[1] (numeric) = 3.76587942421961400E-2 " "
absolute error = 5.98757154968154700000000000000E-14 " "
relative error = 1.5899530694381708000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.635999999999878 " "
y[1] (analytic) = 3.81573551280071900E-2 " "
y[1] (numeric) = 3.81573551279471500E-2 " "
absolute error = 6.00422489505092500000000000000E-14 " "
relative error = 1.57354325919824370000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.634999999999878 " "
y[1] (analytic) = 3.865587785640642000E-2 " "
y[1] (numeric) = 3.86558778563462100E-2 " "
absolute error = 6.02087824042030200000000000000E-14 " "
relative error = 1.5575582742644830000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.633999999999878 " "
y[1] (analytic) = 3.91543619289310100E-2 " "
y[1] (numeric) = 3.91543619288706300E-2 " "
absolute error = 6.0375315857896790000000000000E-14 " "
relative error = 1.54198186060301250000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.632999999999877 " "
y[1] (analytic) = 3.96528068470969330E-2 " "
y[1] (numeric) = 3.96528068470363900E-2 " "
absolute error = 6.05418493115905700000000000000E-14 " "
relative error = 1.52679858313795440000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.631999999999877 " "
y[1] (analytic) = 4.01512121124593170E-2 " "
y[1] (numeric) = 4.01512121123986100E-2 " "
absolute error = 6.07083827652843400000000000000E-14 " "
relative error = 1.51199377481423370000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.630999999999877 " "
y[1] (analytic) = 4.06495772266129300E-2 " "
y[1] (numeric) = 4.06495772265520600E-2 " "
absolute error = 6.08679773250742100000000000000E-14 " "
relative error = 1.49738278914311740000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.629999999999876 " "
y[1] (analytic) = 4.11479016911927060E-2 " "
y[1] (numeric) = 4.11479016911316700E-2 " "
absolute error = 6.10345107787679800000000000000E-14 " "
relative error = 1.48329582482286840000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.628999999999876 " "
y[1] (analytic) = 4.164618500787422600E-2 " "
y[1] (numeric) = 4.16461850078130250E-2 " "
absolute error = 6.12010442324617500000000000000E-14 " "
relative error = 1.4695474320370572000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.627999999999876 " "
y[1] (analytic) = 4.2144426678374200E-2 " "
y[1] (numeric) = 4.214442667831283500E-2 " "
absolute error = 6.13675776861555300000000000000E-14 " "
relative error = 1.45612557870304100000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.626999999999875 " "
y[1] (analytic) = 4.264262620445102000E-2 " "
y[1] (numeric) = 4.26426262043894800E-2 " "
absolute error = 6.1534111139849300000000000000E-14 " "
relative error = 1.44301879637578230000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.625999999999875 " "
y[1] (analytic) = 4.31407830879051700E-2 " "
y[1] (numeric) = 4.31407830878434760E-2 " "
absolute error = 6.16937056996391700000000000000E-14 " "
relative error = 1.43005530460422800000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.624999999999875 " "
y[1] (analytic) = 4.36388968305798400E-2 " "
y[1] (numeric) = 4.36388968305179760E-2 " "
absolute error = 6.18602391533329400000000000000E-14 " "
relative error = 1.41754818856888560000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.623999999999874 " "
y[1] (analytic) = 4.41369669343613100E-2 " "
y[1] (numeric) = 4.413696693429928000E-2 " "
absolute error = 6.20267726070267100000000000000E-14 " "
relative error = 1.4053247632369120000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.622999999999874 " "
y[1] (analytic) = 4.46349929011795300E-2 " "
y[1] (numeric) = 4.46349929011173300E-2 " "
absolute error = 6.2200244954624400000000000000E-14 " "
relative error = 1.3935309700246570000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.621999999999874 " "
y[1] (analytic) = 4.51329742330085600E-2 " "
y[1] (numeric) = 4.5132974232946205E-2 " "
absolute error = 6.23598395144142600000000000000E-14 " "
relative error = 1.3816913370802542000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.620999999999873 " "
y[1] (analytic) = 4.56309104318671300E-2 " "
y[1] (numeric) = 4.5630910431804605E-2 " "
absolute error = 6.25263729681080300000000000000E-14 " "
relative error = 1.37026354232988670000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.619999999999873 " "
y[1] (analytic) = 4.612880099981906400E-2 " "
y[1] (numeric) = 4.61288009997563700E-2 " "
absolute error = 6.26929064218018100000000000000E-14 " "
relative error = 1.35908380584285530000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.618999999999873 " "
y[1] (analytic) = 4.662664543897384600E-2 " "
y[1] (numeric) = 4.662664543891098500E-2 " "
absolute error = 6.28594398754955800000000000000E-14 " "
relative error = 1.34814416271416380000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.617999999999872 " "
y[1] (analytic) = 4.71244432514870700E-2 " "
y[1] (numeric) = 4.71244432514240400E-2 " "
absolute error = 6.30259733291893600000000000000E-14 " "
relative error = 1.33743698557543140000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.616999999999872 " "
y[1] (analytic) = 4.762219393956096400E-2 " "
y[1] (numeric) = 4.76221939394977800E-2 " "
absolute error = 6.31855678889792200000000000000E-14 " "
relative error = 1.3268092597575470000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.615999999999872 " "
y[1] (analytic) = 4.811989700544489500E-2 " "
y[1] (numeric) = 4.811989700538154600E-2 " "
absolute error = 6.335210134267300000000000000E-14 " "
relative error = 1.31654690232409530000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.614999999999871 " "
y[1] (analytic) = 4.86175519514358300E-2 " "
y[1] (numeric) = 4.86175519513723060E-2 " "
absolute error = 6.35186347963667700000000000000E-14 " "
relative error = 1.30649595149948450000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.613999999999871 " "
y[1] (analytic) = 4.91151582798788600E-2 " "
y[1] (numeric) = 4.91151582798151740E-2 " "
absolute error = 6.36851682500605400000000000000E-14 " "
relative error = 1.29664996470449380000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.612999999999870 " "
y[1] (analytic) = 4.96127154931677100E-2 " "
y[1] (numeric) = 4.96127154931038600E-2 " "
absolute error = 6.38517017037543200000000000000E-14 " "
relative error = 1.28700275864858660000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.61199999999987 " "
y[1] (analytic) = 5.0110223093745200E-2 " "
y[1] (numeric) = 5.01102230936811800E-2 " "
absolute error = 6.40182351574480900000000000000E-14 " "
relative error = 1.27754839641571860000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.61099999999987 " "
y[1] (analytic) = 5.06076805841037600E-2 " "
y[1] (numeric) = 5.06076805840395900E-2 " "
absolute error = 6.41778297172379600000000000000E-14 " "
relative error = 1.26814406383596780000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.60999999999987 " "
y[1] (analytic) = 5.11050874667859700E-2 " "
y[1] (numeric) = 5.11050874667216200E-2 " "
absolute error = 6.43443631709317300000000000000E-14 " "
relative error = 1.2590598384700970000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.608999999999870 " "
y[1] (analytic) = 5.16024432443849700E-2 " "
y[1] (numeric) = 5.16024432443204600E-2 " "
absolute error = 6.4510896624625500000000000000E-14 " "
relative error = 1.25015198057788000000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.607999999999869 " "
y[1] (analytic) = 5.20997474195450200E-2 " "
y[1] (numeric) = 5.20997474194803400E-2 " "
absolute error = 6.46774300783192800000000000000E-14 " "
relative error = 1.2414154248674109000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.606999999999869 " "
y[1] (analytic) = 5.25969994949619900E-2 " "
y[1] (numeric) = 5.25969994948971500E-2 " "
absolute error = 6.48439635320130500000000000000E-14 " "
relative error = 1.23284529829927140000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.605999999999868 " "
y[1] (analytic) = 5.309419897338385000E-2 " "
y[1] (numeric) = 5.309419897331884000E-2 " "
absolute error = 6.50104969857068200000000000000E-14 " "
relative error = 1.22443691105117940000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.604999999999868 " "
y[1] (analytic) = 5.35913453576111600E-2 " "
y[1] (numeric) = 5.35913453575459900E-2 " "
absolute error = 6.51700915454966900000000000000E-14 " "
relative error = 1.2160562701052080000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.603999999999868 " "
y[1] (analytic) = 5.40884381504975900E-2 " "
y[1] (numeric) = 5.408843815043225000E-2 " "
absolute error = 6.53366249991904600000000000000E-14 " "
relative error = 1.20795917266820550000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.602999999999867 " "
y[1] (analytic) = 5.45854768549503700E-2 " "
y[1] (numeric) = 5.45854768548848600E-2 " "
absolute error = 6.55031584528842400000000000000E-14 " "
relative error = 1.20001073961386030000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.601999999999867 " "
y[1] (analytic) = 5.50824609739308400E-2 " "
y[1] (numeric) = 5.50824609738651700E-2 " "
absolute error = 6.56696919065780100000000000000E-14 " "
relative error = 1.19220693384883170000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.600999999999867 " "
y[1] (analytic) = 5.55793900104549200E-2 " "
y[1] (numeric) = 5.557939001038908000E-2 " "
absolute error = 6.58362253602717800000000000000E-14 " "
relative error = 1.18454386325376120000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.599999999999866 " "
y[1] (analytic) = 5.60762634675936300E-2 " "
y[1] (numeric) = 5.60762634675276300E-2 " "
absolute error = 6.60027588139655600000000000000E-14 " "
relative error = 1.17701777423362780000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.598999999999866 " "
y[1] (analytic) = 5.65730808484735400E-2 " "
y[1] (numeric) = 5.65730808484073800E-2 " "
absolute error = 6.61623533737554200000000000000E-14 " "
relative error = 1.16950239197624730000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.597999999999866 " "
y[1] (analytic) = 5.70698416562773200E-2 " "
y[1] (numeric) = 5.70698416562110000E-2 " "
absolute error = 6.6328886827449200000000000000E-14 " "
relative error = 1.16224059682761420000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.596999999999865 " "
y[1] (analytic) = 5.756654539424421000E-2 " "
y[1] (numeric) = 5.75665453941777000E-2 " "
absolute error = 6.64954202811429700000000000000E-14 " "
relative error = 1.15510527556846450000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.595999999999865 " "
y[1] (analytic) = 5.80631915656704800E-2 " "
y[1] (numeric) = 5.80631915656038200E-2 " "
absolute error = 6.66550148409328400000000000000E-14 " "
relative error = 1.14797366530471980000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.594999999999865 " "
y[1] (analytic) = 5.85597796739100400E-2 " "
y[1] (numeric) = 5.85597796738432200E-2 " "
absolute error = 6.68215482946266100000000000000E-14 " "
relative error = 1.1410826452340190000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.593999999999864 " "
y[1] (analytic) = 5.9056309222374800E-2 " "
y[1] (numeric) = 5.90563092223078100E-2 " "
absolute error = 6.69880817483203800000000000000E-14 " "
relative error = 1.13430863916806460000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.592999999999864 " "
y[1] (analytic) = 5.95527797145352500E-2 " "
y[1] (numeric) = 5.95527797144681100E-2 " "
absolute error = 6.71476763081102500000000000000E-14 " "
relative error = 1.12753219295523970000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.591999999999864 " "
y[1] (analytic) = 6.00491906539209700E-2 " "
y[1] (numeric) = 6.004919065385366000E-2 " "
absolute error = 6.73142097618040200000000000000E-14 " "
relative error = 1.12098446338358230000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.590999999999863 " "
y[1] (analytic) = 6.05455415441210300E-2 " "
y[1] (numeric) = 6.05455415440535500E-2 " "
absolute error = 6.7480743215497800000000000000E-14 " "
relative error = 1.11454520835894940000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.589999999999863 " "
y[1] (analytic) = 6.104183188878458000E-2 " "
y[1] (numeric) = 6.10418318887169400E-2 " "
absolute error = 6.76472766691915700000000000000E-14 " "
relative error = 1.10821177176402250000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.588999999999863 " "
y[1] (analytic) = 6.15380611916213400E-2 " "
y[1] (numeric) = 6.15380611915535300E-2 " "
absolute error = 6.78138101228853400000000000000E-14 " "
relative error = 1.10198158358811720000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.587999999999862 " "
y[1] (analytic) = 6.20342289564020400E-2 " "
y[1] (numeric) = 6.20342289563340600E-2 " "
absolute error = 6.79803435765791200000000000000E-14 " "
relative error = 1.09585215646600590000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.586999999999862 " "
y[1] (analytic) = 6.25303346869589400E-2 " "
y[1] (numeric) = 6.2530334686890800E-2 " "
absolute error = 6.81399381363689800000000000000E-14 " "
relative error = 1.08971011393898640000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.585999999999862 " "
y[1] (analytic) = 6.30263778871863700E-2 " "
y[1] (numeric) = 6.30263778871180700E-2 " "
absolute error = 6.83064715900627600000000000000E-14 " "
relative error = 1.08377593445600580000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.584999999999861 " "
y[1] (analytic) = 6.35223580610411700E-2 " "
y[1] (numeric) = 6.3522358060972710E-2 " "
absolute error = 6.84730050437565300000000000000E-14 " "
relative error = 1.07793550387342500000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.583999999999861 " "
y[1] (analytic) = 6.4018274712543200E-2 " "
y[1] (numeric) = 6.40182747124745700E-2 " "
absolute error = 6.8639538497450300000000000000E-14 " "
relative error = 1.07218663429556080000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.582999999999860 " "
y[1] (analytic) = 6.45141273457758600E-2 " "
y[1] (numeric) = 6.45141273457070500E-2 " "
absolute error = 6.88060719511440800000000000000E-14 " "
relative error = 1.06652720546562950000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.58199999999986 " "
y[1] (analytic) = 6.50099154648865400E-2 " "
y[1] (numeric) = 6.50099154648175600E-2 " "
absolute error = 6.89726054048378500000000000000E-14 " "
relative error = 1.06095516217201770000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.58099999999986 " "
y[1] (analytic) = 6.55056385740871800E-2 " "
y[1] (numeric) = 6.55056385740180300E-2 " "
absolute error = 6.91391388585316200000000000000E-14 " "
relative error = 1.05546851177299710000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.57999999999986 " "
y[1] (analytic) = 6.60012961776546900E-2 " "
y[1] (numeric) = 6.60012961775853900E-2 " "
absolute error = 6.92917945244175800000000000000E-14 " "
relative error = 1.04985505645079930000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.578999999999860 " "
y[1] (analytic) = 6.64968877799315200E-2 " "
y[1] (numeric) = 6.64968877798620700E-2 " "
absolute error = 6.94583279781113600000000000000E-14 " "
relative error = 1.04453501956333020000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.577999999999859 " "
y[1] (analytic) = 6.69924128853261400E-2 " "
y[1] (numeric) = 6.69924128852565000E-2 " "
absolute error = 6.96248614318051300000000000000E-14 " "
relative error = 1.03929472656829180000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.576999999999859 " "
y[1] (analytic) = 6.74878709983134300E-2 " "
y[1] (numeric) = 6.74878709982436500E-2 " "
absolute error = 6.97775170976910900000000000000E-14 " "
relative error = 1.03392677921985250000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.575999999999858 " "
y[1] (analytic) = 6.79832616234353500E-2 " "
y[1] (numeric) = 6.7983261623365410E-2 " "
absolute error = 6.99440505513848600000000000000E-14 " "
relative error = 1.02884223088339710000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.574999999999858 " "
y[1] (analytic) = 6.84785842653013100E-2 " "
y[1] (numeric) = 6.84785842652312100E-2 " "
absolute error = 7.01105840050786400000000000000E-14 " "
relative error = 1.0238322646019461000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.573999999999858 " "
y[1] (analytic) = 6.89738384285887300E-2 " "
y[1] (numeric) = 6.89738384285184500E-2 " "
absolute error = 7.02771174587724100000000000000E-14 " "
relative error = 1.01889526608748930000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.572999999999857 " "
y[1] (analytic) = 6.94690236180434600E-2 " "
y[1] (numeric) = 6.94690236179730100E-2 " "
absolute error = 7.04436509124661800000000000000E-14 " "
relative error = 1.0140296673778150000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.571999999999857 " "
y[1] (analytic) = 6.99641393384803500E-2 " "
y[1] (numeric) = 6.99641393384097400E-2 " "
absolute error = 7.06101843661599600000000000000E-14 " "
relative error = 1.00923394518660610000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.570999999999857 " "
y[1] (analytic) = 7.04591850947837500E-2 " "
y[1] (numeric) = 7.04591850947129600E-2 " "
absolute error = 7.07767178198537300000000000000E-14 " "
relative error = 1.00450661932355340000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.569999999999856 " "
y[1] (analytic) = 7.09541603919079200E-2 " "
y[1] (numeric) = 7.09541603918369700E-2 " "
absolute error = 7.0943251273547500000000000000E-14 " "
relative error = 9.9984625118104200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.568999999999856 " "
y[1] (analytic) = 7.1449064734877600E-2 " "
y[1] (numeric) = 7.14490647348064900E-2 " "
absolute error = 7.11097847272412800000000000000E-14 " "
relative error = 9.95251442284160400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.567999999999856 " "
y[1] (analytic) = 7.1943897628788500E-2 " "
y[1] (numeric) = 7.19438976287172200E-2 " "
absolute error = 7.12763181809350500000000000000E-14 " "
relative error = 9.90720832900964200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.566999999999855 " "
y[1] (analytic) = 7.24386585788077800E-2 " "
y[1] (numeric) = 7.24386585787363300E-2 " "
absolute error = 7.14567294224366400000000000000E-14 " "
relative error = 9.8644468056648390000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.565999999999855 " "
y[1] (analytic) = 7.29333470901745200E-2 " "
y[1] (numeric) = 7.29333470901029000E-2 " "
absolute error = 7.16232628761304100000000000000E-14 " "
relative error = 9.82037239941499900000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.564999999999855 " "
y[1] (analytic) = 7.34279626682002300E-2 " "
y[1] (numeric) = 7.34279626681284400E-2 " "
absolute error = 7.17897963298241800000000000000E-14 " "
relative error = 9.77690156735269300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.563999999999854 " "
y[1] (analytic) = 7.3922504818269400E-2 " "
y[1] (numeric) = 7.39225048181974400E-2 " "
absolute error = 7.19563297835179600000000000000E-14 " "
relative error = 9.7340221303938400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.562999999999854 " "
y[1] (analytic) = 7.44169730458399200E-2 " "
y[1] (numeric) = 7.44169730457677900E-2 " "
absolute error = 7.21228632372117300000000000000E-14 " "
relative error = 9.69172223556915800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.561999999999854 " "
y[1] (analytic) = 7.49113668564435700E-2 " "
y[1] (numeric) = 7.49113668563712900E-2 " "
absolute error = 7.2289396690905500000000000000E-14 " "
relative error = 9.64999034518183600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.560999999999853 " "
y[1] (analytic) = 7.54056857556866200E-2 " "
y[1] (numeric) = 7.54056857556141700E-2 " "
absolute error = 7.24559301445992800000000000000E-14 " "
relative error = 9.60881522639492800000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = sin(x) / 2.0;"
Iterations = 440
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds
"Expected Time Remaining "= 0 Years 0 Days 1 Hours 5 Minutes 11 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 1 Hours 4 Minutes 41 Seconds
"Expected Total Time "= 0 Years 0 Days 1 Hours 7 Minutes 41 Seconds
"Time to Timeout " Unknown
Percent Done = 4.410000000001473 "%"
(%o57) true
(%o57) diffeq.max