(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_0D1 array_x ,
1 1 1
array_tmp2 : array_const_0D2 + array_tmp1 , array_tmp3 : ln(array_tmp2 ),
1 1 1 1 1
array_tmp4 : array_tmp3 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp2
2
array_tmp3 : -----------, array_tmp4 : array_tmp3 ,
2 array_tmp2 2 2
1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp4 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_tmp2 array_tmp3 1
2 2
---------------------------
array_tmp2
1
array_tmp3 : ---------------------------, array_tmp4 : array_tmp3 ,
3 2 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp4 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_tmp2 array_tmp3 2
2 3
---------------------------
array_tmp2
1
array_tmp3 : ---------------------------, array_tmp4 : array_tmp3 ,
4 3 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp4 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_tmp2 array_tmp3 3
2 4
---------------------------
array_tmp2
1
array_tmp3 : ---------------------------, array_tmp4 : array_tmp3 ,
5 4 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp3 :
kkk
- array_tmp2 array_tmp3 (kkk - 2)
2 kkk - 1
-----------------------------------------
array_tmp2
1
-----------------------------------------, array_tmp4 : array_tmp3 ,
kkk - 1 kkk kkk
order_d : 1, if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp4 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_0D1 array_x ,
1 1 1
array_tmp2 : array_const_0D2 + array_tmp1 , array_tmp3 : ln(array_tmp2 ),
1 1 1 1 1
array_tmp4 : array_tmp3 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp2
2
array_tmp3 : -----------, array_tmp4 : array_tmp3 ,
2 array_tmp2 2 2
1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp4 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_tmp2 array_tmp3 1
2 2
---------------------------
array_tmp2
1
array_tmp3 : ---------------------------, array_tmp4 : array_tmp3 ,
3 2 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp4 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_tmp2 array_tmp3 2
2 3
---------------------------
array_tmp2
1
array_tmp3 : ---------------------------, array_tmp4 : array_tmp3 ,
4 3 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp4 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_tmp2 array_tmp3 3
2 4
---------------------------
array_tmp2
1
array_tmp3 : ---------------------------, array_tmp4 : array_tmp3 ,
5 4 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp3 :
kkk
- array_tmp2 array_tmp3 (kkk - 2)
2 kkk - 1
-----------------------------------------
array_tmp2
1
-----------------------------------------, array_tmp4 : array_tmp3 ,
kkk - 1 kkk kkk
order_d : 1, if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp4 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i32) log_revs(file, revs) := printf(file, revs)
(%o32) log_revs(file, revs) := printf(file, revs)
(%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i35) logstart(file) := printf(file, "")
(%o35) logstart(file) := printf(file, "
")
(%i36) logend(file) := printf(file, "
~%")
(%o36) logend(file) := printf(file, "~%")
(%i37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i40) factorial_2(nnn) := nnn!
(%o40) factorial_2(nnn) := nnn!
(%i41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i46) Si(x) := 0.0
(%o46) Si(x) := 0.0
(%i47) Ci(x) := 0.0
(%o47) Ci(x) := 0.0
(%i48) ln(x) := log(x)
(%o48) ln(x) := log(x)
(%i49) arcsin(x) := asin(x)
(%o49) arcsin(x) := asin(x)
(%i50) arccos(x) := acos(x)
(%o50) arccos(x) := acos(x)
(%i51) arctan(x) := atan(x)
(%o51) arctan(x) := atan(x)
(%i52) omniabs(x) := abs(x)
(%o52) omniabs(x) := abs(x)
(%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i54) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%o54) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%i55) exact_soln_y(x) := block(- 2.0 - x + 10.0 (0.2 + 0.1 x) ln(0.2 + 0.1 x))
(%o55) exact_soln_y(x) := block(- 2.0 - x + 10.0 (0.2 + 0.1 x) ln(0.2 + 0.1 x))
(%i56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/lin_lnpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ;"),
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:20.0,"), omniout_str(ALWAYS, "x_end:30.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.00001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:20,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (10.0* (0.1 * x + 0.2) * ln(0.1 * x + 0.2) - x - 2.0) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term),
term
array_const_0D2 : 0.2, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : 20.0, x_end : 30.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 20,
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 ) = ln (0.1 * x + 0.2) ;"),
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,
"2013-01-13T00:01:13-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_ln"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ;"),
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, "lin_ln diffeq.max"),
logitem_str(html_log_file,
"lin_ln 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/lin_lnpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ;"),
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:20.0,"), omniout_str(ALWAYS, "x_end:30.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.00001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:20,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (10.0* (0.1 * x + 0.2) * ln(0.1 * x + 0.2) - x - 2.0) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term),
term
array_const_0D2 : 0.2, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : 20.0, x_end : 30.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 20,
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 ) = ln (0.1 * x + 0.2) ;"),
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,
"2013-01-13T00:01:13-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_ln"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ;"),
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, "lin_ln diffeq.max"),
logitem_str(html_log_file,
"lin_ln 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/lin_lnpostode.ode#################"
"diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:20.0,"
"x_end:30.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.00001,"
"glob_look_poles:true,"
"glob_max_iter:20,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (10.0* (0.1 * x + 0.2) * ln(0.1 * x + 0.2) - 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 = 4.2316572465437885000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-115 ""
max_value3 = 4.2316572465437885000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-115 ""
value3 = 4.2316572465437885000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-115 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = 20. " "
y[1] (analytic) = -4.653938071986051 " "
y[1] (numeric) = -4.653938071986051 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 20. " "
y[1] (analytic) = -4.653938071986051 " "
y[1] (numeric) = -4.653938071986051 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.001 " "
y[1] (analytic) = -4.653149591898757 " "
y[1] (numeric) = -4.653149591898758 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.817536497199509600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.002000000000002 " "
y[1] (analytic) = -4.652361066358985 " "
y[1] (numeric) = -4.652361066358987 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.818183528886026600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.003000000000004 " "
y[1] (analytic) = -4.6515724953687965 " "
y[1] (numeric) = -4.651572495368801 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 9.54707704313341700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.004000000000005 " "
y[1] (analytic) = -4.65078387893027 " "
y[1] (numeric) = -4.650783878930267 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.72921754367405100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.005000000000006 " "
y[1] (analytic) = -4.649995217045447 " "
y[1] (numeric) = -4.649995217045450 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 7.64025232924401500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.006000000000007 " "
y[1] (analytic) = -4.649206509716410 " "
y[1] (numeric) = -4.649206509716417 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.33727097837177230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.00700000000001 " "
y[1] (analytic) = -4.648417756945225 " "
y[1] (numeric) = -4.648417756945231 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.33749788917135380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.00800000000001 " "
y[1] (analytic) = -4.64762895873395 " "
y[1] (numeric) = -4.647628958733958 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 1.71993200151645630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.00900000000001 " "
y[1] (analytic) = -4.646840115084661 " "
y[1] (numeric) = -4.646840115084663 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.82271994604205800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.010000000000012 " "
y[1] (analytic) = -4.6460512259994005 " "
y[1] (numeric) = -4.646051225999410 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 1.91168451766063230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.011000000000013 " "
y[1] (analytic) = -4.64526229148025 " "
y[1] (numeric) = -4.645262291480262 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 2.48561194860372480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.012000000000015 " "
y[1] (analytic) = -4.644473311529275 " "
y[1] (numeric) = -4.6444733115292856 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 2.29480079257730150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.013000000000016 " "
y[1] (analytic) = -4.643684286148531 " "
y[1] (numeric) = -4.6436842861485434 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 2.6777224956683950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.014000000000017 " "
y[1] (analytic) = -4.64289521534009 " "
y[1] (numeric) = -4.6428952153401 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 2.10428238492686550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.01500000000002 " "
y[1] (analytic) = -4.642106099106002 " "
y[1] (numeric) = -4.642106099106018 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 3.44395651742667950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.01600000000002 " "
y[1] (analytic) = -4.6413169374483445 " "
y[1] (numeric) = -4.6413169374483605 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 3.44454209226908340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.01700000000002 " "
y[1] (analytic) = -4.640527730369175 " "
y[1] (numeric) = -4.640527730369191 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 3.4451278999964940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.018000000000022 " "
y[1] (analytic) = -4.639738477870555 " "
y[1] (numeric) = -4.639738477870574 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 4.01999959753399700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.019000000000023 " "
y[1] (analytic) = -4.638949179954558 " "
y[1] (numeric) = -4.638949179954570 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 2.6804557225012670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.020000000000024 " "
y[1] (analytic) = -4.638159836623224 " "
y[1] (numeric) = -4.638159836623244 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 4.4043552556773036000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.021000000000026 " "
y[1] (analytic) = -4.637370447878638 " "
y[1] (numeric) = -4.6373704478786575 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 4.21357867632534740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.022000000000027 " "
y[1] (analytic) = -4.63658101372285 " "
y[1] (numeric) = -4.636581013722872 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 4.7889728286392010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.023000000000028 " "
y[1] (analytic) = -4.635791534157924 " "
y[1] (numeric) = -4.63579153415795 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 5.5561545383386900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.02400000000003 " "
y[1] (analytic) = -4.635002009185936 " "
y[1] (numeric) = -4.635002009185953 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 3.8324834290896870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.02500000000003 " "
y[1] (analytic) = -4.634212438808923 " "
y[1] (numeric) = -4.6342124388089445 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 4.599763682452519500000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.02600000000003 " "
y[1] (analytic) = -4.633422823028958 " "
y[1] (numeric) = -4.633422823028984 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 5.5589949709069860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.027000000000033 " "
y[1] (analytic) = -4.6326331618481085 " "
y[1] (numeric) = -4.632633161848134 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 5.5599425362288470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.028000000000034 " "
y[1] (analytic) = -4.631843455268427 " "
y[1] (numeric) = -4.631843455268456 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 6.136155011473050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.029000000000035 " "
y[1] (analytic) = -4.631053703291986 " "
y[1] (numeric) = -4.631053703292010 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 4.9864761654108750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.030000000000037 " "
y[1] (analytic) = -4.6302639059208275 " "
y[1] (numeric) = -4.630263905920856 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 6.1382482743716830000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.031000000000038 " "
y[1] (analytic) = -4.629474063157026 " "
y[1] (numeric) = -4.629474063157056 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 6.3311485171420380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.03200000000004 " "
y[1] (analytic) = -4.628684175002636 " "
y[1] (numeric) = -4.62868417500267 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 7.2916575580760020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.03300000000004 " "
y[1] (analytic) = -4.627894241459725 " "
y[1] (numeric) = -4.627894241459758 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 7.2929021683864440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.03400000000004 " "
y[1] (analytic) = -4.627104262530352 " "
y[1] (numeric) = -4.627104262530380 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 6.1424398106952260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.035000000000043 " "
y[1] (analytic) = -4.626314238216562 " "
y[1] (numeric) = -4.626314238216597 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 7.679360925059140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.036000000000044 " "
y[1] (analytic) = -4.625524168520432 " "
y[1] (numeric) = -4.625524168520467 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 7.6806726099907260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.037000000000045 " "
y[1] (analytic) = -4.624734053444012 " "
y[1] (numeric) = -4.624734053444051 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 8.450183300313879000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.038000000000046 " "
y[1] (analytic) = -4.623943892989367 " "
y[1] (numeric) = -4.623943892989407 " "
absolute error = 3.996802888650563500000000000000E-14 " "
relative error = 8.6437097446410440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.039000000000048 " "
y[1] (analytic) = -4.62315368715856 " "
y[1] (numeric) = -4.623153687158594 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 7.4924955370874480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.04000000000005 " "
y[1] (analytic) = -4.6223634359536305 " "
y[1] (numeric) = -4.622363435953672 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 9.0309613911381430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.04100000000005 " "
y[1] (analytic) = -4.6215731393766575 " "
y[1] (numeric) = -4.621573139376700 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 9.0325057003287480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.04200000000005 " "
y[1] (analytic) = -4.6207827974296904 " "
y[1] (numeric) = -4.620782797429734 " "
absolute error = 4.352074256530613600000000000000E-14 " "
relative error = 9.4184783127037560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.043000000000053 " "
y[1] (analytic) = -4.61999241011479 " "
y[1] (numeric) = -4.619992410114834 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 9.6123363509817670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.044000000000054 " "
y[1] (analytic) = -4.61920197743402 " "
y[1] (numeric) = -4.619201977434060 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 8.4603034588486380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.045000000000055 " "
y[1] (analytic) = -4.618411499389424 " "
y[1] (numeric) = -4.618411499389467 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 9.2310016444490140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.046000000000056 " "
y[1] (analytic) = -4.617620975983069 " "
y[1] (numeric) = -4.6176209759831135 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 9.6172728805555150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.047000000000057 " "
y[1] (analytic) = -4.616830407217012 " "
y[1] (numeric) = -4.6168304072170585 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 1.0003676494637935000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.04800000000006 " "
y[1] (analytic) = -4.616039793093310 " "
y[1] (numeric) = -4.616039793093358 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 1.019780122228142000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.04900000000006 " "
y[1] (analytic) = -4.615249133614025 " "
y[1] (numeric) = -4.6152491336140695 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 9.6222153342849630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.05000000000006 " "
y[1] (analytic) = -4.614458428781202 " "
y[1] (numeric) = -4.6144584287812505 " "
absolute error = 4.88498130835068900000000000000E-14 " "
relative error = 1.0586250550838616000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.051000000000062 " "
y[1] (analytic) = -4.613667678596908 " "
y[1] (numeric) = -4.613667678596958 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 1.078057523170658000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.052000000000064 " "
y[1] (analytic) = -4.612876883063194 " "
y[1] (numeric) = -4.612876883063247 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.1552596467005567000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.053000000000065 " "
y[1] (analytic) = -4.612086042182120 " "
y[1] (numeric) = -4.6120860421821765 " "
absolute error = 5.59552404411078900000000000000E-14 " "
relative error = 1.2132306277320389000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.054000000000066 " "
y[1] (analytic) = -4.611295155955752 " "
y[1] (numeric) = -4.611295155955801 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 1.0786121864042371000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.055000000000067 " "
y[1] (analytic) = -4.610504224386123 " "
y[1] (numeric) = -4.610504224386177 " "
absolute error = 5.41788836017076400000000000000E-14 " "
relative error = 1.1751184027799351000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.05600000000007 " "
y[1] (analytic) = -4.609713247475305 " "
y[1] (numeric) = -4.60971324747536 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 1.1945875820273083000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.05700000000007 " "
y[1] (analytic) = -4.608922225225350 " "
y[1] (numeric) = -4.608922225225407 " "
absolute error = 5.77315972805081400000000000000E-14 " "
relative error = 1.2526051527737680000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.05800000000007 " "
y[1] (analytic) = -4.6081311576383115 " "
y[1] (numeric) = -4.608131157638373 " "
absolute error = 6.12843109593086400000000000000E-14 " "
relative error = 1.3299168114545840000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.059000000000072 " "
y[1] (analytic) = -4.60734004471626 " "
y[1] (numeric) = -4.607340044716312 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.137370505621852000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.060000000000073 " "
y[1] (analytic) = -4.606548886461223 " "
y[1] (numeric) = -4.606548886461281 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 1.2725312841570713000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.061000000000075 " "
y[1] (analytic) = -4.6057576828752715 " "
y[1] (numeric) = -4.605757682875335 " "
absolute error = 6.30606677987088900000000000000E-14 " "
relative error = 1.3691703328895394000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.062000000000076 " "
y[1] (analytic) = -4.604966433960463 " "
y[1] (numeric) = -4.604966433960527 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 1.3886929934342723000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.063000000000077 " "
y[1] (analytic) = -4.604175139718848 " "
y[1] (numeric) = -4.6041751397189135 " "
absolute error = 6.57252030578092700000000000000E-14 " "
relative error = 1.4275130954688825000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.064000000000078 " "
y[1] (analytic) = -4.603383800152490 " "
y[1] (numeric) = -4.603383800152548 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 1.2734062212728486000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.06500000000008 " "
y[1] (analytic) = -4.60259241526342 " "
y[1] (numeric) = -4.6025924152634845 " "
absolute error = 6.48370246381091400000000000000E-14 " "
relative error = 1.408706632876992000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.06600000000008 " "
y[1] (analytic) = -4.6018009850537105 " "
y[1] (numeric) = -4.601800985053778 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 1.4668509159011722000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.067000000000082 " "
y[1] (analytic) = -4.6010095095254115 " "
y[1] (numeric) = -4.601009509525482 " "
absolute error = 7.01660951563098900000000000000E-14 " "
relative error = 1.5250152170093526000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.068000000000083 " "
y[1] (analytic) = -4.600217988680576 " "
y[1] (numeric) = -4.600217988680650 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 1.583199548252264000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.069000000000084 " "
y[1] (analytic) = -4.599426422521269 " "
y[1] (numeric) = -4.599426422521334 " "
absolute error = 6.48370246381091400000000000000E-14 " "
relative error = 1.4096763092161263000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.070000000000086 " "
y[1] (analytic) = -4.598634811049521 " "
y[1] (numeric) = -4.598634811049589 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 1.4678608472022592000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.071000000000087 " "
y[1] (analytic) = -4.597843154267398 " "
y[1] (numeric) = -4.597843154267468 " "
absolute error = 7.01660951563098900000000000000E-14 " "
relative error = 1.5260654355115746000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.072000000000088 " "
y[1] (analytic) = -4.597051452176952 " "
y[1] (numeric) = -4.597051452177024 " "
absolute error = 7.19424519957101400000000000000E-14 " "
relative error = 1.5649694754154100000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.07300000000009 " "
y[1] (analytic) = -4.596259704780238 " "
y[1] (numeric) = -4.59625970478031 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 1.584562994551078000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.07400000000009 " "
y[1] (analytic) = -4.595467912079311 " "
y[1] (numeric) = -4.595467912079378 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 1.4688724018674976000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.07500000000009 " "
y[1] (analytic) = -4.594676074076208 " "
y[1] (numeric) = -4.594676074076280 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 1.5851091402575834000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.076000000000093 " "
y[1] (analytic) = -4.593884190772997 " "
y[1] (numeric) = -4.59388419077307 " "
absolute error = 7.3718808835110390000000000000E-14 " "
relative error = 1.6047163092003414000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.077000000000094 " "
y[1] (analytic) = -4.593092262171723 " "
y[1] (numeric) = -4.5930922621717984 " "
absolute error = 7.54951656745106400000000000000E-14 " "
relative error = 1.643667519946894000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.078000000000095 " "
y[1] (analytic) = -4.592300288274440 " "
y[1] (numeric) = -4.592300288274517 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 1.6632915815466384000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.079000000000097 " "
y[1] (analytic) = -4.5915082690832065 " "
y[1] (numeric) = -4.591508269083278 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 1.5475148777244288000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.080000000000098 " "
y[1] (analytic) = -4.590716204600053 " "
y[1] (numeric) = -4.590716204600132 " "
absolute error = 7.90478793533111500000000000000E-14 " "
relative error = 1.7219073414754432000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.0810000000001 " "
y[1] (analytic) = -4.589924094827051 " "
y[1] (numeric) = -4.589924094827132 " "
absolute error = 8.0824236192711400000000000000E-14 " "
relative error = 1.7609057257352503000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.0820000000001 " "
y[1] (analytic) = -4.589131939766247 " "
y[1] (numeric) = -4.589131939766327 " "
absolute error = 7.99360577730112700000000000000E-14 " "
relative error = 1.74185573267878000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.0830000000001 " "
y[1] (analytic) = -4.588339739419688 " "
y[1] (numeric) = -4.588339739419770 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 1.7808710612773007000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.084000000000103 " "
y[1] (analytic) = -4.587547493789433 " "
y[1] (numeric) = -4.5875474937895095 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 1.6650147861709907000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.085000000000104 " "
y[1] (analytic) = -4.586755202877516 " "
y[1] (numeric) = -4.5867552028775975 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 1.7814862794759348000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.086000000000105 " "
y[1] (analytic) = -4.585962866686 " "
y[1] (numeric) = -4.585962866686084 " "
absolute error = 8.4376949871511900000000000000E-14 " "
relative error = 1.83989605507831030000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.087000000000106 " "
y[1] (analytic) = -4.585170485216931 " "
y[1] (numeric) = -4.585170485217020 " "
absolute error = 8.7929663550312400000000000000E-14 " "
relative error = 1.917696710161744800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.088000000000108 " "
y[1] (analytic) = -4.584378058472364 " "
y[1] (numeric) = -4.584378058472453 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 1.937402213281009000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.08900000000011 " "
y[1] (analytic) = -4.583585586454351 " "
y[1] (numeric) = -4.583585586454435 " "
absolute error = 8.34887714518117700000000000000E-14 " "
relative error = 1.821472946824471000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.09000000000011 " "
y[1] (analytic) = -4.582793069164929 " "
y[1] (numeric) = -4.582793069165015 " "
absolute error = 8.61533067109121500000000000000E-14 " "
relative error = 1.879930108356625000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.09100000000011 " "
y[1] (analytic) = -4.582000506606153 " "
y[1] (numeric) = -4.582000506606242 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 1.9384075109105367000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.092000000000112 " "
y[1] (analytic) = -4.581207898780075 " "
y[1] (numeric) = -4.581207898780166 " "
absolute error = 9.05941988094127700000000000000E-14 " "
relative error = 1.977517737920975000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.093000000000114 " "
y[1] (analytic) = -4.580415245688740 " "
y[1] (numeric) = -4.580415245688835 " "
absolute error = 9.41469124882132700000000000000E-14 " "
relative error = 2.0554230880448643000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.094000000000115 " "
y[1] (analytic) = -4.5796225473342105 " "
y[1] (numeric) = -4.579622547334298 " "
absolute error = 8.7929663550312400000000000000E-14 " "
relative error = 1.9200198846408442000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.095000000000116 " "
y[1] (analytic) = -4.578829803718513 " "
y[1] (numeric) = -4.578829803718605 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 2.0173397922280922000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.096000000000117 " "
y[1] (analytic) = -4.578037014843709 " "
y[1] (numeric) = -4.578037014843804 " "
absolute error = 9.5035090907913400000000000000E-14 " "
relative error = 2.0758917107872674000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.09700000000012 " "
y[1] (analytic) = -4.577244180711848 " "
y[1] (numeric) = -4.577244180711942 " "
absolute error = 9.41469124882132700000000000000E-14 " "
relative error = 2.056847062801260800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.09800000000012 " "
y[1] (analytic) = -4.576451301324973 " "
y[1] (numeric) = -4.5764513013250685 " "
absolute error = 9.59232693276135300000000000000E-14 " "
relative error = 2.0960185744758578000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.09900000000012 " "
y[1] (analytic) = -4.575658376685140 " "
y[1] (numeric) = -4.575658376685231 " "
absolute error = 9.05941988094127700000000000000E-14 " "
relative error = 1.979916142145301800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.100000000000122 " "
y[1] (analytic) = -4.57486540679438 " "
y[1] (numeric) = -4.574865406794477 " "
absolute error = 9.68114477473136500000000000000E-14 " "
relative error = 2.1161594744084433000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.101000000000123 " "
y[1] (analytic) = -4.574072391654756 " "
y[1] (numeric) = -4.5740723916548545 " "
absolute error = 9.8587804586713900000000000000E-14 " "
relative error = 2.1553617027702512000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.102000000000125 " "
y[1] (analytic) = -4.57327933126831 " "
y[1] (numeric) = -4.57327933126841 " "
absolute error = 1.00364161426114150000000000000E-13 " "
relative error = 2.1945775483230780000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.103000000000126 " "
y[1] (analytic) = -4.572486225637089 " "
y[1] (numeric) = -4.572486225637192 " "
absolute error = 1.03028696685214530000000000000E-13 " "
relative error = 2.253231428179085000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.104000000000127 " "
y[1] (analytic) = -4.57169307476315 " "
y[1] (numeric) = -4.571693074763246 " "
absolute error = 9.59232693276135300000000000000E-14 " "
relative error = 2.0982001144637888000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.10500000000013 " "
y[1] (analytic) = -4.570899878648518 " "
y[1] (numeric) = -4.5708998786486195 " "
absolute error = 1.01252339845814280000000000000E-13 " "
relative error = 2.2151511197780085000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.10600000000013 " "
y[1] (analytic) = -4.5701066372952575 " "
y[1] (numeric) = -4.57010663729536 " "
absolute error = 1.0214051826551440000000000000E-13 " "
relative error = 2.234970130280474000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.10700000000013 " "
y[1] (analytic) = -4.569313350705407 " "
y[1] (numeric) = -4.569313350705512 " "
absolute error = 1.04805053524614780000000000000E-13 " "
relative error = 2.2936718382081422000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.108000000000132 " "
y[1] (analytic) = -4.568520018881017 " "
y[1] (numeric) = -4.568520018881124 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 2.332952683221915200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.109000000000133 " "
y[1] (analytic) = -4.567726641824137 " "
y[1] (numeric) = -4.56772664182424 " "
absolute error = 1.03028696685214530000000000000E-13 " "
relative error = 2.255579301568485800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.110000000000134 " "
y[1] (analytic) = -4.5669332195368035 " "
y[1] (numeric) = -4.5669332195369075 " "
absolute error = 1.03916875104914650000000000000E-13 " "
relative error = 2.2754191951038494000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.111000000000136 " "
y[1] (analytic) = -4.566139752021062 " "
y[1] (numeric) = -4.566139752021171 " "
absolute error = 1.0924594562311540000000000000E-13 " "
relative error = 2.3925230403813424000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.112000000000137 " "
y[1] (analytic) = -4.565346239278966 " "
y[1] (numeric) = -4.565346239279077 " "
absolute error = 1.11022302462515650000000000000E-13 " "
relative error = 2.4318484654528655000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.113000000000138 " "
y[1] (analytic) = -4.564552681312560 " "
y[1] (numeric) = -4.564552681312671 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 2.451729417876613900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.11400000000014 " "
y[1] (analytic) = -4.563759078123890 " "
y[1] (numeric) = -4.563759078123997 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 2.3353864334098337000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.11500000000014 " "
y[1] (analytic) = -4.562965429714989 " "
y[1] (numeric) = -4.562965429715101 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 2.452582264889214800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.11600000000014 " "
y[1] (analytic) = -4.562171736087912 " "
y[1] (numeric) = -4.562171736088026 " "
absolute error = 1.14575016141316150000000000000E-13 " "
relative error = 2.511413922343153000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.117000000000143 " "
y[1] (analytic) = -4.561377997244705 " "
y[1] (numeric) = -4.5613779972448185 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 2.4923792281693916000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.118000000000144 " "
y[1] (analytic) = -4.560584213187404 " "
y[1] (numeric) = -4.560584213187522 " "
absolute error = 1.18127729820116660000000000000E-13 " "
relative error = 2.590188543795289000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.119000000000145 " "
y[1] (analytic) = -4.55979038391807 " "
y[1] (numeric) = -4.559790383918181 " "
absolute error = 1.11022302462515650000000000000E-13 " "
relative error = 2.434811539891841000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.120000000000147 " "
y[1] (analytic) = -4.558996509438725 " "
y[1] (numeric) = -4.55899650943884 " "
absolute error = 1.15463194561016280000000000000E-13 " "
relative error = 2.5326449432888776000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.121000000000148 " "
y[1] (analytic) = -4.558202589751424 " "
y[1] (numeric) = -4.558202589751542 " "
absolute error = 1.18127729820116660000000000000E-13 " "
relative error = 2.5915418960472010000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.12200000000015 " "
y[1] (analytic) = -4.557408624858212 " "
y[1] (numeric) = -4.557408624858332 " "
absolute error = 1.1990408665951690000000000000E-13 " "
relative error = 2.630970723263756000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.12300000000015 " "
y[1] (analytic) = -4.556614614761130 " "
y[1] (numeric) = -4.556614614761251 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 2.650921249471287000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.12400000000015 " "
y[1] (analytic) = -4.55582055946223 " "
y[1] (numeric) = -4.555820559462345 " "
absolute error = 1.14575016141316150000000000000E-13 " "
relative error = 2.5149150333269626000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.125000000000153 " "
y[1] (analytic) = -4.555026458963535 " "
y[1] (numeric) = -4.555026458963655 " "
absolute error = 1.1990408665951690000000000000E-13 " "
relative error = 2.632346655716249000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.126000000000154 " "
y[1] (analytic) = -4.554232313267104 " "
y[1] (numeric) = -4.554232313267226 " "
absolute error = 1.22568621918617280000000000000E-13 " "
relative error = 2.691312464705809000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.127000000000155 " "
y[1] (analytic) = -4.553438122374974 " "
y[1] (numeric) = -4.553438122375100 " "
absolute error = 1.25233157177717660000000000000E-13 " "
relative error = 2.7502988689434255000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.128000000000156 " "
y[1] (analytic) = -4.552643886289190 " "
y[1] (numeric) = -4.552643886289317 " "
absolute error = 1.27897692436818030000000000000E-13 " "
relative error = 2.809305880962854000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.129000000000158 " "
y[1] (analytic) = -4.551849605011803 " "
y[1] (numeric) = -4.551849605011923 " "
absolute error = 1.1990408665951690000000000000E-13 " "
relative error = 2.6341838387519834000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.13000000000016 " "
y[1] (analytic) = -4.551055278544833 " "
y[1] (numeric) = -4.5510552785449585 " "
absolute error = 1.25233157177717660000000000000E-13 " "
relative error = 2.7517388718196373000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.13100000000016 " "
y[1] (analytic) = -4.55026090689034 " "
y[1] (numeric) = -4.550260906890466 " "
absolute error = 1.25233157177717660000000000000E-13 " "
relative error = 2.75221926259394000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.13200000000016 " "
y[1] (analytic) = -4.5494664900503565 " "
y[1] (numeric) = -4.549466490050486 " "
absolute error = 1.29674049276218280000000000000E-13 " "
relative error = 2.8503133182718080000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.133000000000163 " "
y[1] (analytic) = -4.548672028026932 " "
y[1] (numeric) = -4.548672028027062 " "
absolute error = 1.3056222769591840000000000000E-13 " "
relative error = 2.8703372520914006000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.134000000000164 " "
y[1] (analytic) = -4.547877520822109 " "
y[1] (numeric) = -4.547877520822235 " "
absolute error = 1.26121335597417780000000000000E-13 " "
relative error = 2.7731911209125776000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.135000000000165 " "
y[1] (analytic) = -4.547082968437916 " "
y[1] (numeric) = -4.547082968438046 " "
absolute error = 1.29674049276218280000000000000E-13 " "
relative error = 2.8518074153541545000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.136000000000166 " "
y[1] (analytic) = -4.546288370876404 " "
y[1] (numeric) = -4.546288370876535 " "
absolute error = 1.31450406115618530000000000000E-13 " "
relative error = 2.8913785354596494000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.137000000000167 " "
y[1] (analytic) = -4.545493728139611 " "
y[1] (numeric) = -4.5454937281397445 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 2.9309635195458980000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.13800000000017 " "
y[1] (analytic) = -4.544699040229581 " "
y[1] (numeric) = -4.544699040229714 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 2.931476029010904000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.13900000000017 " "
y[1] (analytic) = -4.543904307148356 " "
y[1] (numeric) = -4.543904307148486 " "
absolute error = 1.29674049276218280000000000000E-13 " "
relative error = 2.853802380305816000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.14000000000017 " "
y[1] (analytic) = -4.543109528897965 " "
y[1] (numeric) = -4.543109528898098 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 2.9325016733051557000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.141000000000172 " "
y[1] (analytic) = -4.542314705480454 " "
y[1] (numeric) = -4.542314705480592 " "
absolute error = 1.38555833473219540000000000000E-13 " "
relative error = 3.050335400716452400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.142000000000174 " "
y[1] (analytic) = -4.541519836897870 " "
y[1] (numeric) = -4.541519836898009 " "
absolute error = 1.39444011892919660000000000000E-13 " "
relative error = 3.0704261326791493000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.143000000000175 " "
y[1] (analytic) = -4.540724923152247 " "
y[1] (numeric) = -4.5407249231523865 " "
absolute error = 1.39444011892919660000000000000E-13 " "
relative error = 3.070963651242615000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.144000000000176 " "
y[1] (analytic) = -4.53992996424563 " "
y[1] (numeric) = -4.539929964245765 " "
absolute error = 1.35003119794419040000000000000E-13 " "
relative error = 2.9736828730319764000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.145000000000177 " "
y[1] (analytic) = -4.539134960180043 " "
y[1] (numeric) = -4.539134960180184 " "
absolute error = 1.4122036873231990000000000000E-13 " "
relative error = 3.111173604027814000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.14600000000018 " "
y[1] (analytic) = -4.538339910957543 " "
y[1] (numeric) = -4.538339910957682 " "
absolute error = 1.39444011892919660000000000000E-13 " "
relative error = 3.0725775201685680000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.14700000000018 " "
y[1] (analytic) = -4.537544816580159 " "
y[1] (numeric) = -4.5375448165803 " "
absolute error = 1.4122036873231990000000000000E-13 " "
relative error = 3.112263888089912000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.14800000000018 " "
y[1] (analytic) = -4.536749677049930 " "
y[1] (numeric) = -4.536749677050075 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 3.2106964500968094000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.149000000000182 " "
y[1] (analytic) = -4.535954492368909 " "
y[1] (numeric) = -4.535954492369046 " "
absolute error = 1.3766765505351940000000000000E-13 " "
relative error = 3.035031662798325000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.150000000000183 " "
y[1] (analytic) = -4.535159262539107 " "
y[1] (numeric) = -4.535159262539253 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 3.2118223947281827000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.151000000000185 " "
y[1] (analytic) = -4.534363987562585 " "
y[1] (numeric) = -4.534363987562732 " "
absolute error = 1.46549439250520660000000000000E-13 " "
relative error = 3.2319734289636780000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.152000000000186 " "
y[1] (analytic) = -4.533568667441376 " "
y[1] (numeric) = -4.533568667441522 " "
absolute error = 1.46549439250520660000000000000E-13 " "
relative error = 3.2325404113318357000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.153000000000187 " "
y[1] (analytic) = -4.532773302177514 " "
y[1] (numeric) = -4.532773302177662 " "
absolute error = 1.48325796089920900000000000000E-13 " "
relative error = 3.272296808196125700000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.154000000000188 " "
y[1] (analytic) = -4.531977891773042 " "
y[1] (numeric) = -4.531977891773189 " "
absolute error = 1.46549439250520660000000000000E-13 " "
relative error = 3.2336750696986793000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.15500000000019 " "
y[1] (analytic) = -4.53118243622999 " "
y[1] (numeric) = -4.53118243623014 " "
absolute error = 1.50102152929321160000000000000E-13 " "
relative error = 3.3126486307227204000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.15600000000019 " "
y[1] (analytic) = -4.5303869355504 " "
y[1] (numeric) = -4.5303869355505535 " "
absolute error = 1.53654866608121670000000000000E-13 " "
relative error = 3.391649958249185000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.157000000000192 " "
y[1] (analytic) = -4.529591389736310 " "
y[1] (numeric) = -4.529591389736466 " "
absolute error = 1.55431223447521920000000000000E-13 " "
relative error = 3.431462356620435000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.158000000000193 " "
y[1] (analytic) = -4.5287957987897585 " "
y[1] (numeric) = -4.528795798789915 " "
absolute error = 1.56319401867222040000000000000E-13 " "
relative error = 3.451676975786713000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.159000000000194 " "
y[1] (analytic) = -4.528000162712786 " "
y[1] (numeric) = -4.528000162712936 " "
absolute error = 1.50102152929321160000000000000E-13 " "
relative error = 3.314976756524517000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.160000000000196 " "
y[1] (analytic) = -4.527204481507411 " "
y[1] (numeric) = -4.527204481507567 " "
absolute error = 1.56319401867222040000000000000E-13 " "
relative error = 3.452890243985020600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.161000000000197 " "
y[1] (analytic) = -4.526408755175687 " "
y[1] (numeric) = -4.5264087551758445 " "
absolute error = 1.57207580286922170000000000000E-13 " "
relative error = 3.4731193930986537000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.162000000000198 " "
y[1] (analytic) = -4.525612983719643 " "
y[1] (numeric) = -4.525612983719804 " "
absolute error = 1.60760293965722670000000000000E-13 " "
relative error = 3.5522324720217746000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.1630000000002 " "
y[1] (analytic) = -4.524817167141322 " "
y[1] (numeric) = -4.5248171671414825 " "
absolute error = 1.60760293965722670000000000000E-13 " "
relative error = 3.5528572321804425000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.1640000000002 " "
y[1] (analytic) = -4.5240213054427585 " "
y[1] (numeric) = -4.524021305442916 " "
absolute error = 1.57207580286922170000000000000E-13 " "
relative error = 3.474952253160013000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.1650000000002 " "
y[1] (analytic) = -4.5232253986259785 " "
y[1] (numeric) = -4.523225398626140 " "
absolute error = 1.60760293965722670000000000000E-13 " "
relative error = 3.554107518377414000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.166000000000203 " "
y[1] (analytic) = -4.522429446693025 " "
y[1] (numeric) = -4.522429446693188 " "
absolute error = 1.63424829224823040000000000000E-13 " "
relative error = 3.613651271980055000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.167000000000204 " "
y[1] (analytic) = -4.5216334496459325 " "
y[1] (numeric) = -4.521633449646099 " "
absolute error = 1.66089364483923420000000000000E-13 " "
relative error = 3.6732160254372030000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.168000000000205 " "
y[1] (analytic) = -4.5208374074867415 " "
y[1] (numeric) = -4.520837407486906 " "
absolute error = 1.64313007644523170000000000000E-13 " "
relative error = 3.63457016552757000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.169000000000207 " "
y[1] (analytic) = -4.520041320217484 " "
y[1] (numeric) = -4.520041320217644 " "
absolute error = 1.60760293965722670000000000000E-13 " "
relative error = 3.5566111585455070000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.170000000000208 " "
y[1] (analytic) = -4.519245187840184 " "
y[1] (numeric) = -4.519245187840350 " "
absolute error = 1.6520118606422330000000000000E-13 " "
relative error = 3.655503943639213400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.17100000000021 " "
y[1] (analytic) = -4.518449010356889 " "
y[1] (numeric) = -4.518449010357054 " "
absolute error = 1.6520118606422330000000000000E-13 " "
relative error = 3.656148065089594000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.17200000000021 " "
y[1] (analytic) = -4.517652787769627 " "
y[1] (numeric) = -4.517652787769795 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 3.7157729734736705000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.17300000000021 " "
y[1] (analytic) = -4.5168565200804345 " "
y[1] (numeric) = -4.516856520080606 " "
absolute error = 1.71418435002124170000000000000E-13 " "
relative error = 3.795082580995325000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.174000000000213 " "
y[1] (analytic) = -4.516060207291353 " "
y[1] (numeric) = -4.51606020729152 " "
absolute error = 1.66977542903623540000000000000E-13 " "
relative error = 3.6974162265160204000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.175000000000214 " "
y[1] (analytic) = -4.515263849404402 " "
y[1] (numeric) = -4.515263849404572 " "
absolute error = 1.69642078162723920000000000000E-13 " "
relative error = 3.7570800693098144000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.176000000000215 " "
y[1] (analytic) = -4.514467446421623 " "
y[1] (numeric) = -4.514467446421794 " "
absolute error = 1.71418435002124170000000000000E-13 " "
relative error = 3.797090953396915000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.177000000000216 " "
y[1] (analytic) = -4.513670998345049 " "
y[1] (numeric) = -4.513670998345222 " "
absolute error = 1.73194791841524420000000000000E-13 " "
relative error = 3.837115995052072000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.178000000000218 " "
y[1] (analytic) = -4.512874505176711 " "
y[1] (numeric) = -4.512874505176888 " "
absolute error = 1.76747505520324920000000000000E-13 " "
relative error = 3.9165171847251260000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.17900000000022 " "
y[1] (analytic) = -4.512077966918653 " "
y[1] (numeric) = -4.512077966918826 " "
absolute error = 1.7230661342182430000000000000E-13 " "
relative error = 3.8187862595710936000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.18000000000022 " "
y[1] (analytic) = -4.511281383572893 " "
y[1] (numeric) = -4.511281383573068 " "
absolute error = 1.74971148680924670000000000000E-13 " "
relative error = 3.8785243881717074000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.18100000000022 " "
y[1] (analytic) = -4.510484755141470 " "
y[1] (numeric) = -4.510484755141647 " "
absolute error = 1.77635683940025050000000000000E-13 " "
relative error = 3.938283656485911400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.182000000000222 " "
y[1] (analytic) = -4.509688081626418 " "
y[1] (numeric) = -4.509688081626596 " "
absolute error = 1.77635683940025050000000000000E-13 " "
relative error = 3.938979386706513700000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.183000000000224 " "
y[1] (analytic) = -4.508891363029765 " "
y[1] (numeric) = -4.508891363029948 " "
absolute error = 1.8296475445822580000000000000E-13 " "
relative error = 4.05786566423907000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.184000000000225 " "
y[1] (analytic) = -4.508094599353559 " "
y[1] (numeric) = -4.508094599353734 " "
absolute error = 1.74971148680924670000000000000E-13 " "
relative error = 3.881266127512381000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.185000000000226 " "
y[1] (analytic) = -4.507297790599804 " "
y[1] (numeric) = -4.507297790599986 " "
absolute error = 1.82076576038525670000000000000E-13 " "
relative error = 4.0395949967684747000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.186000000000227 " "
y[1] (analytic) = -4.5065009367705535 " "
y[1] (numeric) = -4.5065009367707365 " "
absolute error = 1.8296475445822580000000000000E-13 " "
relative error = 4.06001811661315050000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.18700000000023 " "
y[1] (analytic) = -4.505704037867833 " "
y[1] (numeric) = -4.505704037868018 " "
absolute error = 1.84741111297626050000000000000E-13 " "
relative error = 4.100160812716148000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.18800000000023 " "
y[1] (analytic) = -4.504907093893674 " "
y[1] (numeric) = -4.504907093893861 " "
absolute error = 1.8651746813702630000000000000E-13 " "
relative error = 4.140317752387115400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.18900000000023 " "
y[1] (analytic) = -4.504110104850117 " "
y[1] (numeric) = -4.504110104850297 " "
absolute error = 1.80300219199125420000000000000E-13 " "
relative error = 4.00301535712847050000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.190000000000232 " "
y[1] (analytic) = -4.503313070739175 " "
y[1] (numeric) = -4.503313070739358 " "
absolute error = 1.8296475445822580000000000000E-13 " "
relative error = 4.062892177029875400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.191000000000233 " "
y[1] (analytic) = -4.502515991562888 " "
y[1] (numeric) = -4.502515991563073 " "
absolute error = 1.85629289717326170000000000000E-13 " "
relative error = 4.122790236951309000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.192000000000235 " "
y[1] (analytic) = -4.501718867323284 " "
y[1] (numeric) = -4.501718867323475 " "
absolute error = 1.90958360235526920000000000000E-13 " "
relative error = 4.241898836056604600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.193000000000236 " "
y[1] (analytic) = -4.5009216980224025 " "
y[1] (numeric) = -4.500921698022593 " "
absolute error = 1.9007018181582680000000000000E-13 " "
relative error = 4.2229168727671734000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.194000000000237 " "
y[1] (analytic) = -4.5001244836622725 " "
y[1] (numeric) = -4.500124483662458 " "
absolute error = 1.85629289717326170000000000000E-13 " "
relative error = 4.124981217547522600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.19500000000024 " "
y[1] (analytic) = -4.499327224244912 " "
y[1] (numeric) = -4.499327224245100 " "
absolute error = 1.89182003396126670000000000000E-13 " "
relative error = 4.2046731426135750000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.19600000000024 " "
y[1] (analytic) = -4.498529919772360 " "
y[1] (numeric) = -4.498529919772551 " "
absolute error = 1.91846538655227050000000000000E-13 " "
relative error = 4.264649609464754600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.19700000000024 " "
y[1] (analytic) = -4.497732570246644 " "
y[1] (numeric) = -4.497732570246838 " "
absolute error = 1.94511073914327430000000000000E-13 " "
relative error = 4.32464738346283960000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.198000000000242 " "
y[1] (analytic) = -4.4969351756697975 " "
y[1] (numeric) = -4.496935175669993 " "
absolute error = 1.95399252334027550000000000000E-13 " "
relative error = 4.345164977943533000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.199000000000243 " "
y[1] (analytic) = -4.496137736043853 " "
y[1] (numeric) = -4.4961377360440435 " "
absolute error = 1.90958360235526920000000000000E-13 " "
relative error = 4.247164376319818600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.200000000000244 " "
y[1] (analytic) = -4.495340251370827 " "
y[1] (numeric) = -4.49534025137102 " "
absolute error = 1.92734717074927180000000000000E-13 " "
relative error = 4.287433348702668000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.201000000000246 " "
y[1] (analytic) = -4.494542721652753 " "
y[1] (numeric) = -4.494542721652950 " "
absolute error = 1.98063787593127930000000000000E-13 " "
relative error = 4.406761707680355000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.202000000000247 " "
y[1] (analytic) = -4.493745146891670 " "
y[1] (numeric) = -4.493745146891866 " "
absolute error = 1.9717560917342780000000000000E-13 " "
relative error = 4.3877790735376815000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.203000000000248 " "
y[1] (analytic) = -4.492947527089594 " "
y[1] (numeric) = -4.492947527089794 " "
absolute error = 1.99840144432528180000000000000E-13 " "
relative error = 4.447862861242428700000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.20400000000025 " "
y[1] (analytic) = -4.492149862248570 " "
y[1] (numeric) = -4.4921498622487634 " "
absolute error = 1.92734717074927180000000000000E-13 " "
relative error = 4.290478345227172000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.20500000000025 " "
y[1] (analytic) = -4.491352152370602 " "
y[1] (numeric) = -4.491352152370802 " "
absolute error = 1.99840144432528180000000000000E-13 " "
relative error = 4.449442788115592400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.20600000000025 " "
y[1] (analytic) = -4.490554397457739 " "
y[1] (numeric) = -4.490554397457939 " "
absolute error = 1.99840144432528180000000000000E-13 " "
relative error = 4.4502332394785090000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.207000000000253 " "
y[1] (analytic) = -4.489756597512002 " "
y[1] (numeric) = -4.489756597512202 " "
absolute error = 1.99840144432528180000000000000E-13 " "
relative error = 4.451024016385866600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.208000000000254 " "
y[1] (analytic) = -4.488958752535414 " "
y[1] (numeric) = -4.488958752535619 " "
absolute error = 2.05169214950728930000000000000E-13 " "
relative error = 4.5705301888739136000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.209000000000255 " "
y[1] (analytic) = -4.48816086253002 " "
y[1] (numeric) = -4.488160862530218 " "
absolute error = 1.98063787593127930000000000000E-13 " "
relative error = 4.4130278227478115000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.210000000000257 " "
y[1] (analytic) = -4.4873629274978235 " "
y[1] (numeric) = -4.487362927498025 " "
absolute error = 2.01616501271928430000000000000E-13 " "
relative error = 4.492984065016351000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.211000000000258 " "
y[1] (analytic) = -4.486564947440861 " "
y[1] (numeric) = -4.486564947441070 " "
absolute error = 2.0783375020982930000000000000E-13 " "
relative error = 4.632357998704058600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.21200000000026 " "
y[1] (analytic) = -4.485766922361169 " "
y[1] (numeric) = -4.4857669223613765 " "
absolute error = 2.0783375020982930000000000000E-13 " "
relative error = 4.6331821025697000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.21300000000026 " "
y[1] (analytic) = -4.484968852260764 " "
y[1] (numeric) = -4.484968852260974 " "
absolute error = 2.10498285468929680000000000000E-13 " "
relative error = 4.6934168865592596000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.21400000000026 " "
y[1] (analytic) = -4.484170737141685 " "
y[1] (numeric) = -4.484170737141889 " "
absolute error = 2.03392858111328680000000000000E-13 " "
relative error = 4.535796472392486000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.215000000000263 " "
y[1] (analytic) = -4.483372577005937 " "
y[1] (numeric) = -4.483372577006147 " "
absolute error = 2.09610107049229550000000000000E-13 " "
relative error = 4.675277449040612400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.216000000000264 " "
y[1] (analytic) = -4.482574371855566 " "
y[1] (numeric) = -4.482574371855776 " "
absolute error = 2.09610107049229550000000000000E-13 " "
relative error = 4.6761099685326857000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.217000000000265 " "
y[1] (analytic) = -4.48177612169259 " "
y[1] (numeric) = -4.481776121692802 " "
absolute error = 2.1138646388862980000000000000E-13 " "
relative error = 4.7165779402831365000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.218000000000266 " "
y[1] (analytic) = -4.480977826519034 " "
y[1] (numeric) = -4.48097782651925 " "
absolute error = 2.15827355987130430000000000000E-13 " "
relative error = 4.816523632628461600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.219000000000268 " "
y[1] (analytic) = -4.480179486336937 " "
y[1] (numeric) = -4.480179486337146 " "
absolute error = 2.09610107049229550000000000000E-13 " "
relative error = 4.678609588934348000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.22000000000027 " "
y[1] (analytic) = -4.479381101148302 " "
y[1] (numeric) = -4.479381101148516 " "
absolute error = 2.14050999147730180000000000000E-13 " "
relative error = 4.778584235506499000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.22100000000027 " "
y[1] (analytic) = -4.47858267095517 " "
y[1] (numeric) = -4.478582670955386 " "
absolute error = 2.15827355987130430000000000000E-13 " "
relative error = 4.8190995197393516000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.22200000000027 " "
y[1] (analytic) = -4.477784195759565 " "
y[1] (numeric) = -4.477784195759780 " "
absolute error = 2.15827355987130430000000000000E-13 " "
relative error = 4.819958858033347400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.223000000000273 " "
y[1] (analytic) = -4.476985675563508 " "
y[1] (numeric) = -4.476985675563725 " "
absolute error = 2.16715534406830560000000000000E-13 " "
relative error = 4.84065731078206050000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.224000000000274 " "
y[1] (analytic) = -4.4761871103690325 " "
y[1] (numeric) = -4.476187110369245 " "
absolute error = 2.12274642308329930000000000000E-13 " "
relative error = 4.742309404729716000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.225000000000275 " "
y[1] (analytic) = -4.475388500178145 " "
y[1] (numeric) = -4.475388500178364 " "
absolute error = 2.19380069665930930000000000000E-13 " "
relative error = 4.901922361761406600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.226000000000276 " "
y[1] (analytic) = -4.474589844992888 " "
y[1] (numeric) = -4.474589844993107 " "
absolute error = 2.19380069665930930000000000000E-13 " "
relative error = 4.9027972901565375000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.227000000000277 " "
y[1] (analytic) = -4.47379114481528 " "
y[1] (numeric) = -4.473791144815500 " "
absolute error = 2.19380069665930930000000000000E-13 " "
relative error = 4.903672580249362500000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.22800000000028 " "
y[1] (analytic) = -4.472992399647342 " "
y[1] (numeric) = -4.4729923996475645 " "
absolute error = 2.2204460492503130000000000000E-13 " "
relative error = 4.9641176439856605000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.22900000000028 " "
y[1] (analytic) = -4.472193609491107 " "
y[1] (numeric) = -4.472193609491327 " "
absolute error = 2.19380069665930930000000000000E-13 " "
relative error = 4.905424246400063000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.23000000000028 " "
y[1] (analytic) = -4.471394774348585 " "
y[1] (numeric) = -4.471394774348810 " "
absolute error = 2.23820961764431560000000000000E-13 " "
relative error = 5.0056184492687490000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.231000000000282 " "
y[1] (analytic) = -4.4705958942218125 " "
y[1] (numeric) = -4.470595894222036 " "
absolute error = 2.23820961764431560000000000000E-13 " "
relative error = 5.006512936087945000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.232000000000284 " "
y[1] (analytic) = -4.4697969691128066 " "
y[1] (numeric) = -4.469796969113031 " "
absolute error = 2.24709140184131680000000000000E-13 " "
relative error = 5.027278458885648000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.233000000000285 " "
y[1] (analytic) = -4.468997999023589 " "
y[1] (numeric) = -4.468997999023818 " "
absolute error = 2.2915003228263230000000000000E-13 " "
relative error = 5.127548330357236000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.234000000000286 " "
y[1] (analytic) = -4.468198983956200 " "
y[1] (numeric) = -4.46819898395642 " "
absolute error = 2.20268248085631060000000000000E-13 " "
relative error = 4.92968752905903030000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.235000000000287 " "
y[1] (analytic) = -4.46739992391263 " "
y[1] (numeric) = -4.467399923912858 " "
absolute error = 2.27373675443232060000000000000E-13 " "
relative error = 5.089619897832967000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.23600000000029 " "
y[1] (analytic) = -4.466600818894928 " "
y[1] (numeric) = -4.466600818895156 " "
absolute error = 2.27373675443232060000000000000E-13 " "
relative error = 5.09053046516670900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.23700000000029 " "
y[1] (analytic) = -4.465801668905108 " "
y[1] (numeric) = -4.465801668905337 " "
absolute error = 2.2915003228263230000000000000E-13 " "
relative error = 5.131218295657398000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.23800000000029 " "
y[1] (analytic) = -4.465002473945194 " "
y[1] (numeric) = -4.4650024739454235 " "
absolute error = 2.2915003228263230000000000000E-13 " "
relative error = 5.132136737209007000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.239000000000292 " "
y[1] (analytic) = -4.464203234017209 " "
y[1] (numeric) = -4.464203234017437 " "
absolute error = 2.2826185386293218000000000000E-13 " "
relative error = 5.113159995126967000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.240000000000293 " "
y[1] (analytic) = -4.463403949123169 " "
y[1] (numeric) = -4.4634039491234 " "
absolute error = 2.30926389122032560000000000000E-13 " "
relative error = 5.173773016161753000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.241000000000295 " "
y[1] (analytic) = -4.462604619265104 " "
y[1] (numeric) = -4.462604619265334 " "
absolute error = 2.30038210702332440000000000000E-13 " "
relative error = 5.154797037345756000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.242000000000296 " "
y[1] (analytic) = -4.461805244445028 " "
y[1] (numeric) = -4.461805244445261 " "
absolute error = 2.33590924381132940000000000000E-13 " "
relative error = 5.235345596313397000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.243000000000297 " "
y[1] (analytic) = -4.461005824664966 " "
y[1] (numeric) = -4.461005824665203 " "
absolute error = 2.37143638059933440000000000000E-13 " "
relative error = 5.315923076109043000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.244000000000298 " "
y[1] (analytic) = -4.46020635992695 " "
y[1] (numeric) = -4.46020635992718 " "
absolute error = 2.30038210702332440000000000000E-13 " "
relative error = 5.1575687790844740000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.2450000000003 " "
y[1] (analytic) = -4.4594068502329804 " "
y[1] (numeric) = -4.459406850233214 " "
absolute error = 2.33590924381132940000000000000E-13 " "
relative error = 5.238161312169332000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.2460000000003 " "
y[1] (analytic) = -4.4586072955850895 " "
y[1] (numeric) = -4.458607295585326 " "
absolute error = 2.3625545964023330000000000000E-13 " "
relative error = 5.298862267465748000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.247000000000302 " "
y[1] (analytic) = -4.457807695985295 " "
y[1] (numeric) = -4.457807695985536 " "
absolute error = 2.40696351738733940000000000000E-13 " "
relative error = 5.399433267511860000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.248000000000303 " "
y[1] (analytic) = -4.457008051435622 " "
y[1] (numeric) = -4.457008051435865 " "
absolute error = 2.4336088699783430000000000000E-13 " "
relative error = 5.460185043180407000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.249000000000304 " "
y[1] (analytic) = -4.456208361938096 " "
y[1] (numeric) = -4.456208361938335 " "
absolute error = 2.3891999489933370000000000000E-13 " "
relative error = 5.361508607632128000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.250000000000306 " "
y[1] (analytic) = -4.455408627494723 " "
y[1] (numeric) = -4.455408627494963 " "
absolute error = 2.3980817331903380000000000000E-13 " "
relative error = 5.382405821076798000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.251000000000307 " "
y[1] (analytic) = -4.454608848107530 " "
y[1] (numeric) = -4.454608848107771 " "
absolute error = 2.41584530158434060000000000000E-13 " "
relative error = 5.423249007846502000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.252000000000308 " "
y[1] (analytic) = -4.453809023778533 " "
y[1] (numeric) = -4.453809023778779 " "
absolute error = 2.4602542225693470000000000000E-13 " "
relative error = 5.523932906494744000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.25300000000031 " "
y[1] (analytic) = -4.453009154509761 " "
y[1] (numeric) = -4.4530091545100055 " "
absolute error = 2.44249065417534440000000000000E-13 " "
relative error = 5.485033983596744000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.25400000000031 " "
y[1] (analytic) = -4.452209240303233 " "
y[1] (numeric) = -4.452209240303471 " "
absolute error = 2.38031816479633560000000000000E-13 " "
relative error = 5.346375330361194000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.25500000000031 " "
y[1] (analytic) = -4.451409281160952 " "
y[1] (numeric) = -4.451409281161196 " "
absolute error = 2.4336088699783430000000000000E-13 " "
relative error = 5.4670526034928980000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.256000000000313 " "
y[1] (analytic) = -4.450609277084950 " "
y[1] (numeric) = -4.450609277085197 " "
absolute error = 2.4602542225693470000000000000E-13 " "
relative error = 5.527904314666684000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.257000000000314 " "
y[1] (analytic) = -4.449809228077246 " "
y[1] (numeric) = -4.449809228077494 " "
absolute error = 2.47801779096334940000000000000E-13 " "
relative error = 5.56881804129409000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.258000000000315 " "
y[1] (analytic) = -4.449009134139857 " "
y[1] (numeric) = -4.449009134140106 " "
absolute error = 2.4957813593573520000000000000E-13 " "
relative error = 5.609746539304129000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.259000000000317 " "
y[1] (analytic) = -4.448208995274808 " "
y[1] (numeric) = -4.448208995275053 " "
absolute error = 2.45137243837234560000000000000E-13 " "
relative error = 5.510920105094795000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.260000000000318 " "
y[1] (analytic) = -4.447408811484102 " "
y[1] (numeric) = -4.447408811484351 " "
absolute error = 2.48689957516035070000000000000E-13 " "
relative error = 5.591794414623358000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.26100000000032 " "
y[1] (analytic) = -4.446608582769766 " "
y[1] (numeric) = -4.446608582770020 " "
absolute error = 2.5313084961453570000000000000E-13 " "
relative error = 5.692672177069878000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.26200000000032 " "
y[1] (analytic) = -4.445808309133824 " "
y[1] (numeric) = -4.445808309134075 " "
absolute error = 2.51354492775135440000000000000E-13 " "
relative error = 5.653741126416375000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.26300000000032 " "
y[1] (analytic) = -4.445007990578283 " "
y[1] (numeric) = -4.445007990578538 " "
absolute error = 2.54907206453935940000000000000E-13 " "
relative error = 5.7346849993125260000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.264000000000323 " "
y[1] (analytic) = -4.444207627105175 " "
y[1] (numeric) = -4.444207627105424 " "
absolute error = 2.48689957516035070000000000000E-13 " "
relative error = 5.59582221134938900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.265000000000324 " "
y[1] (analytic) = -4.443407218716498 " "
y[1] (numeric) = -4.443407218716751 " "
absolute error = 2.5313084961453570000000000000E-13 " "
relative error = 5.6967736053607510000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.266000000000325 " "
y[1] (analytic) = -4.442606765414283 " "
y[1] (numeric) = -4.442606765414537 " "
absolute error = 2.5401902803423580000000000000E-13 " "
relative error = 5.717792310851713000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.267000000000326 " "
y[1] (analytic) = -4.4418062672005405 " "
y[1] (numeric) = -4.441806267200798 " "
absolute error = 2.5757174171303630000000000000E-13 " "
relative error = 5.798806301279131000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.268000000000328 " "
y[1] (analytic) = -4.441005724077293 " "
y[1] (numeric) = -4.441005724077552 " "
absolute error = 2.59348098552436570000000000000E-13 " "
relative error = 5.839850580384498000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.26900000000033 " "
y[1] (analytic) = -4.440205136046561 " "
y[1] (numeric) = -4.440205136046816 " "
absolute error = 2.54907206453935940000000000000E-13 " "
relative error = 5.7408880590795950000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.27000000000033 " "
y[1] (analytic) = -4.439404503110346 " "
y[1] (numeric) = -4.439404503110606 " "
absolute error = 2.6023627697213670000000000000E-13 " "
relative error = 5.861963621242654000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.27100000000033 " "
y[1] (analytic) = -4.438603825270675 " "
y[1] (numeric) = -4.438603825270938 " "
absolute error = 2.62900812231237070000000000000E-13 " "
relative error = 5.923051990683238000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.272000000000332 " "
y[1] (analytic) = -4.437803102529564 " "
y[1] (numeric) = -4.437803102529829 " "
absolute error = 2.6467716907063730000000000000E-13 " "
relative error = 5.9641485427726690000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.273000000000334 " "
y[1] (analytic) = -4.43700233488903 " "
y[1] (numeric) = -4.437002334889294 " "
absolute error = 2.6378899065093720000000000000E-13 " "
relative error = 5.945207388707281000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.274000000000335 " "
y[1] (analytic) = -4.436201522351090 " "
y[1] (numeric) = -4.436201522351350 " "
absolute error = 2.58459920132736440000000000000E-13 " "
relative error = 5.826153722515254000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.275000000000336 " "
y[1] (analytic) = -4.435400664917747 " "
y[1] (numeric) = -4.435400664918012 " "
absolute error = 2.6467716907063730000000000000E-13 " "
relative error = 5.967379027651962000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.276000000000337 " "
y[1] (analytic) = -4.434599762591027 " "
y[1] (numeric) = -4.434599762591295 " "
absolute error = 2.6822988274943780000000000000E-13 " "
relative error = 6.048570268102791000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.27700000000034 " "
y[1] (analytic) = -4.433798815372949 " "
y[1] (numeric) = -4.433798815373216 " "
absolute error = 2.6734170432973770000000000000E-13 " "
relative error = 6.029630920618356000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.27800000000034 " "
y[1] (analytic) = -4.43299782326552 " "
y[1] (numeric) = -4.43299782326579 " "
absolute error = 2.70006239588838070000000000000E-13 " "
relative error = 6.090827254003497000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.27900000000034 " "
y[1] (analytic) = -4.432196786270765 " "
y[1] (numeric) = -4.432196786271030 " "
absolute error = 2.65565347490337440000000000000E-13 " "
relative error = 5.991731872396920000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.280000000000342 " "
y[1] (analytic) = -4.431395704390685 " "
y[1] (numeric) = -4.431395704390953 " "
absolute error = 2.6822988274943780000000000000E-13 " "
relative error = 6.0529436015761840000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.281000000000343 " "
y[1] (analytic) = -4.4305945776273 " "
y[1] (numeric) = -4.430594577627572 " "
absolute error = 2.7178259642823830000000000000E-13 " "
relative error = 6.134224011391831000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.282000000000345 " "
y[1] (analytic) = -4.429793405982629 " "
y[1] (numeric) = -4.429793405982902 " "
absolute error = 2.72670774847938450000000000000E-13 " "
relative error = 6.155383555352371000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.283000000000346 " "
y[1] (analytic) = -4.428992189458683 " "
y[1] (numeric) = -4.428992189458957 " "
absolute error = 2.7444713168733870000000000000E-13 " "
relative error = 6.196604553526702000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.284000000000347 " "
y[1] (analytic) = -4.428190928057482 " "
y[1] (numeric) = -4.428190928057751 " "
absolute error = 2.69118061169137950000000000000E-13 " "
relative error = 6.077381611167163000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.28500000000035 " "
y[1] (analytic) = -4.427389621781025 " "
y[1] (numeric) = -4.427389621781300 " "
absolute error = 2.7444713168733870000000000000E-13 " "
relative error = 6.1988475181214280000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.28600000000035 " "
y[1] (analytic) = -4.426588270631338 " "
y[1] (numeric) = -4.426588270631614 " "
absolute error = 2.7533531010703880000000000000E-13 " "
relative error = 6.220034330587727000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.28700000000035 " "
y[1] (analytic) = -4.425786874610430 " "
y[1] (numeric) = -4.425786874610709 " "
absolute error = 2.7799984536613920000000000000E-13 " "
relative error = 6.281365398793847000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.288000000000352 " "
y[1] (analytic) = -4.424985433720316 " "
y[1] (numeric) = -4.424985433720598 " "
absolute error = 2.8155255904493970000000000000E-13 " "
relative error = 6.362790641058083000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.289000000000353 " "
y[1] (analytic) = -4.424183947963020 " "
y[1] (numeric) = -4.424183947963293 " "
absolute error = 2.73558953267638570000000000000E-13 " "
relative error = 6.183263546118837000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.290000000000354 " "
y[1] (analytic) = -4.42338241734053 " "
y[1] (numeric) = -4.423382417340808 " "
absolute error = 2.7799984536613920000000000000E-13 " "
relative error = 6.284779816375926000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.291000000000356 " "
y[1] (analytic) = -4.422580841854877 " "
y[1] (numeric) = -4.422580841855156 " "
absolute error = 2.7888802378583930000000000000E-13 " "
relative error = 6.3060017161579050000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.292000000000357 " "
y[1] (analytic) = -4.421779221508064 " "
y[1] (numeric) = -4.421779221508350 " "
absolute error = 2.8510527272374020000000000000E-13 " "
relative error = 6.447750067143877000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.293000000000358 " "
y[1] (analytic) = -4.420977556302116 " "
y[1] (numeric) = -4.4209775563024 " "
absolute error = 2.84217094304040100000000000000E-13 " "
relative error = 6.428829160168158000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.29400000000036 " "
y[1] (analytic) = -4.420175846239044 " "
y[1] (numeric) = -4.420175846239320 " "
absolute error = 2.77111666946439100000000000000E-13 " "
relative error = 6.269245310279288000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.29500000000036 " "
y[1] (analytic) = -4.41937409132084 " "
y[1] (numeric) = -4.4193740913211235 " "
absolute error = 2.83328915884339950000000000000E-13 " "
relative error = 6.4110643278822320000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.29600000000036 " "
y[1] (analytic) = -4.418572291549534 " "
y[1] (numeric) = -4.41857229154982 " "
absolute error = 2.8599345114344030000000000000E-13 " "
relative error = 6.472530769506687000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.297000000000363 " "
y[1] (analytic) = -4.417770446927136 " "
y[1] (numeric) = -4.417770446927422 " "
absolute error = 2.8599345114344030000000000000E-13 " "
relative error = 6.473705562097924000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.298000000000364 " "
y[1] (analytic) = -4.416968557455654 " "
y[1] (numeric) = -4.416968557455942 " "
absolute error = 2.8776980798284060000000000000E-13 " "
relative error = 6.5150974981947160000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.299000000000365 " "
y[1] (analytic) = -4.416166623137109 " "
y[1] (numeric) = -4.41616662313739 " "
absolute error = 2.8155255904493970000000000000E-13 " "
relative error = 6.375496738955321000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.300000000000367 " "
y[1] (analytic) = -4.41536464397349 " "
y[1] (numeric) = -4.415364643973778 " "
absolute error = 2.8776980798284060000000000000E-13 " "
relative error = 6.517464154984712000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.301000000000368 " "
y[1] (analytic) = -4.414562619966826 " "
y[1] (numeric) = -4.414562619967116 " "
absolute error = 2.89546164822240800000000000000E-13 " "
relative error = 6.558886796908018000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.30200000000037 " "
y[1] (analytic) = -4.413760551119125 " "
y[1] (numeric) = -4.413760551119416 " "
absolute error = 2.90434343241940950000000000000E-13 " "
relative error = 6.580201618964133000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.30300000000037 " "
y[1] (analytic) = -4.412958437432394 " "
y[1] (numeric) = -4.412958437432688 " "
absolute error = 2.93987056920741450000000000000E-13 " "
relative error = 6.661904051192308000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.30400000000037 " "
y[1] (analytic) = -4.412156278908654 " "
y[1] (numeric) = -4.412156278908943 " "
absolute error = 2.8865798640254070000000000000E-13 " "
relative error = 6.542333683473701000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.305000000000373 " "
y[1] (analytic) = -4.411354075549898 " "
y[1] (numeric) = -4.41135407555019 " "
absolute error = 2.9221070008134120000000000000E-13 " "
relative error = 6.6240590774821360000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.306000000000374 " "
y[1] (analytic) = -4.4105518273581445 " "
y[1] (numeric) = -4.41055182735844 " "
absolute error = 2.9576341376014170000000000000E-13 " "
relative error = 6.705814268535636000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.307000000000375 " "
y[1] (analytic) = -4.409749534335408 " "
y[1] (numeric) = -4.409749534335703 " "
absolute error = 2.9576341376014170000000000000E-13 " "
relative error = 6.7070342988247780000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.308000000000376 " "
y[1] (analytic) = -4.408947196483691 " "
y[1] (numeric) = -4.408947196483989 " "
absolute error = 2.97539770599541950000000000000E-13 " "
relative error = 6.748544660204632000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.309000000000378 " "
y[1] (analytic) = -4.408144813805013 " "
y[1] (numeric) = -4.408144813805306 " "
absolute error = 2.93098878501041300000000000000E-13 " "
relative error = 6.649030167592087000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.31000000000038 " "
y[1] (analytic) = -4.407342386301370 " "
y[1] (numeric) = -4.407342386301665 " "
absolute error = 2.9576341376014170000000000000E-13 " "
relative error = 6.710697464290847000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.31100000000038 " "
y[1] (analytic) = -4.406539913974775 " "
y[1] (numeric) = -4.406539913975075 " "
absolute error = 2.9931612743894220000000000000E-13 " "
relative error = 6.792543203562041000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.31200000000038 " "
y[1] (analytic) = -4.4057373968272415 " "
y[1] (numeric) = -4.405737396827544 " "
absolute error = 3.0286884111774270000000000000E-13 " "
relative error = 6.874418827954917000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.313000000000383 " "
y[1] (analytic) = -4.404934834860782 " "
y[1] (numeric) = -4.404934834861082 " "
absolute error = 3.00204305858642330000000000000E-13 " "
relative error = 6.8151815432731650000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.314000000000384 " "
y[1] (analytic) = -4.404132228077401 " "
y[1] (numeric) = -4.404132228077698 " "
absolute error = 2.96651592179841800000000000000E-13 " "
relative error = 6.7357558042562080000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.315000000000385 " "
y[1] (analytic) = -4.403329576479095 " "
y[1] (numeric) = -4.403329576479399 " "
absolute error = 3.03757019537442830000000000000E-13 " "
relative error = 6.898348494284798000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.316000000000386 " "
y[1] (analytic) = -4.402526880067889 " "
y[1] (numeric) = -4.402526880068193 " "
absolute error = 3.04645197957142950000000000000E-13 " "
relative error = 6.919780531866854000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.317000000000387 " "
y[1] (analytic) = -4.401724138845783 " "
y[1] (numeric) = -4.40172413884609 " "
absolute error = 3.07309733216243330000000000000E-13 " "
relative error = 6.981576389674113000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.31800000000039 " "
y[1] (analytic) = -4.4009213528147875 " "
y[1] (numeric) = -4.4009213528150966 " "
absolute error = 3.0908609005564360000000000000E-13 " "
relative error = 7.0232132155225880000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.31900000000039 " "
y[1] (analytic) = -4.400118521976918 " "
y[1] (numeric) = -4.4001185219772205 " "
absolute error = 3.0286884111774270000000000000E-13 " "
relative error = 6.883197341276788000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.32000000000039 " "
y[1] (analytic) = -4.399315646334163 " "
y[1] (numeric) = -4.39931564633447 " "
absolute error = 3.07309733216243330000000000000E-13 " "
relative error = 6.985398591990476000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.321000000000392 " "
y[1] (analytic) = -4.398512725888544 " "
y[1] (numeric) = -4.3985127258888514 " "
absolute error = 3.07309733216243330000000000000E-13 " "
relative error = 6.986673731952513000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.322000000000394 " "
y[1] (analytic) = -4.397709760642062 " "
y[1] (numeric) = -4.397709760642373 " "
absolute error = 3.10862446895043830000000000000E-13 " "
relative error = 7.068734951022738000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.323000000000395 " "
y[1] (analytic) = -4.396906750596727 " "
y[1] (numeric) = -4.396906750597041 " "
absolute error = 3.1352698215414420000000000000E-13 " "
relative error = 7.130626141015927000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.324000000000396 " "
y[1] (analytic) = -4.396103695754558 " "
y[1] (numeric) = -4.396103695754863 " "
absolute error = 3.04645197957142950000000000000E-13 " "
relative error = 6.929891081762868000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.325000000000397 " "
y[1] (analytic) = -4.395300596117533 " "
y[1] (numeric) = -4.3953005961178455 " "
absolute error = 3.1263880373444410000000000000E-13 " "
relative error = 7.113024397252942000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.3260000000004 " "
y[1] (analytic) = -4.3944974516876805 " "
y[1] (numeric) = -4.394497451687995 " "
absolute error = 3.14415160573844330000000000000E-13 " "
relative error = 7.154746681058947000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.3270000000004 " "
y[1] (analytic) = -4.393694262467001 " "
y[1] (numeric) = -4.393694262467317 " "
absolute error = 3.1619151741324460000000000000E-13 " "
relative error = 7.196484291460628000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.3280000000004 " "
y[1] (analytic) = -4.392891028457502 " "
y[1] (numeric) = -4.392891028457819 " "
absolute error = 3.1707969583294470000000000000E-13 " "
relative error = 7.218018698366905000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.329000000000402 " "
y[1] (analytic) = -4.392087749661194 " "
y[1] (numeric) = -4.392087749661505 " "
absolute error = 3.11750625314743960000000000000E-13 " "
relative error = 7.098005392510485000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.330000000000403 " "
y[1] (analytic) = -4.391284426080066 " "
y[1] (numeric) = -4.391284426080383 " "
absolute error = 3.1707969583294470000000000000E-13 " "
relative error = 7.220659494288094000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.331000000000405 " "
y[1] (analytic) = -4.390481057716137 " "
y[1] (numeric) = -4.390481057716458 " "
absolute error = 3.2063240951174520000000000000E-13 " "
relative error = 7.302899279072017000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.332000000000406 " "
y[1] (analytic) = -4.389677644571414 " "
y[1] (numeric) = -4.3896776445717345 " "
absolute error = 3.2063240951174520000000000000E-13 " "
relative error = 7.304235879558536000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.333000000000407 " "
y[1] (analytic) = -4.388874186647897 " "
y[1] (numeric) = -4.388874186648218 " "
absolute error = 3.21520587931445330000000000000E-13 " "
relative error = 7.325810088372893000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.334000000000408 " "
y[1] (analytic) = -4.388070683947596 " "
y[1] (numeric) = -4.388070683947914 " "
absolute error = 3.17967874252644830000000000000E-13 " "
relative error = 7.246188522346103000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.33500000000041 " "
y[1] (analytic) = -4.387267136472506 " "
y[1] (numeric) = -4.387267136472827 " "
absolute error = 3.21520587931445330000000000000E-13 " "
relative error = 7.328493522962395000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.33600000000041 " "
y[1] (analytic) = -4.38646354422464 " "
y[1] (numeric) = -4.386463544224962 " "
absolute error = 3.22408766351145460000000000000E-13 " "
relative error = 7.350084255815583000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.337000000000412 " "
y[1] (analytic) = -4.385659907205998 " "
y[1] (numeric) = -4.385659907206323 " "
absolute error = 3.25073301610245840000000000000E-13 " "
relative error = 7.412186728754864000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.338000000000413 " "
y[1] (analytic) = -4.384856225418588 " "
y[1] (numeric) = -4.384856225418915 " "
absolute error = 3.2684965844964610000000000000E-13 " "
relative error = 7.454056453548699000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.339000000000414 " "
y[1] (analytic) = -4.3840524988644205 " "
y[1] (numeric) = -4.384052498864741 " "
absolute error = 3.2063240951174520000000000000E-13 " "
relative error = 7.313607891210178000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.340000000000416 " "
y[1] (analytic) = -4.383248727545482 " "
y[1] (numeric) = -4.383248727545807 " "
absolute error = 3.25073301610245840000000000000E-13 " "
relative error = 7.416264095792698000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.341000000000417 " "
y[1] (analytic) = -4.382444911463786 " "
y[1] (numeric) = -4.382444911464115 " "
absolute error = 3.29514193708746460000000000000E-13 " "
relative error = 7.518958032918777000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.342000000000418 " "
y[1] (analytic) = -4.38164105062134 " "
y[1] (numeric) = -4.38164105062167 " "
absolute error = 3.29514193708746460000000000000E-13 " "
relative error = 7.520337469497178000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.34300000000042 " "
y[1] (analytic) = -4.380837145020141 " "
y[1] (numeric) = -4.3808371450204735 " "
absolute error = 3.32178728967846840000000000000E-13 " "
relative error = 7.58254000255285900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.34400000000042 " "
y[1] (analytic) = -4.380033194662204 " "
y[1] (numeric) = -4.380033194662530 " "
absolute error = 3.2684965844964610000000000000E-13 " "
relative error = 7.462264414981297000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.34500000000042 " "
y[1] (analytic) = -4.379229199549513 " "
y[1] (numeric) = -4.379229199549844 " "
absolute error = 3.3040237212844660000000000000E-13 " "
relative error = 7.544760894507068000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.346000000000423 " "
y[1] (analytic) = -4.378425159684081 " "
y[1] (numeric) = -4.378425159684416 " "
absolute error = 3.3484326422694720000000000000E-13 " "
relative error = 7.647573088838804000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.347000000000424 " "
y[1] (analytic) = -4.377621075067914 " "
y[1] (numeric) = -4.377621075068249 " "
absolute error = 3.3484326422694720000000000000E-13 " "
relative error = 7.648977800614057000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.348000000000425 " "
y[1] (analytic) = -4.376816945703009 " "
y[1] (numeric) = -4.376816945703347 " "
absolute error = 3.3750779948604760000000000000E-13 " "
relative error = 7.711261486898596000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.349000000000427 " "
y[1] (analytic) = -4.37601277159138 " "
y[1] (numeric) = -4.376012771591710 " "
absolute error = 3.3040237212844660000000000000E-13 " "
relative error = 7.550306394747849000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.350000000000428 " "
y[1] (analytic) = -4.375208552735007 " "
y[1] (numeric) = -4.3752085527353435 " "
absolute error = 3.36619621066347460000000000000E-13 " "
relative error = 7.693796010156398000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.35100000000043 " "
y[1] (analytic) = -4.37440428913591 " "
y[1] (numeric) = -4.374404289136247 " "
absolute error = 3.36619621066347460000000000000E-13 " "
relative error = 7.6952105662104000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.35200000000043 " "
y[1] (analytic) = -4.373599980796083 " "
y[1] (numeric) = -4.373599980796422 " "
absolute error = 3.39284156325447840000000000000E-13 " "
relative error = 7.75754887998905000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.35300000000043 " "
y[1] (analytic) = -4.3727956277175295 " "
y[1] (numeric) = -4.372795627717872 " "
absolute error = 3.42836870004248340000000000000E-13 " "
relative error = 7.840221661198447000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.354000000000433 " "
y[1] (analytic) = -4.371991229902264 " "
y[1] (numeric) = -4.371991229902598 " "
absolute error = 3.3395508580724710000000000000E-13 " "
relative error = 7.638512253253369000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.355000000000434 " "
y[1] (analytic) = -4.371186787352261 " "
y[1] (numeric) = -4.371186787352600 " "
absolute error = 3.39284156325447840000000000000E-13 " "
relative error = 7.76183157643008900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.356000000000435 " "
y[1] (analytic) = -4.37038230006954 " "
y[1] (numeric) = -4.370382300069881 " "
absolute error = 3.4106051316484810000000000000E-13 " "
relative error = 7.803905694003503000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.357000000000436 " "
y[1] (analytic) = -4.3695777680560965 " "
y[1] (numeric) = -4.36957776805644 " "
absolute error = 3.43725048423948460000000000000E-13 " "
relative error = 7.866321797423054000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.358000000000438 " "
y[1] (analytic) = -4.3687731913139345 " "
y[1] (numeric) = -4.368773191314279 " "
absolute error = 3.4461322684364860000000000000E-13 " "
relative error = 7.888100657841753000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.35900000000044 " "
y[1] (analytic) = -4.367968569845061 " "
y[1] (numeric) = -4.367968569845399 " "
absolute error = 3.3750779948604760000000000000E-13 " "
relative error = 7.726882510466863000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.36000000000044 " "
y[1] (analytic) = -4.367163903651452 " "
y[1] (numeric) = -4.367163903651798 " "
absolute error = 3.46389583683048840000000000000E-13 " "
relative error = 7.931682696713701000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.36100000000044 " "
y[1] (analytic) = -4.366359192735132 " "
y[1] (numeric) = -4.366359192735480 " "
absolute error = 3.47277762102748970000000000000E-13 " "
relative error = 7.953485885461719000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.362000000000442 " "
y[1] (analytic) = -4.365554437098094 " "
y[1] (numeric) = -4.365554437098441 " "
absolute error = 3.47277762102748970000000000000E-13 " "
relative error = 7.954952048051752000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.363000000000444 " "
y[1] (analytic) = -4.3647496367423315 " "
y[1] (numeric) = -4.364749636742684 " "
absolute error = 3.5260683262094970000000000000E-13 " "
relative error = 8.078512216433126000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.364000000000445 " "
y[1] (analytic) = -4.363944791669862 " "
y[1] (numeric) = -4.363944791670207 " "
absolute error = 3.4461322684364860000000000000E-13 " "
relative error = 7.896828289428989000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.365000000000446 " "
y[1] (analytic) = -4.363139901882661 " "
y[1] (numeric) = -4.3631399018830095 " "
absolute error = 3.4816594052244910000000000000E-13 " "
relative error = 7.979710675154336000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.366000000000447 " "
y[1] (analytic) = -4.36233496738274 " "
y[1] (numeric) = -4.362334967383092 " "
absolute error = 3.5171865420124960000000000000E-13 " "
relative error = 8.062623728600773000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.36700000000045 " "
y[1] (analytic) = -4.3615299881721015 " "
y[1] (numeric) = -4.361529988172452 " "
absolute error = 3.50830475781549470000000000000E-13 " "
relative error = 8.043747875927846000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.36800000000045 " "
y[1] (analytic) = -4.360724964252732 " "
y[1] (numeric) = -4.36072496425309 " "
absolute error = 3.57935903139150470000000000000E-13 " "
relative error = 8.208174238764161000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.36900000000045 " "
y[1] (analytic) = -4.359919895626653 " "
y[1] (numeric) = -4.359919895627004 " "
absolute error = 3.50830475781549470000000000000E-13 " "
relative error = 8.04671838428637900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.370000000000452 " "
y[1] (analytic) = -4.359114782295837 " "
y[1] (numeric) = -4.359114782296193 " "
absolute error = 3.5615954629975020000000000000E-13 " "
relative error = 8.170455794058487000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.371000000000453 " "
y[1] (analytic) = -4.358309624262297 " "
y[1] (numeric) = -4.358309624262655 " "
absolute error = 3.57935903139150470000000000000E-13 " "
relative error = 8.21272314262747900000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.372000000000455 " "
y[1] (analytic) = -4.357504421528027 " "
y[1] (numeric) = -4.357504421528388 " "
absolute error = 3.60600438398250840000000000000E-13 " "
relative error = 8.275388927128172000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.373000000000456 " "
y[1] (analytic) = -4.356699174095030 " "
y[1] (numeric) = -4.35669917409539 " "
absolute error = 3.5971225997855070000000000000E-13 " "
relative error = 8.256531966159214000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.374000000000457 " "
y[1] (analytic) = -4.355893881965304 " "
y[1] (numeric) = -4.3558938819656605 " "
absolute error = 3.5615954629975020000000000000E-13 " "
relative error = 8.176497314922125000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.37500000000046 " "
y[1] (analytic) = -4.355088545140834 " "
y[1] (numeric) = -4.355088545141196 " "
absolute error = 3.61488616817950970000000000000E-13 " "
relative error = 8.300373530207094000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.37600000000046 " "
y[1] (analytic) = -4.354283163623630 " "
y[1] (numeric) = -4.354283163623993 " "
absolute error = 3.6237679523765110000000000000E-13 " "
relative error = 8.322306602956007000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.37700000000046 " "
y[1] (analytic) = -4.353477737415687 " "
y[1] (numeric) = -4.353477737416050 " "
absolute error = 3.6326497365735120000000000000E-13 " "
relative error = 8.344247876480302000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.378000000000462 " "
y[1] (analytic) = -4.352672266518997 " "
y[1] (numeric) = -4.352672266519365 " "
absolute error = 3.67705865755851850000000000000E-13 " "
relative error = 8.447818793624006000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.379000000000463 " "
y[1] (analytic) = -4.351866750935570 " "
y[1] (numeric) = -4.351866750935933 " "
absolute error = 3.6237679523765110000000000000E-13 " "
relative error = 8.3269276376568000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.380000000000464 " "
y[1] (analytic) = -4.351061190667387 " "
y[1] (numeric) = -4.351061190667752 " "
absolute error = 3.65041330496751470000000000000E-13 " "
relative error = 8.389708039034947000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.381000000000466 " "
y[1] (analytic) = -4.35025558571645 " "
y[1] (numeric) = -4.350255585716819 " "
absolute error = 3.68594044175551970000000000000E-13 " "
relative error = 8.472928473117464000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.382000000000467 " "
y[1] (analytic) = -4.34944993608476 " "
y[1] (numeric) = -4.349449936085130 " "
absolute error = 3.6948222259525210000000000000E-13 " "
relative error = 8.494918392550773000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.383000000000468 " "
y[1] (analytic) = -4.348644241774310 " "
y[1] (numeric) = -4.3486442417746805 " "
absolute error = 3.71258579434652350000000000000E-13 " "
relative error = 8.537340807699034000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.38400000000047 " "
y[1] (analytic) = -4.347838502787102 " "
y[1] (numeric) = -4.347838502787468 " "
absolute error = 3.6592950891645160000000000000E-13 " "
relative error = 8.416354670990637000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.38500000000047 " "
y[1] (analytic) = -4.347032719125117 " "
y[1] (numeric) = -4.347032719125488 " "
absolute error = 3.7037040101495220000000000000E-13 " "
relative error = 8.520073920434923000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.38600000000047 " "
y[1] (analytic) = -4.346226890790362 " "
y[1] (numeric) = -4.346226890790735 " "
absolute error = 3.7303493627405260000000000000E-13 " "
relative error = 8.58296047692568000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.387000000000473 " "
y[1] (analytic) = -4.345421017784833 " "
y[1] (numeric) = -4.345421017785206 " "
absolute error = 3.7303493627405260000000000000E-13 " "
relative error = 8.584552215937289000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.388000000000474 " "
y[1] (analytic) = -4.34461510011052 " "
y[1] (numeric) = -4.344615100110897 " "
absolute error = 3.7658764995285310000000000000E-13 " "
relative error = 8.667917439758319000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.389000000000475 " "
y[1] (analytic) = -4.34380913776943 " "
y[1] (numeric) = -4.343809137769801 " "
absolute error = 3.71258579434652350000000000000E-13 " "
relative error = 8.546843741511527000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.390000000000477 " "
y[1] (analytic) = -4.343003130763538 " "
y[1] (numeric) = -4.343003130763915 " "
absolute error = 3.7658764995285310000000000000E-13 " "
relative error = 8.671134664520624000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.391000000000478 " "
y[1] (analytic) = -4.342197079094856 " "
y[1] (numeric) = -4.342197079095232 " "
absolute error = 3.7658764995285310000000000000E-13 " "
relative error = 8.672744306468788000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.39200000000048 " "
y[1] (analytic) = -4.341390982765368 " "
y[1] (numeric) = -4.341390982765750 " "
absolute error = 3.8102854205135370000000000000E-13 " "
relative error = 8.776646553235504000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.39300000000048 " "
y[1] (analytic) = -4.34058484177708 " "
y[1] (numeric) = -4.340584841777459 " "
absolute error = 3.79252185211953500000000000000E-13 " "
relative error = 8.737352201061546000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.39400000000048 " "
y[1] (analytic) = -4.339778656131983 " "
y[1] (numeric) = -4.339778656132356 " "
absolute error = 3.7303493627405260000000000000E-13 " "
relative error = 8.595713418401302000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.395000000000483 " "
y[1] (analytic) = -4.338972425832054 " "
y[1] (numeric) = -4.338972425832436 " "
absolute error = 3.81916720471053850000000000000E-13 " "
relative error = 8.802008470883896000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.396000000000484 " "
y[1] (analytic) = -4.33816615087931 " "
y[1] (numeric) = -4.338166150879691 " "
absolute error = 3.8102854205135370000000000000E-13 " "
relative error = 8.78317078690318000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.397000000000485 " "
y[1] (analytic) = -4.33735983127573 " "
y[1] (numeric) = -4.337359831276116 " "
absolute error = 3.85469434149854350000000000000E-13 " "
relative error = 8.887190575481440000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.398000000000486 " "
y[1] (analytic) = -4.336553467023318 " "
y[1] (numeric) = -4.336553467023704 " "
absolute error = 3.85469434149854350000000000000E-13 " "
relative error = 8.888843111957454000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.399000000000488 " "
y[1] (analytic) = -4.335747058124067 " "
y[1] (numeric) = -4.335747058124448 " "
absolute error = 3.8102854205135370000000000000E-13 " "
relative error = 8.788071281450909000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.40000000000049 " "
y[1] (analytic) = -4.3349406045799554 " "
y[1] (numeric) = -4.334940604580342 " "
absolute error = 3.8635761256955450000000000000E-13 " "
relative error = 8.912639129619436000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.40100000000049 " "
y[1] (analytic) = -4.334134106392991 " "
y[1] (numeric) = -4.334134106393378 " "
absolute error = 3.8724579098925460000000000000E-13 " "
relative error = 8.934790236833103000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.40200000000049 " "
y[1] (analytic) = -4.33332756356516 " "
y[1] (numeric) = -4.33332756356555 " "
absolute error = 3.9079850466805510000000000000E-13 " "
relative error = 9.018439038717242000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.403000000000493 " "
y[1] (analytic) = -4.332520976098458 " "
y[1] (numeric) = -4.332520976098851 " "
absolute error = 3.9346303992715550000000000000E-13 " "
relative error = 9.08161881033704000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.404000000000494 " "
y[1] (analytic) = -4.331714343994886 " "
y[1] (numeric) = -4.331714343995273 " "
absolute error = 3.8724579098925460000000000000E-13 " "
relative error = 8.939781348373046000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.405000000000495 " "
y[1] (analytic) = -4.330907667256419 " "
y[1] (numeric) = -4.330907667256808 " "
absolute error = 3.89022147828654850000000000000E-13 " "
relative error = 8.982462285442718000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.406000000000496 " "
y[1] (analytic) = -4.330100945885057 " "
y[1] (numeric) = -4.330100945885449 " "
absolute error = 3.91686683087755200000000000000E-13 " "
relative error = 9.045670943537227000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.407000000000497 " "
y[1] (analytic) = -4.32929417988279 " "
y[1] (numeric) = -4.329294179883187 " "
absolute error = 3.970157536059560000000000000E-13 " "
relative error = 9.170449895754246000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.4080000000005 " "
y[1] (analytic) = -4.328487369251615 " "
y[1] (numeric) = -4.328487369252015 " "
absolute error = 3.99680288865056350000000000000E-13 " "
relative error = 9.23371734209681000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.4090000000005 " "
y[1] (analytic) = -4.327680513993531 " "
y[1] (numeric) = -4.327680513993923 " "
absolute error = 3.91686683087755200000000000000E-13 " "
relative error = 9.050730104064717000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.4100000000005 " "
y[1] (analytic) = -4.326873614110510 " "
y[1] (numeric) = -4.326873614110904 " "
absolute error = 3.9346303992715550000000000000E-13 " "
relative error = 9.093471985038345000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.411000000000502 " "
y[1] (analytic) = -4.32606666960455 " "
y[1] (numeric) = -4.326066669604950 " "
absolute error = 3.98792110445356230000000000000E-13 " "
relative error = 9.21835331959436000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.412000000000504 " "
y[1] (analytic) = -4.32525968047765 " "
y[1] (numeric) = -4.325259680478049 " "
absolute error = 3.98792110445356230000000000000E-13 " "
relative error = 9.220073241968134000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.413000000000505 " "
y[1] (analytic) = -4.3244526467317925 " "
y[1] (numeric) = -4.324452646732195 " "
absolute error = 4.02344824124156730000000000000E-13 " "
relative error = 9.303947967339382000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.414000000000506 " "
y[1] (analytic) = -4.323645568368981 " "
y[1] (numeric) = -4.323645568369377 " "
absolute error = 3.96127575186255850000000000000E-13 " "
relative error = 9.16188824736825100000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.415000000000507 " "
y[1] (analytic) = -4.322838445391184 " "
y[1] (numeric) = -4.322838445391587 " "
absolute error = 4.02344824124156730000000000000E-13 " "
relative error = 9.307422176582117000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.41600000000051 " "
y[1] (analytic) = -4.322031277800410 " "
y[1] (numeric) = -4.322031277800813 " "
absolute error = 4.041211809635570000000000000E-13 " "
relative error = 9.350260444418265000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.41700000000051 " "
y[1] (analytic) = -4.321224065598646 " "
y[1] (numeric) = -4.321224065599049 " "
absolute error = 4.03233002543856860000000000000E-13 " "
relative error = 9.33145322766304000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.41800000000051 " "
y[1] (analytic) = -4.320416808787876 " "
y[1] (numeric) = -4.3204168087882815 " "
absolute error = 4.05897537802957230000000000000E-13 " "
relative error = 9.394869887954972000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.419000000000512 " "
y[1] (analytic) = -4.319609507370103 " "
y[1] (numeric) = -4.319609507370502 " "
absolute error = 3.98792110445356230000000000000E-13 " "
relative error = 9.232133362169392000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.420000000000513 " "
y[1] (analytic) = -4.318802161347296 " "
y[1] (numeric) = -4.3188021613477 " "
absolute error = 4.041211809635570000000000000E-13 " "
relative error = 9.357251521738775000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = 20.421000000000515 " "
y[1] (analytic) = -4.317994770721459 " "
y[1] (numeric) = -4.3179947707218655 " "
absolute error = 4.06785716222657360000000000000E-13 " "
relative error = 9.42070886655314000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ;"
Iterations = 422
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 58 Seconds
"Expected Time Remaining "= 0 Years 0 Days 1 Hours 8 Minutes 2 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 1 Hours 7 Minutes 30 Seconds
"Expected Total Time "= 0 Years 0 Days 1 Hours 10 Minutes 30 Seconds
"Time to Timeout " Unknown
Percent Done = 4.23000000000517 "%"
(%o57) true
(%o57) diffeq.max