(%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, hdrc_BBB, m,
n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new,
ratio, term], n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float 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) rm0 - convfloat(m - 1) rm1,
array_y_higher
1, m - 2
if omniabs(hdrc) > glob_small_float glob_small_float
glob_h
then (rcs : ------, ord_no :
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
-----------------------------------------------------,
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_sing : 0, if (1 # found_sing) 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_sing : 1,
1, 2 1, 2
array_type_pole : 2, if glob_display_flag
1
then (if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1"))),
if (1 # found_sing) 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 > - 1.0 glob_smallish_float)
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, 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 for equation 1"))),
if (1 # found_sing) 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_sing : 1, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE for equation 1")),
if (1 # found_sing) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole > - 1.0
1, 1 1, 2
glob_smallish_float))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, 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 for equation 1"))),
if (1 # found_sing) 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,
1, 2 1, 2 1
found_sing : 1, if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))),
if 1 # found_sing 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 for equation 1")),
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, hdrc_BBB, m,
n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new,
ratio, term], n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float 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) rm0 - convfloat(m - 1) rm1,
array_y_higher
1, m - 2
if omniabs(hdrc) > glob_small_float glob_small_float
glob_h
then (rcs : ------, ord_no :
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
-----------------------------------------------------,
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_sing : 0, if (1 # found_sing) 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_sing : 1,
1, 2 1, 2
array_type_pole : 2, if glob_display_flag
1
then (if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1"))),
if (1 # found_sing) 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 > - 1.0 glob_smallish_float)
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, 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 for equation 1"))),
if (1 # found_sing) 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_sing : 1, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE for equation 1")),
if (1 # found_sing) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole > - 1.0
1, 1 1, 2
glob_smallish_float))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, 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 for equation 1"))),
if (1 # found_sing) 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,
1, 2 1, 2 1
found_sing : 1, if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))),
if 1 # found_sing 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 for equation 1")),
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_2D0 array_x ,
1 1 1
array_tmp2 : array_const_1D0 + array_tmp1 ,
1 1 1
array_tmp3 : array_const_3D0 array_x ,
1 1 1
array_tmp4 : array_const_2D0 + array_tmp3 ,
1 1 1
array_tmp5 : expt(array_tmp2 , array_tmp4 ),
1 1 1
array_tmp2
2
array_tmp5_a1 : ln(array_tmp2 ), array_tmp5_a1 : -----------,
1 1 2 array_tmp2
1
array_tmp6 : array_const_2D0 array_x ,
1 1 1
array_tmp7 : array_const_1D0 + array_tmp6 , array_tmp8 : ln(array_tmp7 ),
1 1 1 1 1
array_tmp9 : array_const_3D0 array_tmp8 ,
1 1 1
array_tmp10 : array_const_3D0 array_x ,
1 1 1
array_tmp11 : array_const_2D0 + array_tmp10 ,
1 1 1
array_tmp12 : array_const_2D0 array_tmp11 ,
1 1 1
array_tmp13 : array_const_2D0 array_x ,
1 1 1
array_tmp12
1
array_tmp14 : array_const_1D0 + array_tmp13 , array_tmp15 : ------------,
1 1 1 1 array_tmp14
1
array_tmp16 : array_tmp15 + array_tmp9 ,
1 1 1
array_tmp17 : array_tmp5 array_tmp16 ,
1 1 1
array_tmp18 : array_tmp17 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp18 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_2D0 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp3 : array_const_3D0 array_x , array_tmp4 : array_tmp3 ,
2 1 2 2 2
array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4
2 1 1 2
array_tmp5_a2 : -------------------------------------------------------,
1 glob_h
array_tmp5 : array_tmp5 array_tmp5_a2 glob_h,
2 1 1
array_tmp6 : array_const_2D0 array_x , array_tmp7 : array_tmp6 ,
2 1 2 2 2
array_tmp7
2
array_tmp8 : -----------, array_tmp9 : array_const_3D0 array_tmp8 ,
2 array_tmp7 2 1 2
1
array_tmp10 : array_const_3D0 array_x , array_tmp11 : array_tmp10 ,
2 1 2 2 2
array_tmp12 : array_const_2D0 array_tmp11 ,
2 1 2
array_tmp13 : array_const_2D0 array_x , array_tmp14 : array_tmp13 ,
2 1 2 2 2
array_tmp12 - array_tmp15 array_tmp14
2 1 2
array_tmp15 : ----------------------------------------,
2 array_tmp14
1
array_tmp16 : array_tmp15 + array_tmp9 ,
2 2 2
array_tmp17 : ats(2, array_tmp5, array_tmp16, 1),
2
array_tmp18 : array_tmp17 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp18 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
- array_tmp5_a1 array_tmp2 1
2 2
------------------------------
array_tmp2
1
array_tmp5_a1 : ------------------------------,
3 2
(array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4 ) 2
3 1 2 2
array_tmp5_a2 : -----------------------------------------------------------,
2 glob_h
ats(2, array_tmp5, array_tmp5_a2, 1) glob_h
array_tmp5 : -------------------------------------------,
3 2
- array_tmp7 array_tmp8 1
2 2
---------------------------
array_tmp7
1
array_tmp8 : ---------------------------,
3 2
array_tmp9 : array_const_3D0 array_tmp8 ,
3 1 3
- array_tmp15 array_tmp14
2 2
array_tmp15 : ---------------------------,
3 array_tmp14
1
array_tmp16 : array_tmp15 + array_tmp9 ,
3 3 3
array_tmp17 : ats(3, array_tmp5, array_tmp16, 1),
3
array_tmp18 : array_tmp17 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp18 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
- array_tmp5_a1 array_tmp2 2
3 2
------------------------------
array_tmp2
1
array_tmp5_a1 : ------------------------------,
4 3
(array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4 ) 3
4 1 3 2
array_tmp5_a2 : -----------------------------------------------------------,
3 glob_h
ats(3, array_tmp5, array_tmp5_a2, 1) glob_h
array_tmp5 : -------------------------------------------,
4 3
- array_tmp7 array_tmp8 2
2 3
---------------------------
array_tmp7
1
array_tmp8 : ---------------------------,
4 3
array_tmp9 : array_const_3D0 array_tmp8 ,
4 1 4
- array_tmp15 array_tmp14
3 2
array_tmp15 : ---------------------------,
4 array_tmp14
1
array_tmp16 : array_tmp15 + array_tmp9 ,
4 4 4
array_tmp17 : ats(4, array_tmp5, array_tmp16, 1),
4
array_tmp18 : array_tmp17 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp18 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
- array_tmp5_a1 array_tmp2 3
4 2
------------------------------
array_tmp2
1
array_tmp5_a1 : ------------------------------,
5 4
(array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4 ) 4
5 1 4 2
array_tmp5_a2 : -----------------------------------------------------------,
4 glob_h
ats(4, array_tmp5, array_tmp5_a2, 1) glob_h
array_tmp5 : -------------------------------------------,
5 4
- array_tmp7 array_tmp8 3
2 4
---------------------------
array_tmp7
1
array_tmp8 : ---------------------------,
5 4
array_tmp9 : array_const_3D0 array_tmp8 ,
5 1 5
- array_tmp15 array_tmp14
4 2
array_tmp15 : ---------------------------,
5 array_tmp14
1
array_tmp16 : array_tmp15 + array_tmp9 ,
5 5 5
array_tmp17 : ats(5, array_tmp5, array_tmp16, 1),
5
array_tmp18 : array_tmp17 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp18 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp5_a1 :
kkk
- array_tmp5_a1 array_tmp4 (kkk - 2)
kkk - 1 2
--------------------------------------------
array_tmp2
1
--------------------------------------------,
kkk - 1
array_tmp5_a2 : ((array_tmp5_a1 array_tmp4
kkk - 1 kkk 1
+ array_tmp5_a1 array_tmp4 ) (kkk - 1))/glob_h,
kkk - 1 2
ats(kkk - 1, array_tmp5, array_tmp5_a2, 1) glob_h
array_tmp5 : -------------------------------------------------,
kkk kkk - 1
- array_tmp7 array_tmp8 (kkk - 2)
2 kkk - 1
-----------------------------------------
array_tmp7
1
array_tmp8 : -----------------------------------------,
kkk kkk - 1
array_tmp9 : array_const_3D0 array_tmp8 ,
kkk 1 kkk
- array_tmp15 array_tmp14
kkk - 1 2
array_tmp15 : ---------------------------------,
kkk array_tmp14
1
array_tmp16 : array_tmp15 + array_tmp9 ,
kkk kkk kkk
array_tmp17 : ats(kkk, array_tmp5, array_tmp16, 1),
kkk
array_tmp18 : array_tmp17 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp18 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_2D0 array_x ,
1 1 1
array_tmp2 : array_const_1D0 + array_tmp1 ,
1 1 1
array_tmp3 : array_const_3D0 array_x ,
1 1 1
array_tmp4 : array_const_2D0 + array_tmp3 ,
1 1 1
array_tmp5 : expt(array_tmp2 , array_tmp4 ),
1 1 1
array_tmp2
2
array_tmp5_a1 : ln(array_tmp2 ), array_tmp5_a1 : -----------,
1 1 2 array_tmp2
1
array_tmp6 : array_const_2D0 array_x ,
1 1 1
array_tmp7 : array_const_1D0 + array_tmp6 , array_tmp8 : ln(array_tmp7 ),
1 1 1 1 1
array_tmp9 : array_const_3D0 array_tmp8 ,
1 1 1
array_tmp10 : array_const_3D0 array_x ,
1 1 1
array_tmp11 : array_const_2D0 + array_tmp10 ,
1 1 1
array_tmp12 : array_const_2D0 array_tmp11 ,
1 1 1
array_tmp13 : array_const_2D0 array_x ,
1 1 1
array_tmp12
1
array_tmp14 : array_const_1D0 + array_tmp13 , array_tmp15 : ------------,
1 1 1 1 array_tmp14
1
array_tmp16 : array_tmp15 + array_tmp9 ,
1 1 1
array_tmp17 : array_tmp5 array_tmp16 ,
1 1 1
array_tmp18 : array_tmp17 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp18 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_2D0 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp3 : array_const_3D0 array_x , array_tmp4 : array_tmp3 ,
2 1 2 2 2
array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4
2 1 1 2
array_tmp5_a2 : -------------------------------------------------------,
1 glob_h
array_tmp5 : array_tmp5 array_tmp5_a2 glob_h,
2 1 1
array_tmp6 : array_const_2D0 array_x , array_tmp7 : array_tmp6 ,
2 1 2 2 2
array_tmp7
2
array_tmp8 : -----------, array_tmp9 : array_const_3D0 array_tmp8 ,
2 array_tmp7 2 1 2
1
array_tmp10 : array_const_3D0 array_x , array_tmp11 : array_tmp10 ,
2 1 2 2 2
array_tmp12 : array_const_2D0 array_tmp11 ,
2 1 2
array_tmp13 : array_const_2D0 array_x , array_tmp14 : array_tmp13 ,
2 1 2 2 2
array_tmp12 - array_tmp15 array_tmp14
2 1 2
array_tmp15 : ----------------------------------------,
2 array_tmp14
1
array_tmp16 : array_tmp15 + array_tmp9 ,
2 2 2
array_tmp17 : ats(2, array_tmp5, array_tmp16, 1),
2
array_tmp18 : array_tmp17 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp18 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
- array_tmp5_a1 array_tmp2 1
2 2
------------------------------
array_tmp2
1
array_tmp5_a1 : ------------------------------,
3 2
(array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4 ) 2
3 1 2 2
array_tmp5_a2 : -----------------------------------------------------------,
2 glob_h
ats(2, array_tmp5, array_tmp5_a2, 1) glob_h
array_tmp5 : -------------------------------------------,
3 2
- array_tmp7 array_tmp8 1
2 2
---------------------------
array_tmp7
1
array_tmp8 : ---------------------------,
3 2
array_tmp9 : array_const_3D0 array_tmp8 ,
3 1 3
- array_tmp15 array_tmp14
2 2
array_tmp15 : ---------------------------,
3 array_tmp14
1
array_tmp16 : array_tmp15 + array_tmp9 ,
3 3 3
array_tmp17 : ats(3, array_tmp5, array_tmp16, 1),
3
array_tmp18 : array_tmp17 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp18 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
- array_tmp5_a1 array_tmp2 2
3 2
------------------------------
array_tmp2
1
array_tmp5_a1 : ------------------------------,
4 3
(array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4 ) 3
4 1 3 2
array_tmp5_a2 : -----------------------------------------------------------,
3 glob_h
ats(3, array_tmp5, array_tmp5_a2, 1) glob_h
array_tmp5 : -------------------------------------------,
4 3
- array_tmp7 array_tmp8 2
2 3
---------------------------
array_tmp7
1
array_tmp8 : ---------------------------,
4 3
array_tmp9 : array_const_3D0 array_tmp8 ,
4 1 4
- array_tmp15 array_tmp14
3 2
array_tmp15 : ---------------------------,
4 array_tmp14
1
array_tmp16 : array_tmp15 + array_tmp9 ,
4 4 4
array_tmp17 : ats(4, array_tmp5, array_tmp16, 1),
4
array_tmp18 : array_tmp17 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp18 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
- array_tmp5_a1 array_tmp2 3
4 2
------------------------------
array_tmp2
1
array_tmp5_a1 : ------------------------------,
5 4
(array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4 ) 4
5 1 4 2
array_tmp5_a2 : -----------------------------------------------------------,
4 glob_h
ats(4, array_tmp5, array_tmp5_a2, 1) glob_h
array_tmp5 : -------------------------------------------,
5 4
- array_tmp7 array_tmp8 3
2 4
---------------------------
array_tmp7
1
array_tmp8 : ---------------------------,
5 4
array_tmp9 : array_const_3D0 array_tmp8 ,
5 1 5
- array_tmp15 array_tmp14
4 2
array_tmp15 : ---------------------------,
5 array_tmp14
1
array_tmp16 : array_tmp15 + array_tmp9 ,
5 5 5
array_tmp17 : ats(5, array_tmp5, array_tmp16, 1),
5
array_tmp18 : array_tmp17 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp18 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp5_a1 :
kkk
- array_tmp5_a1 array_tmp4 (kkk - 2)
kkk - 1 2
--------------------------------------------
array_tmp2
1
--------------------------------------------,
kkk - 1
array_tmp5_a2 : ((array_tmp5_a1 array_tmp4
kkk - 1 kkk 1
+ array_tmp5_a1 array_tmp4 ) (kkk - 1))/glob_h,
kkk - 1 2
ats(kkk - 1, array_tmp5, array_tmp5_a2, 1) glob_h
array_tmp5 : -------------------------------------------------,
kkk kkk - 1
- array_tmp7 array_tmp8 (kkk - 2)
2 kkk - 1
-----------------------------------------
array_tmp7
1
array_tmp8 : -----------------------------------------,
kkk kkk - 1
array_tmp9 : array_const_3D0 array_tmp8 ,
kkk 1 kkk
- array_tmp15 array_tmp14
kkk - 1 2
array_tmp15 : ---------------------------------,
kkk array_tmp14
1
array_tmp16 : array_tmp15 + array_tmp9 ,
kkk kkk kkk
array_tmp17 : ats(kkk, array_tmp5, array_tmp16, 1),
kkk
array_tmp18 : array_tmp17 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp18 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_debug(typ, radius, order2) :=
(if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS,
"DBG Radius of convergence ", 4, radius, 4, " "),
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " "))
(%o27) display_pole_debug(typ, radius, order2) :=
(if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS,
"DBG Radius of convergence ", 4, radius, 4, " "),
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " "))
(%i28) 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
(%o28) 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
(%i29) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o29) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i30) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o30) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i31) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o31) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i32) 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, " | "))
(%o32) 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, " | "))
(%i33) log_revs(file, revs) := printf(file, revs)
(%o33) log_revs(file, revs) := printf(file, revs)
(%i34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i35) 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, " | "))
(%o35) 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, " | "))
(%i36) logstart(file) := printf(file, "")
(%o36) logstart(file) := printf(file, "
")
(%i37) logend(file) := printf(file, "
~%")
(%o37) logend(file) := printf(file, "~%")
(%i38) 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())
(%o38) 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())
(%i39) 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
(%o39) 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
(%i40) 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
(%o40) 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
(%i41) factorial_2(nnn) := nnn!
(%o41) factorial_2(nnn) := nnn!
(%i42) 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
(%o42) 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
(%i43) 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)
(%o43) 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)
(%i44) convfp(mmm) := mmm
(%o44) convfp(mmm) := mmm
(%i45) convfloat(mmm) := mmm
(%o45) convfloat(mmm) := mmm
(%i46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i47) Si(x) := 0.0
(%o47) Si(x) := 0.0
(%i48) Ci(x) := 0.0
(%o48) Ci(x) := 0.0
(%i49) ln(x) := log(x)
(%o49) ln(x) := log(x)
(%i50) arcsin(x) := asin(x)
(%o50) arcsin(x) := asin(x)
(%i51) arccos(x) := acos(x)
(%o51) arccos(x) := acos(x)
(%i52) arctan(x) := atan(x)
(%o52) arctan(x) := atan(x)
(%i53) omniabs(x) := abs(x)
(%o53) omniabs(x) := abs(x)
(%i54) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o54) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i55) 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)
(%o55) 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)
(%i56) exact_soln_y(x) := block(expt(1.0 + 2.0 x, 2.0 + 3.0 x))
(%o56) exact_soln_y(x) := block(expt(1.0 + 2.0 x, 2.0 + 3.0 x))
(%i57) 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, 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_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_max_h, 0.1, 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_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-201, 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_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/expt_lin_lin_newpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 \
) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0\
) ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:1.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
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, " (expt(2.0*x+1.0,3.0*x+2.0)) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32,
max_terms : 30, glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5_c1, 1 + max_terms), array(array_tmp5_a1, 1 + max_terms),
array(array_tmp5_a2, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms),
array(array_tmp8, 1 + max_terms), array(array_tmp9, 1 + max_terms),
array(array_tmp10, 1 + max_terms), array(array_tmp11, 1 + max_terms),
array(array_tmp12, 1 + max_terms), array(array_tmp13, 1 + max_terms),
array(array_tmp14, 1 + max_terms), array(array_tmp15, 1 + max_terms),
array(array_tmp16, 1 + max_terms), array(array_tmp17, 1 + max_terms),
array(array_tmp18, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5_c1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5_a1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp5_a2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp9 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp10 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp11 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp12 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp13 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp14 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp15 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp16 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp17 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp18 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp5_c1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5_c1 : 0.0, term : 1 + term),
term
array(array_tmp5_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5_a1 : 0.0, term : 1 + term),
term
array(array_tmp5_a2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5_a2 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_tmp7, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term),
term
array(array_tmp8, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term),
term
array(array_tmp9, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term),
term
array(array_tmp10, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp10 : 0.0, term : 1 + term),
term
array(array_tmp11, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp11 : 0.0, term : 1 + term),
term
array(array_tmp12, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp12 : 0.0, term : 1 + term),
term
array(array_tmp13, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp13 : 0.0, term : 1 + term),
term
array(array_tmp14, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp14 : 0.0, term : 1 + term),
term
array(array_tmp15, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp15 : 0.0, term : 1 + term),
term
array(array_tmp16, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp16 : 0.0, term : 1 + term),
term
array(array_tmp17, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp17 : 0.0, term : 1 + term),
term
array(array_tmp18, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp18 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term),
term
array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 1.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
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),
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, if glob_max_h < glob_h
then glob_h : glob_max_h, 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_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 )\
= expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 \
* ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-28T14:03:08-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file,
"expt_lin_lin_new"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x\
+ 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * \
x + 1.0) ) ;"), logitem_float(html_log_file, x_start),
logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ),
1
logitem_float(html_log_file, glob_h), logitem_str(html_log_file, "16"),
logitem_good_digits(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_max_terms),
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, " 165 | "), logitem_str(html_log_file, "expt_lin_lin_new diffeq.max"),
logitem_str(html_log_file, "expt_li\
n_lin_new maxima results"), logitem_str(html_log_file,
"All Tests - All Languages"), logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%o57) 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, 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_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_max_h, 0.1, 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_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-201, 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_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/expt_lin_lin_newpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 \
) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0\
) ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:1.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
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, " (expt(2.0*x+1.0,3.0*x+2.0)) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32,
max_terms : 30, glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5_c1, 1 + max_terms), array(array_tmp5_a1, 1 + max_terms),
array(array_tmp5_a2, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms),
array(array_tmp8, 1 + max_terms), array(array_tmp9, 1 + max_terms),
array(array_tmp10, 1 + max_terms), array(array_tmp11, 1 + max_terms),
array(array_tmp12, 1 + max_terms), array(array_tmp13, 1 + max_terms),
array(array_tmp14, 1 + max_terms), array(array_tmp15, 1 + max_terms),
array(array_tmp16, 1 + max_terms), array(array_tmp17, 1 + max_terms),
array(array_tmp18, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5_c1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5_a1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp5_a2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp9 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp10 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp11 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp12 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp13 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp14 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp15 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp16 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp17 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp18 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp5_c1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5_c1 : 0.0, term : 1 + term),
term
array(array_tmp5_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5_a1 : 0.0, term : 1 + term),
term
array(array_tmp5_a2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5_a2 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_tmp7, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term),
term
array(array_tmp8, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term),
term
array(array_tmp9, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term),
term
array(array_tmp10, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp10 : 0.0, term : 1 + term),
term
array(array_tmp11, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp11 : 0.0, term : 1 + term),
term
array(array_tmp12, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp12 : 0.0, term : 1 + term),
term
array(array_tmp13, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp13 : 0.0, term : 1 + term),
term
array(array_tmp14, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp14 : 0.0, term : 1 + term),
term
array(array_tmp15, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp15 : 0.0, term : 1 + term),
term
array(array_tmp16, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp16 : 0.0, term : 1 + term),
term
array(array_tmp17, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp17 : 0.0, term : 1 + term),
term
array(array_tmp18, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp18 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term),
term
array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 1.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
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),
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, if glob_max_h < glob_h
then glob_h : glob_max_h, 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_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 )\
= expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 \
* ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-28T14:03:08-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file,
"expt_lin_lin_new"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x\
+ 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * \
x + 1.0) ) ;"), logitem_float(html_log_file, x_start),
logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ),
1
logitem_float(html_log_file, glob_h), logitem_str(html_log_file, "16"),
logitem_good_digits(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_max_terms),
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, " 165 | "), logitem_str(html_log_file, "expt_lin_lin_new diffeq.max"),
logitem_str(html_log_file, "expt_li\
n_lin_new maxima results"), logitem_str(html_log_file,
"All Tests - All Languages"), logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i58) main()
"##############ECHO OF PROBLEM#################"
"##############temp/expt_lin_lin_newpostode.ode#################"
"diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.1,"
"x_end:1.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"/* 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("
" (expt(2.0*x+1.0,3.0*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 = 0.9 ""
estimated_steps = 900. ""
step_error = 1.11111111111111100000000000000E-13 ""
est_needed_step_err = 1.11111111111111100000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 1.058672991960640700000000000000000000000000000000000000000000000000000000000000000000000000E-74 ""
max_value3 = 1.058672991960640700000000000000000000000000000000000000000000000000000000000000000000000000E-74 ""
value3 = 1.058672991960640700000000000000000000000000000000000000000000000000000000000000000000000000E-74 ""
best_h = 1.000E-3 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (analytic) = 1.5209567545525315 " "
y[1] (numeric) = 1.5209567545525315 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.101 " "
y[1] (analytic) = 1.5276363683101828 " "
y[1] (numeric) = 1.5276363683101828 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10200000000000001 " "
y[1] (analytic) = 1.5343508520732434 " "
y[1] (numeric) = 1.5343508520732434 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10300000000000001 " "
y[1] (analytic) = 1.541100401960597 " "
y[1] (numeric) = 1.541100401960597 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10400000000000001 " "
y[1] (analytic) = 1.5478852152658196 " "
y[1] (numeric) = 1.5478852152658196 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10500000000000001 " "
y[1] (analytic) = 1.5547054904645634 " "
y[1] (numeric) = 1.5547054904645634 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10600000000000001 " "
y[1] (analytic) = 1.5615614272219898 " "
y[1] (numeric) = 1.5615614272219895 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.421939611559486200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10700000000000001 " "
y[1] (analytic) = 1.5684532264002486 " "
y[1] (numeric) = 1.5684532264002484 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.415691594671554800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10800000000000001 " "
y[1] (analytic) = 1.5753810900660097 " "
y[1] (numeric) = 1.5753810900660095 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.40946597826515400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10900000000000001 " "
y[1] (analytic) = 1.5823452214980398 " "
y[1] (numeric) = 1.5823452214980396 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.40326271352351900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000001 " "
y[1] (analytic) = 1.5893458251948314 " "
y[1] (numeric) = 1.589345825194831 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.79416350306028300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11100000000000002 " "
y[1] (analytic) = 1.5963831068822798 " "
y[1] (numeric) = 1.5963831068822794 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.78184608654099600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11200000000000002 " "
y[1] (analytic) = 1.603457273521412 " "
y[1] (numeric) = 1.6034572735214117 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.769573079267536600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11300000000000002 " "
y[1] (analytic) = 1.6105685333161648 " "
y[1] (numeric) = 1.6105685333161643 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.757344382829098300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11400000000000002 " "
y[1] (analytic) = 1.6177170957212128 " "
y[1] (numeric) = 1.6177170957212124 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.74515989862911200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11500000000000002 " "
y[1] (analytic) = 1.6249031714498503 " "
y[1] (numeric) = 1.6249031714498499 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.733019527888641600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11600000000000002 " "
y[1] (analytic) = 1.6321269724819214 " "
y[1] (numeric) = 1.6321269724819212 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.360461585824878600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11700000000000002 " "
y[1] (analytic) = 1.6393887120718058 " "
y[1] (numeric) = 1.6393887120718054 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.708870730778896000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11800000000000002 " "
y[1] (analytic) = 1.6466886047564515 " "
y[1] (numeric) = 1.646688604756451 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.696862105970207500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11900000000000002 " "
y[1] (analytic) = 1.6540268663634659 " "
y[1] (numeric) = 1.6540268663634652 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.02734579662331600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000002 " "
y[1] (analytic) = 1.6614037140192548 " "
y[1] (numeric) = 1.6614037140192541 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.009463859711666000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12100000000000002 " "
y[1] (analytic) = 1.6688193661572188 " "
y[1] (numeric) = 1.6688193661572182 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.99164719851613800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12200000000000003 " "
y[1] (analytic) = 1.676274042526 " "
y[1] (numeric) = 1.6762740425259992 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.29852755079185700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12300000000000003 " "
y[1] (analytic) = 1.683767964197784 " "
y[1] (numeric) = 1.6837679641977834 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.95620910326837900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12400000000000003 " "
y[1] (analytic) = 1.6913013535766572 " "
y[1] (numeric) = 1.6913013535766566 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.93858736863419500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12500000000000003 " "
y[1] (analytic) = 1.698874434407017 " "
y[1] (numeric) = 1.6988744344070164 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.92103030856194100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12600000000000003 " "
y[1] (analytic) = 1.7064874317820384 " "
y[1] (numeric) = 1.7064874317820378 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.903537772203037000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12700000000000003 " "
y[1] (analytic) = 1.7141405721521958 " "
y[1] (numeric) = 1.714140572152195 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.18147947799269100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12800000000000003 " "
y[1] (analytic) = 1.7218340833338395 " "
y[1] (numeric) = 1.7218340833338386 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.158327554885088000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12900000000000003 " "
y[1] (analytic) = 1.7295681945178305 " "
y[1] (numeric) = 1.7295681945178296 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.13526105831133100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13000000000000003 " "
y[1] (analytic) = 1.7373431362782308 " "
y[1] (numeric) = 1.73734313627823 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.11227978603465600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13100000000000003 " "
y[1] (analytic) = 1.74515914058105 " "
y[1] (numeric) = 1.7451591405810492 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.089383535557718000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13200000000000003 " "
y[1] (analytic) = 1.7530164407930502 " "
y[1] (numeric) = 1.7530164407930493 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.06657210412881600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13300000000000003 " "
y[1] (analytic) = 1.7609152716906087 " "
y[1] (numeric) = 1.7609152716906078 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.043845288748098000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13400000000000004 " "
y[1] (analytic) = 1.7688558694686385 " "
y[1] (numeric) = 1.7688558694686374 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 6.2765036077171500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13500000000000004 " "
y[1] (analytic) = 1.7768384717495669 " "
y[1] (numeric) = 1.7768384717495658 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 6.24830586615998800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13600000000000004 " "
y[1] (analytic) = 1.784863317592375 " "
y[1] (numeric) = 1.7848633175923736 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 7.46425575795518500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13700000000000004 " "
y[1] (analytic) = 1.7929306475016928 " "
y[1] (numeric) = 1.7929306475016917 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 6.19222514921123500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13800000000000004 " "
y[1] (analytic) = 1.80104070343696 " "
y[1] (numeric) = 1.8010407034369589 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 6.16434166371974300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13900000000000004 " "
y[1] (analytic) = 1.8091937288216398 " "
y[1] (numeric) = 1.8091937288216386 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 6.13656241970429900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14000000000000004 " "
y[1] (analytic) = 1.8173899685524986 " "
y[1] (numeric) = 1.8173899685524977 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.887109729165805500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14100000000000004 " "
y[1] (analytic) = 1.8256296690089457 " "
y[1] (numeric) = 1.8256296690089446 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 6.08131563302127900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14200000000000004 " "
y[1] (analytic) = 1.8339130780624315 " "
y[1] (numeric) = 1.8339130780624306 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.843078062557385500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14300000000000004 " "
y[1] (analytic) = 1.8422404450859124 " "
y[1] (numeric) = 1.8422404450859113 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 6.02648274054900400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14400000000000004 " "
y[1] (analytic) = 1.8506120209633727 " "
y[1] (numeric) = 1.8506120209633716 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.99922086341581300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14500000000000005 " "
y[1] (analytic) = 1.8590280580994132 " "
y[1] (numeric) = 1.8590280580994125 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.58323701394867200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14600000000000005 " "
y[1] (analytic) = 1.8674888104289022 " "
y[1] (numeric) = 1.8674888104289016 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.56700297776940570000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14700000000000005 " "
y[1] (analytic) = 1.8759945334266876 " "
y[1] (numeric) = 1.8759945334266868 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.73444034017402200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14800000000000005 " "
y[1] (analytic) = 1.8845454841173745 " "
y[1] (numeric) = 1.8845454841173739 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.53471869153148700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14900000000000005 " "
y[1] (analytic) = 1.8931419210851703 " "
y[1] (numeric) = 1.8931419210851692 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.86444688726117300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000005 " "
y[1] (analytic) = 1.9017841044837869 " "
y[1] (numeric) = 1.901784104483786 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.67023789717292360000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15100000000000005 " "
y[1] (analytic) = 1.9104722960464176 " "
y[1] (numeric) = 1.9104722960464167 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.64899921102308270000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15200000000000005 " "
y[1] (analytic) = 1.9192067590957729 " "
y[1] (numeric) = 1.9192067590957718 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.78480155597322900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15300000000000005 " "
y[1] (analytic) = 1.927987758554184 " "
y[1] (numeric) = 1.9279877585541831 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.60676379172748730000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15400000000000005 " "
y[1] (analytic) = 1.9368155609537758 " "
y[1] (numeric) = 1.936815560953775 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.5857666450322500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15500000000000005 " "
y[1] (analytic) = 1.9456904344467032 " "
y[1] (numeric) = 1.9456904344467023 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.56484959773519600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15600000000000006 " "
y[1] (analytic) = 1.9546126488154565 " "
y[1] (numeric) = 1.9546126488154556 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.544012442763957000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15700000000000006 " "
y[1] (analytic) = 1.9635824754832358 " "
y[1] (numeric) = 1.963582475483235 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.523254972936879000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15800000000000006 " "
y[1] (analytic) = 1.9726001875243924 " "
y[1] (numeric) = 1.9726001875243915 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.50257698096838700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15900000000000006 " "
y[1] (analytic) = 1.9816660596749396 " "
y[1] (numeric) = 1.9816660596749387 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.481978259474336000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000006 " "
y[1] (analytic) = 1.9907803683431335 " "
y[1] (numeric) = 1.9907803683431324 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.576823251221639000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16100000000000006 " "
y[1] (analytic) = 1.999943391620122 " "
y[1] (numeric) = 1.999943391620121 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.441017797911901000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16200000000000006 " "
y[1] (analytic) = 2.009155409290667 " "
y[1] (numeric) = 2.009155409290666 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.420655642629939000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16300000000000006 " "
y[1] (analytic) = 2.018416702843935 " "
y[1] (numeric) = 2.018416702843934 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.400371927405714600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16400000000000006 " "
y[1] (analytic) = 2.0277275554843586 " "
y[1] (numeric) = 2.0277275554843577 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.38016644444114260000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16500000000000006 " "
y[1] (analytic) = 2.0370882521425737 " "
y[1] (numeric) = 2.037088252142573 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.3600389858709104000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16600000000000006 " "
y[1] (analytic) = 2.046499079486424 " "
y[1] (numeric) = 2.046499079486423 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.339989343767585700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16700000000000007 " "
y[1] (analytic) = 2.055960325932041 " "
y[1] (numeric) = 2.0559603259320403 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.32001731014669200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16800000000000007 " "
y[1] (analytic) = 2.065472281654999 " "
y[1] (numeric) = 2.065472281654998 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.30012267697175500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16900000000000007 " "
y[1] (analytic) = 2.0750352386015387 " "
y[1] (numeric) = 2.075035238601538 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.28030523615931140000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000007 " "
y[1] (analytic) = 2.0846494904998707 " "
y[1] (numeric) = 2.08464949049987 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.26056477958389130000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17100000000000007 " "
y[1] (analytic) = 2.0943153328715507 " "
y[1] (numeric) = 2.09431533287155 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.24090109908295900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17200000000000007 " "
y[1] (analytic) = 2.10403306304293 " "
y[1] (numeric) = 2.104033063042929 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.221313986461834000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17300000000000007 " "
y[1] (analytic) = 2.113802980156683 " "
y[1] (numeric) = 2.113802980156682 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.20180323349856400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17400000000000007 " "
y[1] (analytic) = 2.123625385183412 " "
y[1] (numeric) = 2.123625385183411 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.182368631948782400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17500000000000007 " "
y[1] (analytic) = 2.133500580933325 " "
y[1] (numeric) = 2.1335005809333243 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.16300997355051600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17600000000000007 " "
y[1] (analytic) = 2.1434288720679957 " "
y[1] (numeric) = 2.143428872067995 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.143727050028976300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17700000000000007 " "
y[1] (analytic) = 2.153410565112197 " "
y[1] (numeric) = 2.1534105651121966 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.062259826550654200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17800000000000007 " "
y[1] (analytic) = 2.163445968465819 " "
y[1] (numeric) = 2.163445968465818 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.10538757448130800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17900000000000008 " "
y[1] (analytic) = 2.1735353924158556 " "
y[1] (numeric) = 2.173535392415855 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.043165302942057700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000008 " "
y[1] (analytic) = 2.1836791491484853 " "
y[1] (numeric) = 2.1836791491484853 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18100000000000008 " "
y[1] (analytic) = 2.1938775527612187 " "
y[1] (numeric) = 2.193877552761218 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.024220582826653500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18200000000000008 " "
y[1] (analytic) = 2.204130919275132 " "
y[1] (numeric) = 2.2041309192751317 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.01480413874920500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18300000000000008 " "
y[1] (analytic) = 2.2144395666471857 " "
y[1] (numeric) = 2.2144395666471848 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.01084966633290700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18400000000000008 " "
y[1] (analytic) = 2.2248038147826157 " "
y[1] (numeric) = 2.224803814782615 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.99216512394783300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18500000000000008 " "
y[1] (analytic) = 2.2352239855474174 " "
y[1] (numeric) = 2.2352239855474165 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.97355444216301200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18600000000000008 " "
y[1] (analytic) = 2.245700402780905 " "
y[1] (numeric) = 2.2457004027809035 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.93252611924729100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18700000000000008 " "
y[1] (analytic) = 2.2562333923083546 " "
y[1] (numeric) = 2.2562333923083537 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.93655382784415300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18800000000000008 " "
y[1] (analytic) = 2.2668232819537386 " "
y[1] (numeric) = 2.2668232819537377 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.91816347913375330000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18900000000000008 " "
y[1] (analytic) = 2.277470401552535 " "
y[1] (numeric) = 2.277470401552534 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.8998461586796496000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000009 " "
y[1] (analytic) = 2.288175082964628 " "
y[1] (numeric) = 2.288175082964627 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.88160165851196500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1910000000000001 " "
y[1] (analytic) = 2.2989376600872937 " "
y[1] (numeric) = 2.2989376600872924 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.79514465607388400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1920000000000001 " "
y[1] (analytic) = 2.30975846886827 " "
y[1] (numeric) = 2.3097584688682686 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.7679954311541900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1930000000000001 " "
y[1] (analytic) = 2.320637847318916 " "
y[1] (numeric) = 2.3206378473189146 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.74095450132120400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1940000000000001 " "
y[1] (analytic) = 2.331576135527457 " "
y[1] (numeric) = 2.3315761355274556 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.71402155498901500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1950000000000001 " "
y[1] (analytic) = 2.3425736756723183 " "
y[1] (numeric) = 2.342573675672317 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.68719628067974000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1960000000000001 " "
y[1] (analytic) = 2.3536308120355485 " "
y[1] (numeric) = 2.3536308120355476 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.77365224468649800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1970000000000001 " "
y[1] (analytic) = 2.364747891016332 " "
y[1] (numeric) = 2.364747891016331 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.633867502795825000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1980000000000001 " "
y[1] (analytic) = 2.3759252611445887 " "
y[1] (numeric) = 2.375925261144588 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.738242251240892500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1990000000000001 " "
y[1] (analytic) = 2.3871632730946706 " "
y[1] (numeric) = 2.3871632730946692 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.58096567824228800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2000000000000001 " "
y[1] (analytic) = 2.3984622796991406 " "
y[1] (numeric) = 2.3984622796991397 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.7031160640622500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2010000000000001 " "
y[1] (analytic) = 2.4098226359626547 " "
y[1] (numeric) = 2.409822635962654 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.68565887980931650000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2020000000000001 " "
y[1] (analytic) = 2.421244699075925 " "
y[1] (numeric) = 2.4212446990759244 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.834136012851367600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2030000000000001 " "
y[1] (analytic) = 2.432728828429784 " "
y[1] (numeric) = 2.432728828429783 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.65095529481353700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2040000000000001 " "
y[1] (analytic) = 2.4442753856293375 " "
y[1] (numeric) = 2.4442753856293367 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.633708480321018500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2050000000000001 " "
y[1] (analytic) = 2.455884734508218 " "
y[1] (numeric) = 2.455884734508217 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.61653137551661100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2060000000000001 " "
y[1] (analytic) = 2.4675572411429254 " "
y[1] (numeric) = 2.4675572411429245 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.59942377380772700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2070000000000001 " "
y[1] (analytic) = 2.47929327386727 " "
y[1] (numeric) = 2.479293273867269 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.582385468721576700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2080000000000001 " "
y[1] (analytic) = 2.491093203286909 " "
y[1] (numeric) = 2.4910932032869075 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.34812438086342300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2090000000000001 " "
y[1] (analytic) = 2.502957402293979 " "
y[1] (numeric) = 2.5029574022939776 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.322773884721949000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2100000000000001 " "
y[1] (analytic) = 2.51488624608183 " "
y[1] (numeric) = 2.5148862460818293 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.531684270347811000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2110000000000001 " "
y[1] (analytic) = 2.5268801121598554 " "
y[1] (numeric) = 2.526880112159854 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.272381634328626000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2120000000000001 " "
y[1] (analytic) = 2.5389393803684173 " "
y[1] (numeric) = 2.538939380368416 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.247339262416210000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2130000000000001 " "
y[1] (analytic) = 2.5510644328938805 " "
y[1] (numeric) = 2.551064432893879 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.22239898127107700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2140000000000001 " "
y[1] (analytic) = 2.5632556542837386 " "
y[1] (numeric) = 2.5632556542837373 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.197560482598327000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2150000000000001 " "
y[1] (analytic) = 2.575513431461846 " "
y[1] (numeric) = 2.575513431461845 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.17282345832691200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2160000000000001 " "
y[1] (analytic) = 2.58783815374375 " "
y[1] (numeric) = 2.5878381537437485 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.14818760061495900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2170000000000001 " "
y[1] (analytic) = 2.600230212852124 " "
y[1] (numeric) = 2.600230212852123 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.12365260185504300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2180000000000001 " "
y[1] (analytic) = 2.61269000293231 " "
y[1] (numeric) = 2.612690002932309 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.09921815467942600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2190000000000001 " "
y[1] (analytic) = 2.6252179205679558 " "
y[1] (numeric) = 2.6252179205679544 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 5.07488395196524100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2200000000000001 " "
y[1] (analytic) = 2.637814364796764 " "
y[1] (numeric) = 2.637814364796763 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.36709979122642600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2210000000000001 " "
y[1] (analytic) = 2.650479737126346 " "
y[1] (numeric) = 2.650479737126345 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.351010035123262500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22200000000000011 " "
y[1] (analytic) = 2.663214441550177 " "
y[1] (numeric) = 2.663214441550176 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.334986495428972000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22300000000000011 " "
y[1] (analytic) = 2.676018884563663 " "
y[1] (numeric) = 2.6760188845636623 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.3190289680819896000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22400000000000012 " "
y[1] (analytic) = 2.688893475180315 " "
y[1] (numeric) = 2.688893475180314 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.303137249200862600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22500000000000012 " "
y[1] (analytic) = 2.701838624948026 " "
y[1] (numeric) = 2.7018386249480257 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.643655567543769700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22600000000000012 " "
y[1] (analytic) = 2.714854747965468 " "
y[1] (numeric) = 2.714854747965467 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.27155042223062800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22700000000000012 " "
y[1] (analytic) = 2.727942260898585 " "
y[1] (numeric) = 2.7279422608985837 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.88378236096294200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22800000000000012 " "
y[1] (analytic) = 2.741101582997207 " "
y[1] (numeric) = 2.7411015829972065 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.620112193596566800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22900000000000012 " "
y[1] (analytic) = 2.7543331361117755 " "
y[1] (numeric) = 2.754333136111775 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.612329329475999700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000012 " "
y[1] (analytic) = 2.767637344710172 " "
y[1] (numeric) = 2.767637344710171 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.209157519852499000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23100000000000012 " "
y[1] (analytic) = 2.781014635894668 " "
y[1] (numeric) = 2.781014635894667 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.19372076736443800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23200000000000012 " "
y[1] (analytic) = 2.7944654394189863 " "
y[1] (numeric) = 2.7944654394189854 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.178348199163242000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23300000000000012 " "
y[1] (analytic) = 2.807990187705476 " "
y[1] (numeric) = 2.807990187705475 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.16303961313302300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23400000000000012 " "
y[1] (analytic) = 2.821589315862403 " "
y[1] (numeric) = 2.8215893158624024 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.573897403684807000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23500000000000013 " "
y[1] (analytic) = 2.835263261701359 " "
y[1] (numeric) = 2.835263261701358 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.69892037027536070000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23600000000000013 " "
y[1] (analytic) = 2.8490124657547797 " "
y[1] (numeric) = 2.8490124657547793 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.55874786505158900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23700000000000013 " "
y[1] (analytic) = 2.8628373712935944 " "
y[1] (numeric) = 2.862837371293594 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.55122052793867800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23800000000000013 " "
y[1] (analytic) = 2.8767384243449787 " "
y[1] (numeric) = 2.876738424344978 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.0874493564786300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23900000000000013 " "
y[1] (analytic) = 2.890716073710237 " "
y[1] (numeric) = 2.8907160737102364 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.536260215553005300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000013 " "
y[1] (analytic) = 2.904770770982803 " "
y[1] (numeric) = 2.904770770982802 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.05765407918786700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24100000000000013 " "
y[1] (analytic) = 2.918902970566357 " "
y[1] (numeric) = 2.9189029705663567 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.521425050192386500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24200000000000013 " "
y[1] (analytic) = 2.9331131296930733 " "
y[1] (numeric) = 2.9331131296930724 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.02810829459232600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24300000000000013 " "
y[1] (analytic) = 2.947401708441978 " "
y[1] (numeric) = 2.9474017084419777 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.506714230971970300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24400000000000013 " "
y[1] (analytic) = 2.961769169757446 " "
y[1] (numeric) = 2.9617691697574458 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.49940520140680400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24500000000000013 " "
y[1] (analytic) = 2.9762159794678067 " "
y[1] (numeric) = 2.9762159794678062 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.492126958909321400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24600000000000014 " "
y[1] (analytic) = 2.9907426063040865 " "
y[1] (numeric) = 2.9907426063040856 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.9697588078223900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24700000000000014 " "
y[1] (analytic) = 3.0053495219188706 " "
y[1] (numeric) = 3.0053495219188697 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.95532487393691400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24800000000000014 " "
y[1] (analytic) = 3.020037200905297 " "
y[1] (numeric) = 3.0200372009052963 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.94095191752565700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24900000000000014 " "
y[1] (analytic) = 3.0348061208161736 " "
y[1] (numeric) = 3.034806120816173 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.463319870103037300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (analytic) = 3.0496567621832282 " "
y[1] (numeric) = 3.0496567621832273 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.91238814385224250000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2510000000000001 " "
y[1] (analytic) = 3.0645896085364828 " "
y[1] (numeric) = 3.0645896085364823 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.449098465298721300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2520000000000001 " "
y[1] (analytic) = 3.079605146423766 " "
y[1] (numeric) = 3.0796051464237655 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.442032951418357500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2530000000000001 " "
y[1] (analytic) = 3.09470386543035 " "
y[1] (numeric) = 3.0947038654303496 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.434997431614696800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2540000000000001 " "
y[1] (analytic) = 3.1098862581987237 " "
y[1] (numeric) = 3.109886258198723 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.427991807350804700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2550000000000001 " "
y[1] (analytic) = 3.1251528204484975 " "
y[1] (numeric) = 3.125152820448497 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.42101598022438600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2560000000000001 " "
y[1] (analytic) = 3.140504050996444 " "
y[1] (numeric) = 3.1405040509964435 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.414069851969012600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2570000000000001 " "
y[1] (analytic) = 3.1559404517766723 " "
y[1] (numeric) = 3.1559404517766714 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.814306648910676000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2580000000000001 " "
y[1] (analytic) = 3.1714625278609376 " "
y[1] (numeric) = 3.1714625278609367 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.80053259938460200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2590000000000001 " "
y[1] (analytic) = 3.187070787479092 " "
y[1] (numeric) = 3.1870707874790916 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.393408679828313800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (analytic) = 3.20276574203967 " "
y[1] (numeric) = 3.202765742039669 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.77316073430488200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2610000000000001 " "
y[1] (analytic) = 3.2185479061506097 " "
y[1] (numeric) = 3.218547906150609 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.759562528191132300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2620000000000001 " "
y[1] (analytic) = 3.234417797640122 " "
y[1] (numeric) = 3.2344177976401216 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.373011273231542800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2630000000000001 " "
y[1] (analytic) = 3.2503759375776964 " "
y[1] (numeric) = 3.2503759375776955 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.7325405945566700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2640000000000001 " "
y[1] (analytic) = 3.2664228502952453 " "
y[1] (numeric) = 3.2664228502952444 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.719116478198297400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2650000000000001 " "
y[1] (analytic) = 3.282559063408397 " "
y[1] (numeric) = 3.2825590634083968 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.352875001703546200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2660000000000001 " "
y[1] (analytic) = 3.2987851078379324 " "
y[1] (numeric) = 3.298785107837932 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.346220488248549800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2670000000000001 " "
y[1] (analytic) = 3.3151015178313585 " "
y[1] (numeric) = 3.3151015178313585 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2680000000000001 " "
y[1] (analytic) = 3.3315088309846397 " "
y[1] (numeric) = 3.3315088309846397 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.26900000000000013 " "
y[1] (analytic) = 3.3480075882640654 " "
y[1] (numeric) = 3.348007588264066 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.326428325332207300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (analytic) = 3.3645983340282744 " "
y[1] (numeric) = 3.3645983340282744 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27100000000000013 " "
y[1] (analytic) = 3.381281616050418 " "
y[1] (numeric) = 3.3812816160504187 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.31337540103740600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27200000000000013 " "
y[1] (analytic) = 3.3980579855404875 " "
y[1] (numeric) = 3.398057985540488 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.306891205917508000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27300000000000013 " "
y[1] (analytic) = 3.4149279971677764 " "
y[1] (numeric) = 3.4149279971677764 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27400000000000013 " "
y[1] (analytic) = 3.431892209083506 " "
y[1] (numeric) = 3.431892209083506 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27500000000000013 " "
y[1] (analytic) = 3.4489511829436004 " "
y[1] (numeric) = 3.4489511829436013 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.575213079537082600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27600000000000013 " "
y[1] (analytic) = 3.4661054839316194 " "
y[1] (numeric) = 3.466105483931619 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.281233972563149400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27700000000000014 " "
y[1] (analytic) = 3.483355680781835 " "
y[1] (numeric) = 3.4833556807818344 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.274889074062018600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27800000000000014 " "
y[1] (analytic) = 3.5007023458024813 " "
y[1] (numeric) = 3.5007023458024813 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27900000000000014 " "
y[1] (analytic) = 3.5181460548991508 " "
y[1] (numeric) = 3.5181460548991503 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.262281903366836200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (analytic) = 3.535687387598348 " "
y[1] (numeric) = 3.535687387598348 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28100000000000014 " "
y[1] (analytic) = 3.553326927071211 " "
y[1] (numeric) = 3.5533269270712116 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.249784269684686800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28200000000000014 " "
y[1] (analytic) = 3.57106526015739 " "
y[1] (numeric) = 3.5710652601573893 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.243576293059651400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28300000000000014 " "
y[1] (analytic) = 3.5889029773890777 " "
y[1] (numeric) = 3.5889029773890786 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.474790835238109300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28400000000000014 " "
y[1] (analytic) = 3.6068406730152294 " "
y[1] (numeric) = 3.6068406730152294 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28500000000000014 " "
y[1] (analytic) = 3.624878945025911 " "
y[1] (numeric) = 3.624878945025911 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28600000000000014 " "
y[1] (analytic) = 3.643018395176845 " "
y[1] (numeric) = 3.643018395176845 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28700000000000014 " "
y[1] (analytic) = 3.6612596290141033 " "
y[1] (numeric) = 3.6612596290141033 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28800000000000014 " "
y[1] (analytic) = 3.679603255898975 " "
y[1] (numeric) = 3.6796032558989755 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.206894273555494500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28900000000000015 " "
y[1] (analytic) = 3.6980498890330034 " "
y[1] (numeric) = 3.698049889033004 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.200874036791825800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (analytic) = 3.716600145483188 " "
y[1] (numeric) = 3.7166001454831883 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.194880246640918800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29100000000000015 " "
y[1] (analytic) = 3.735254646207364 " "
y[1] (numeric) = 3.735254646207365 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.377825620542224300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29200000000000015 " "
y[1] (analytic) = 3.754014016079751 " "
y[1] (numeric) = 3.754014016079752 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.36594327004573600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29300000000000015 " "
y[1] (analytic) = 3.7728788839166745 " "
y[1] (numeric) = 3.7728788839166754 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.35411325681914200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29400000000000015 " "
y[1] (analytic) = 3.7918498825024636 " "
y[1] (numeric) = 3.7918498825024645 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.342335396236636700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29500000000000015 " "
y[1] (analytic) = 3.8109276486155252 " "
y[1] (numeric) = 3.810927648615526 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.330609504021395600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29600000000000015 " "
y[1] (analytic) = 3.8301128230545953 " "
y[1] (numeric) = 3.830112823054596 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.31893539624711180000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29700000000000015 " "
y[1] (analytic) = 3.8494060506651664 " "
y[1] (numeric) = 3.8494060506651673 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.30731288933951400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29800000000000015 " "
y[1] (analytic) = 3.8688079803660993 " "
y[1] (numeric) = 3.8688079803660997 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.147870900038929100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29900000000000015 " "
y[1] (analytic) = 3.8883192651764094 " "
y[1] (numeric) = 3.88831926517641 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.14211097279820390000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (analytic) = 3.907940562242244 " "
y[1] (numeric) = 3.9079405622422443 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.136376571692941100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30100000000000016 " "
y[1] (analytic) = 3.927672532864034 " "
y[1] (numeric) = 3.927672532864035 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.261335211294896500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30200000000000016 " "
y[1] (analytic) = 3.94751584252384 " "
y[1] (numeric) = 3.94751584252384 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30300000000000016 " "
y[1] (analytic) = 3.9674711609128717 " "
y[1] (numeric) = 3.9674711609128717 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30400000000000016 " "
y[1] (analytic) = 3.9875391619592095 " "
y[1] (numeric) = 3.98753916195921 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.113692409811636600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30500000000000016 " "
y[1] (analytic) = 4.007720523855706 " "
y[1] (numeric) = 4.007720523855706 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30600000000000016 " "
y[1] (analytic) = 4.0280159290880775 " "
y[1] (numeric) = 4.0280159290880775 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30700000000000016 " "
y[1] (analytic) = 4.04842606446319 " "
y[1] (numeric) = 4.04842606446319 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30800000000000016 " "
y[1] (analytic) = 4.068951621137539 " "
y[1] (numeric) = 4.068951621137539 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30900000000000016 " "
y[1] (analytic) = 4.089593294645918 " "
y[1] (numeric) = 4.089593294645917 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.171801339910561500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (analytic) = 4.1103517849302875 " "
y[1] (numeric) = 4.110351784930287 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.160833101819748500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31100000000000017 " "
y[1] (analytic) = 4.13122779636884 " "
y[1] (numeric) = 4.131227796368838 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 4.29982786464011200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31200000000000017 " "
y[1] (analytic) = 4.152222037805259 " "
y[1] (numeric) = 4.152222037805259 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31300000000000017 " "
y[1] (analytic) = 4.1733352225781895 " "
y[1] (numeric) = 4.173335222578189 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.128222086965324600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31400000000000017 " "
y[1] (analytic) = 4.194568068550890 " "
y[1] (numeric) = 4.19456806855089 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.117449055981029400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31500000000000017 " "
y[1] (analytic) = 4.215921298141107 " "
y[1] (numeric) = 4.215921298141107 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31600000000000017 " "
y[1] (analytic) = 4.237395638351142 " "
y[1] (numeric) = 4.237395638351141 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.09604789239301200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31700000000000017 " "
y[1] (analytic) = 4.258991820798123 " "
y[1] (numeric) = 4.258991820798121 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 4.17083881383779300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31800000000000017 " "
y[1] (analytic) = 4.28071058174449 " "
y[1] (numeric) = 4.280710581744488 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 4.14967750208504700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3190000000000002 " "
y[1] (analytic) = 4.302552662128686 " "
y[1] (numeric) = 4.302552662128684 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 4.12861149855490400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (analytic) = 4.324518807596050 " "
y[1] (numeric) = 4.32451880759605 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.053820226518689200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3210000000000002 " "
y[1] (analytic) = 4.346609768529942 " "
y[1] (numeric) = 4.34660976852994 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 4.08676401608748200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3220000000000002 " "
y[1] (analytic) = 4.368826300083045 " "
y[1] (numeric) = 4.368826300083043 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 4.065981839027302000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3230000000000002 " "
y[1] (analytic) = 4.3911691622089215 " "
y[1] (numeric) = 4.391169162208920 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.02264678697401470000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3240000000000002 " "
y[1] (analytic) = 4.413639119693759 " "
y[1] (numeric) = 4.413639119693758 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.012349436855978600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3250000000000002 " "
y[1] (analytic) = 4.436236942188342 " "
y[1] (numeric) = 4.436236942188339 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 6.00629608793166300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3260000000000002 " "
y[1] (analytic) = 4.458963404240234 " "
y[1] (numeric) = 4.458963404240231 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.97568317462876300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3270000000000002 " "
y[1] (analytic) = 4.4818192853262 " "
y[1] (numeric) = 4.481819285326198 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.963472702293399700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3280000000000002 " "
y[1] (analytic) = 4.504805369884829 " "
y[1] (numeric) = 4.504805369884827 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.943248805543102500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3290000000000002 " "
y[1] (analytic) = 4.52792244734939 " "
y[1] (numeric) = 4.527922447349387 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.88467512437226800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (analytic) = 4.551171312180909 " "
y[1] (numeric) = 4.551171312180906 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.85461428790633100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3310000000000002 " "
y[1] (analytic) = 4.57455276390148 " "
y[1] (numeric) = 4.574552763901478 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.883126790924270600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3320000000000002 " "
y[1] (analytic) = 4.598067607127797 " "
y[1] (numeric) = 4.5980676071277955 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.863268205640541500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3330000000000002 " "
y[1] (analytic) = 4.6217166516049195 " "
y[1] (numeric) = 4.621716651604917 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.7652501439591700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3340000000000002 " "
y[1] (analytic) = 4.64550071224026 " "
y[1] (numeric) = 4.645500712240256 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 7.64764424519317300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3350000000000002 " "
y[1] (analytic) = 4.66942060913782 " "
y[1] (numeric) = 4.669420609137816 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 7.60846789395673600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3360000000000002 " "
y[1] (analytic) = 4.693477167632652 " "
y[1] (numeric) = 4.693477167632649 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 7.5694704627538600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3370000000000002 " "
y[1] (analytic) = 4.717671218325554 " "
y[1] (numeric) = 4.7176712183255525 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.765325638845035000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3380000000000002 " "
y[1] (analytic) = 4.742003597118016 " "
y[1] (numeric) = 4.742003597118012 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 7.49200966646184400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3390000000000002 " "
y[1] (analytic) = 4.7664751452473775 " "
y[1] (numeric) = 4.766475145247375 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.59015871876971200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (analytic) = 4.791086709322268 " "
y[1] (numeric) = 4.791086709322267 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.707628242135338500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3410000000000002 " "
y[1] (analytic) = 4.815839141358256 " "
y[1] (numeric) = 4.8158391413582535 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.5328576825115290000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3420000000000002 " "
y[1] (analytic) = 4.840733298813750 " "
y[1] (numeric) = 4.840733298813748 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.50440417726243100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3430000000000002 " "
y[1] (analytic) = 4.8657700446261645 " "
y[1] (numeric) = 4.86577004462616 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 9.1268022487113210000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3440000000000002 " "
y[1] (analytic) = 4.890950247248301 " "
y[1] (numeric) = 4.890950247248298 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.4478887013816400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3450000000000002 " "
y[1] (analytic) = 4.916274780685021 " "
y[1] (numeric) = 4.916274780685020 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.61321715860791900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3460000000000002 " "
y[1] (analytic) = 4.941744524530132 " "
y[1] (numeric) = 4.9417445245301295 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.3918919642122200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3470000000000002 " "
y[1] (analytic) = 4.967360364003544 " "
y[1] (numeric) = 4.967360364003541 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.36408688688903600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3480000000000002 " "
y[1] (analytic) = 4.993123189988686 " "
y[1] (numeric) = 4.993123189988683 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.336410013762174000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3490000000000002 " "
y[1] (analytic) = 5.019033899070170 " "
y[1] (numeric) = 5.019033899070168 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.308860853866736000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3500000000000002 " "
y[1] (analytic) = 5.04509339357172 " "
y[1] (numeric) = 5.045093393571717 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.28143891745479400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3510000000000002 " "
y[1] (analytic) = 5.071302581594355 " "
y[1] (numeric) = 5.071302581594352 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.254143715997082000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3520000000000002 " "
y[1] (analytic) = 5.097662377054844 " "
y[1] (numeric) = 5.097662377054842 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.484649841456417500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3530000000000002 " "
y[1] (analytic) = 5.12417369972442 " "
y[1] (numeric) = 5.124173699724417 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 5.1999315699303400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3540000000000002 " "
y[1] (analytic) = 5.150837475267752 " "
y[1] (numeric) = 5.150837475267750 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.44867576958038550000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3550000000000002 " "
y[1] (analytic) = 5.1776546352822095 " "
y[1] (numeric) = 5.177654635282209 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.71540684395554500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3560000000000002 " "
y[1] (analytic) = 5.204626117337368 " "
y[1] (numeric) = 5.204626117337368 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3570000000000002 " "
y[1] (analytic) = 5.2317528650148075 " "
y[1] (numeric) = 5.231752865014806 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.39533782506988300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3580000000000002 " "
y[1] (analytic) = 5.259035827948169 " "
y[1] (numeric) = 5.259035827948168 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.68886170156907100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3590000000000002 " "
y[1] (analytic) = 5.286475961863508 " "
y[1] (numeric) = 5.286475961863507 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.680095447529545000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3600000000000002 " "
y[1] (analytic) = 5.314074228619905 " "
y[1] (numeric) = 5.314074228619903 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.34273998250412150000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3610000000000002 " "
y[1] (analytic) = 5.34183159625036 " "
y[1] (numeric) = 5.341831596250360 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.662685173983343700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3620000000000002 " "
y[1] (analytic) = 5.369749039002985 " "
y[1] (numeric) = 5.3697490390029845 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.654040837381546300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3630000000000002 " "
y[1] (analytic) = 5.397827537382455 " "
y[1] (numeric) = 5.397827537382456 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.645436823516643300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3640000000000002 " "
y[1] (analytic) = 5.426068078191772 " "
y[1] (numeric) = 5.426068078191771 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.636872974870800500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3650000000000002 " "
y[1] (analytic) = 5.454471654574283 " "
y[1] (numeric) = 5.454471654574283 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3660000000000002 " "
y[1] (analytic) = 5.483039266056028 " "
y[1] (numeric) = 5.483039266056027 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.619865145228105400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3670000000000002 " "
y[1] (analytic) = 5.5117719185883445 " "
y[1] (numeric) = 5.511771918588343 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.22284170251951330000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3680000000000002 " "
y[1] (analytic) = 5.540670624590788 " "
y[1] (numeric) = 5.5406706245907875 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.603016096568134200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3690000000000002 " "
y[1] (analytic) = 5.569736402994343 " "
y[1] (numeric) = 5.569736402994343 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (analytic) = 5.598970279284926 " "
y[1] (numeric) = 5.598970279284924 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.75897375086741400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3710000000000002 " "
y[1] (analytic) = 5.6283732855471875 " "
y[1] (numeric) = 5.6283732855471875 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3720000000000002 " "
y[1] (analytic) = 5.657946460508643 " "
y[1] (numeric) = 5.657946460508643 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3730000000000002 " "
y[1] (analytic) = 5.687690849584065 " "
y[1] (numeric) = 5.6876908495840635 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.12315997190697140000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3740000000000002 " "
y[1] (analytic) = 5.717607504920213 " "
y[1] (numeric) = 5.717607504920213 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3750000000000002 " "
y[1] (analytic) = 5.747697485440875 " "
y[1] (numeric) = 5.747697485440872 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.63583072325873100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3760000000000002 " "
y[1] (analytic) = 5.777961856892184 " "
y[1] (numeric) = 5.777961856892182 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.61154871751534900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3770000000000002 " "
y[1] (analytic) = 5.8084016918883 " "
y[1] (numeric) = 5.808401691888298 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.587381177203225000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3780000000000002 " "
y[1] (analytic) = 5.839018069957364 " "
y[1] (numeric) = 5.839018069957362 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 3.042218431451474400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3790000000000002 " "
y[1] (analytic) = 5.869812077587790 " "
y[1] (numeric) = 5.869812077587788 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.513129224513647400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000002 " "
y[1] (analytic) = 5.9007848082748735 " "
y[1] (numeric) = 5.900784808274873 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.505186934549116500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3810000000000002 " "
y[1] (analytic) = 5.931937362567726 " "
y[1] (numeric) = 5.931937362567724 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.99456439073275800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38200000000000023 " "
y[1] (analytic) = 5.963270848116519 " "
y[1] (numeric) = 5.963270848116518 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.48941485691640800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38300000000000023 " "
y[1] (analytic) = 5.994786379720080 " "
y[1] (numeric) = 5.994786379720079 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.96316953913409560000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38400000000000023 " "
y[1] (analytic) = 6.026485079373796 " "
y[1] (numeric) = 6.026485079373793 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.421375352309417000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38500000000000023 " "
y[1] (analytic) = 6.0583680763178505 " "
y[1] (numeric) = 6.058368076317849 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.93207150345325800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38600000000000023 " "
y[1] (analytic) = 6.090436507085818 " "
y[1] (numeric) = 6.0904365070858155 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.37494957217001770000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38700000000000023 " "
y[1] (analytic) = 6.1226915155535595 " "
y[1] (numeric) = 6.122691515553557 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.35190185938915800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38800000000000023 " "
y[1] (analytic) = 6.155134252988482 " "
y[1] (numeric) = 6.155134252988480 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.328963674198776000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38900000000000023 " "
y[1] (analytic) = 6.187765878099134 " "
y[1] (numeric) = 6.187765878099130 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 7.17689095868775400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39000000000000024 " "
y[1] (analytic) = 6.22058755708513 " "
y[1] (numeric) = 6.2205875570851275 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.283414122297050700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39100000000000024 " "
y[1] (analytic) = 6.253600463687455 " "
y[1] (numeric) = 6.253600463687452 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.68106916876111400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39200000000000024 " "
y[1] (analytic) = 6.286805779239072 " "
y[1] (numeric) = 6.286805779239067 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 7.06382900067597300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39300000000000024 " "
y[1] (analytic) = 6.320204692715914 " "
y[1] (numeric) = 6.32020469271591 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 7.02650042904273200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39400000000000024 " "
y[1] (analytic) = 6.353798400788223 " "
y[1] (numeric) = 6.353798400788220 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.193610012508149000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39500000000000024 " "
y[1] (analytic) = 6.387588107872241 " "
y[1] (numeric) = 6.387588107872238 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.17142623178305500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39600000000000024 " "
y[1] (analytic) = 6.421575026182249 " "
y[1] (numeric) = 6.4215750261822455 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.53246464351076500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39700000000000024 " "
y[1] (analytic) = 6.455760375782990 " "
y[1] (numeric) = 6.455760375782985 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.87896055615603700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39800000000000024 " "
y[1] (analytic) = 6.490145384642433 " "
y[1] (numeric) = 6.49014538464243 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.10550935485272700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39900000000000024 " "
y[1] (analytic) = 6.524731288684930 " "
y[1] (numeric) = 6.524731288684926 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.444996156334518000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (analytic) = 6.559519331844706 " "
y[1] (numeric) = 6.559519331844702 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.77014865546822400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40100000000000025 " "
y[1] (analytic) = 6.594510766119752 " "
y[1] (numeric) = 6.594510766119749 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.38738020878376400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40200000000000025 " "
y[1] (analytic) = 6.6297068516260795 " "
y[1] (numeric) = 6.629706851626076 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.358779442757896000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40300000000000025 " "
y[1] (analytic) = 6.665108856652347 " "
y[1] (numeric) = 6.665108856652345 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.99773704587126470000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40400000000000025 " "
y[1] (analytic) = 6.700718057714878 " "
y[1] (numeric) = 6.700718057714876 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.97649212539626300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40500000000000025 " "
y[1] (analytic) = 6.73653573961305 " "
y[1] (numeric) = 6.736535739613047 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.95534939929440400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40600000000000025 " "
y[1] (analytic) = 6.772563195485073 " "
y[1] (numeric) = 6.772563195485070 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.934308447467403400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40700000000000025 " "
y[1] (analytic) = 6.808801726864162 " "
y[1] (numeric) = 6.808801726864158 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.217825134756460000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40800000000000025 " "
y[1] (analytic) = 6.845252643735082 " "
y[1] (numeric) = 6.845252643735077 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.48755032082712700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40900000000000025 " "
y[1] (analytic) = 6.881917264591107 " "
y[1] (numeric) = 6.881917264591104 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.871792055405784400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (analytic) = 6.91879691649137 " "
y[1] (numeric) = 6.918796916491367 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 5.13487203292872100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41100000000000025 " "
y[1] (analytic) = 6.955892935118594 " "
y[1] (numeric) = 6.955892935118591 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.83061568651781870000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41200000000000025 " "
y[1] (analytic) = 6.993206664837249 " "
y[1] (numeric) = 6.993206664837246 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.81017662826697900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41300000000000026 " "
y[1] (analytic) = 7.030739458752100 " "
y[1] (numeric) = 7.030739458752099 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.526557625725956400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41400000000000026 " "
y[1] (analytic) = 7.06849267876717 " "
y[1] (numeric) = 7.068492678767167 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.7695947073755800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41500000000000026 " "
y[1] (analytic) = 7.1064676956450965 " "
y[1] (numeric) = 7.106467695645092 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.24908504294199900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41600000000000026 " "
y[1] (analytic) = 7.144665889066925 " "
y[1] (numeric) = 7.144665889066921 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.97253998152246200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41700000000000026 " "
y[1] (analytic) = 7.183088647692311 " "
y[1] (numeric) = 7.183088647692306 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 7.41891236426938100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41800000000000026 " "
y[1] (analytic) = 7.221737369220123 " "
y[1] (numeric) = 7.221737369220118 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 7.37920841723470100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41900000000000026 " "
y[1] (analytic) = 7.260613460449496 " "
y[1] (numeric) = 7.260613460449492 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.89313154894291400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (analytic) = 7.299718337341295 " "
y[1] (numeric) = 7.299718337341291 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.86691885168609300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42100000000000026 " "
y[1] (analytic) = 7.339053425080002 " "
y[1] (numeric) = 7.339053425079998 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.05104206398690400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42200000000000026 " "
y[1] (analytic) = 7.378620158136045 " "
y[1] (numeric) = 7.378620158136040 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 6.01859426739004800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42300000000000026 " "
y[1] (analytic) = 7.418419980328562 " "
y[1] (numeric) = 7.418419980328557 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 7.18356541195006100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42400000000000027 " "
y[1] (analytic) = 7.458454344888593 " "
y[1] (numeric) = 7.458454344888586 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 9.52667540623946200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42500000000000027 " "
y[1] (analytic) = 7.498724714522711 " "
y[1] (numeric) = 7.498724714522709 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.55331787809198400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42600000000000027 " "
y[1] (analytic) = 7.539232561477135 " "
y[1] (numeric) = 7.539232561477130 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 5.89037685505557200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42700000000000027 " "
y[1] (analytic) = 7.5799793676022125 " "
y[1] (numeric) = 7.579979367602209 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.68697011760381200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42800000000000027 " "
y[1] (analytic) = 7.620966624417436 " "
y[1] (numeric) = 7.620966624417433 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.49632191087578600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42900000000000027 " "
y[1] (analytic) = 7.662195833176864 " "
y[1] (numeric) = 7.662195833176859 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.95501737912542700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000027 " "
y[1] (analytic) = 7.703668504935000 " "
y[1] (numeric) = 7.703668504934995 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 8.07050424602003800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43100000000000027 " "
y[1] (analytic) = 7.745386160613159 " "
y[1] (numeric) = 7.7453861606131555 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.58687740692228060000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4320000000000003 " "
y[1] (analytic) = 7.787350331066277 " "
y[1] (numeric) = 7.787350331066272 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 5.70269977553785100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4330000000000003 " "
y[1] (analytic) = 7.8295625571501795 " "
y[1] (numeric) = 7.829562557150174 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.80634515568700800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4340000000000003 " "
y[1] (analytic) = 7.872024389789340 " "
y[1] (numeric) = 7.8720243897893365 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.384815807426227500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4350000000000003 " "
y[1] (analytic) = 7.914737390045109 " "
y[1] (numeric) = 7.914737390045105 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.48873222662950900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4360000000000003 " "
y[1] (analytic) = 7.957703129184402 " "
y[1] (numeric) = 7.957703129184397 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.69674456522096600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4370000000000003 " "
y[1] (analytic) = 8.000923188748882 " "
y[1] (numeric) = 8.000923188748876 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.66056952739483500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4380000000000003 " "
y[1] (analytic) = 8.044399160624632 " "
y[1] (numeric) = 8.044399160624625 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 8.83276328750608600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4390000000000003 " "
y[1] (analytic) = 8.08813264711229 " "
y[1] (numeric) = 8.088132647112289 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.196250873845972000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (analytic) = 8.132125260997725 " "
y[1] (numeric) = 8.132125260997718 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 8.73747898557239100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4410000000000003 " "
y[1] (analytic) = 8.176378625623112 " "
y[1] (numeric) = 8.176378625623109 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.34509437670488600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4420000000000003 " "
y[1] (analytic) = 8.220894374958633 " "
y[1] (numeric) = 8.220894374958629 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.32156589874490200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4430000000000003 " "
y[1] (analytic) = 8.265674153674565 " "
y[1] (numeric) = 8.265674153674562 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.29815355982925640000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4440000000000003 " "
y[1] (analytic) = 8.31071961721394 " "
y[1] (numeric) = 8.310719617213937 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.13742843125268500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4450000000000003 " "
y[1] (analytic) = 8.35603243186569 " "
y[1] (numeric) = 8.356032431865685 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.37751296641497700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4460000000000003 " "
y[1] (analytic) = 8.401614274838296 " "
y[1] (numeric) = 8.401614274838295 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.114304205467037500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4470000000000003 " "
y[1] (analytic) = 8.447466834333992 " "
y[1] (numeric) = 8.447466834333987 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.30848350483154200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4480000000000003 " "
y[1] (analytic) = 8.493591809623425 " "
y[1] (numeric) = 8.49359180962342 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.27422489524725900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4490000000000003 " "
y[1] (analytic) = 8.539990911120896 " "
y[1] (numeric) = 8.539990911120894 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.080045351204125600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (analytic) = 8.586665860460114 " "
y[1] (numeric) = 8.58666586046011 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.13747749887420200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4510000000000003 " "
y[1] (analytic) = 8.633618390570447 " "
y[1] (numeric) = 8.633618390570444 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.11497650009727100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4520000000000003 " "
y[1] (analytic) = 8.680850245753755 " "
y[1] (numeric) = 8.680850245753753 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.04629361077753500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4530000000000003 " "
y[1] (analytic) = 8.728363181761736 " "
y[1] (numeric) = 8.72836318176173 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.10546377049944200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4540000000000003 " "
y[1] (analytic) = 8.776158965873801 " "
y[1] (numeric) = 8.776158965873798 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.04814189512208100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4550000000000003 " "
y[1] (analytic) = 8.82423937697555 " "
y[1] (numeric) = 8.824239376975543 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 8.05216977243464200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4560000000000003 " "
y[1] (analytic) = 8.872606205637716 " "
y[1] (numeric) = 8.87260620563771 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.00620651327298100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE for equation 1"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ;"
Iterations = 357
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds
"Expected Time Remaining "= 0 Years 0 Days 0 Hours 4 Minutes 33 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 4 Minutes 32 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 7 Minutes 33 Seconds
"Time to Timeout " Unknown
Percent Done = 39.777777777777814 "%"
(%o58) true
(%o58) diffeq.max