(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/local/share/maxima/5.26.0/share/contrib/stringproc/stringproc.mac
(%i3) display_alot(iter) := if iter >= 0
then (ind_var : array_x , omniout_float(ALWAYS,
1
"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 : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
abserr 100.0
20, " "), if abs(analytic_val_y) # 0.0 then relerr : -------------------
abs(analytic_val_y)
else relerr : - 1.0, 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_float(ALWAYS, "h ", 4, glob_h,
20, " "))
(%o3) display_alot(iter) := if iter >= 0
then (ind_var : array_x , omniout_float(ALWAYS,
1
"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 : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
abserr 100.0
20, " "), if abs(analytic_val_y) # 0.0 then relerr : -------------------
abs(analytic_val_y)
else relerr : - 1.0, 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_float(ALWAYS, "h ", 4, glob_h,
20, " "))
(%i4) adjust_for_pole(h_param) := block(hnew : h_param,
glob_normmax : glob_small_float, if !array_y_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if glob_look_poles
and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float)
! 1! 1
array_pole
1
then (sz2 : -----------, if sz2 < hnew
10.0
then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(),
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)
1
(%o4) adjust_for_pole(h_param) := block(hnew : h_param,
glob_normmax : glob_small_float, if !array_y_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if glob_look_poles
and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float)
! 1! 1
array_pole
1
then (sz2 : -----------, if sz2 < hnew
10.0
then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(),
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)
1
(%i5) prog_report(x_start, x_end) := (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)), 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, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o5) prog_report(x_start, x_end) := (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)), 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, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((!array_y_higher ! < glob_small_float)
! 1, m!
or (!array_y_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y_higher ! < glob_small_float)) do m : m - 1,
! 1, m - 2!
array_y_higher array_y_higher
1, m 1, m - 1
if m > 10 then (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
hdrc : convfloat(m - 1) rm0 - convfloat(m - 2) rm1,
glob_h
if abs(hdrc) > glob_small_float then (rcs : ------,
hdrc
convfloat(m - 1) rm0
ord_no : 2.0 - convfloat(m) + --------------------, array_real_pole : rcs,
hdrc 1, 1
array_real_pole : ord_no) else (array_real_pole : glob_large_float,
1, 2 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 !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 (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
elseif (!array_y_higher ! >= glob_large_float)
! 1, m!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 5!
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
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 (abs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (abs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) 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,
1, 1
array_complex_pole : ord_no), found : false,
1, 2
if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
1, 1 1, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
1, 1 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 : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float,
1
array_pole : glob_large_float, if array_pole > array_poles
2 1 1, 1
then (array_pole : array_poles , array_pole : array_poles ),
1 1, 1 2 1, 2
display_pole())
(%o6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((!array_y_higher ! < glob_small_float)
! 1, m!
or (!array_y_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y_higher ! < glob_small_float)) do m : m - 1,
! 1, m - 2!
array_y_higher array_y_higher
1, m 1, m - 1
if m > 10 then (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
hdrc : convfloat(m - 1) rm0 - convfloat(m - 2) rm1,
glob_h
if abs(hdrc) > glob_small_float then (rcs : ------,
hdrc
convfloat(m - 1) rm0
ord_no : 2.0 - convfloat(m) + --------------------, array_real_pole : rcs,
hdrc 1, 1
array_real_pole : ord_no) else (array_real_pole : glob_large_float,
1, 2 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 !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 (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
elseif (!array_y_higher ! >= glob_large_float)
! 1, m!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y_higher ! >= glob_large_float)
! 1, m - 5!
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
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 (abs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (abs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) 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,
1, 1
array_complex_pole : ord_no), found : false,
1, 2
if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
1, 1 1, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
1, 1 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 : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float,
1
array_pole : glob_large_float, if array_pole > array_poles
2 1 1, 1
then (array_pole : array_poles , array_pole : array_poles ),
1 1, 1 2 1, 2
display_pole())
(%i7) get_norms() := if not glob_initial_pass
then (set_z(array_norms, 1 + glob_max_terms), iii : 1,
while iii <= glob_max_terms do (if !array_y ! > array_norms
! iii! iii
then array_norms : !array_y !, iii : 1 + iii))
iii ! iii!
(%o7) get_norms() := if not glob_initial_pass
then (set_z(array_norms, 1 + glob_max_terms), iii : 1,
while iii <= glob_max_terms do (if !array_y ! > array_norms
! iii! iii
then array_norms : !array_y !, iii : 1 + iii))
iii ! iii!
(%i8) atomall() := (array_tmp1 : array_m1 array_const_2D0 ,
1 1 1
array_tmp1 array_tmp2
1 1
array_tmp2 : -----------, array_tmp3 : -----------,
1 array_x 1 array_x
1 1
array_tmp3
1
array_tmp4 : -----------, array_tmp5 : array_tmp4 + array_const_0D0 ,
1 array_x 1 1 1
1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp5 glob_h factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : ats(2, array_m1, array_const_2D0, 1),
2
array_tmp1 - ats(2, array_x, array_tmp2, 2)
2
array_tmp2 : --------------------------------------------,
2 array_x
1
array_tmp2 - ats(2, array_x, array_tmp3, 2)
2
array_tmp3 : --------------------------------------------,
2 array_x
1
array_tmp3 - ats(2, array_x, array_tmp4, 2)
2
array_tmp4 : --------------------------------------------,
2 array_x
1
array_tmp5 : array_tmp4 + array_const_0D0 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
1
then (temporary : array_tmp5 glob_h factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1 : ats(3, array_m1, array_const_2D0, 1),
3
array_tmp1 - ats(3, array_x, array_tmp2, 2)
3
array_tmp2 : --------------------------------------------,
3 array_x
1
array_tmp2 - ats(3, array_x, array_tmp3, 2)
3
array_tmp3 : --------------------------------------------,
3 array_x
1
array_tmp3 - ats(3, array_x, array_tmp4, 2)
3
array_tmp4 : --------------------------------------------,
3 array_x
1
array_tmp5 : array_tmp4 + array_const_0D0 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
1
then (temporary : array_tmp5 glob_h factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp1 : ats(4, array_m1, array_const_2D0, 1),
4
array_tmp1 - ats(4, array_x, array_tmp2, 2)
4
array_tmp2 : --------------------------------------------,
4 array_x
1
array_tmp2 - ats(4, array_x, array_tmp3, 2)
4
array_tmp3 : --------------------------------------------,
4 array_x
1
array_tmp3 - ats(4, array_x, array_tmp4, 2)
4
array_tmp4 : --------------------------------------------,
4 array_x
1
array_tmp5 : array_tmp4 + array_const_0D0 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
1
then (temporary : array_tmp5 glob_h factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp1 : ats(5, array_m1, array_const_2D0, 1),
5
array_tmp1 - ats(5, array_x, array_tmp2, 2)
5
array_tmp2 : --------------------------------------------,
5 array_x
1
array_tmp2 - ats(5, array_x, array_tmp3, 2)
5
array_tmp3 : --------------------------------------------,
5 array_x
1
array_tmp3 - ats(5, array_x, array_tmp4, 2)
5
array_tmp4 : --------------------------------------------,
5 array_x
1
array_tmp5 : array_tmp4 + array_const_0D0 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
1
then (temporary : array_tmp5 glob_h factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 :
kkk
ats(kkk, array_m1, array_const_2D0, 1),
array_tmp1 - ats(kkk, array_x, array_tmp2, 2)
kkk
array_tmp2 : ------------------------------------------------,
kkk array_x
1
array_tmp2 - ats(kkk, array_x, array_tmp3, 2)
kkk
array_tmp3 : ------------------------------------------------,
kkk array_x
1
array_tmp3 - ats(kkk, array_x, array_tmp4, 2)
kkk
array_tmp4 : ------------------------------------------------,
kkk array_x
1
array_tmp5 : array_tmp4 + array_const_0D0 , order_d : 1,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
order_d
array_tmp5 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y : temporary, array_y_higher : temporary,
order_d + kkk 1, order_d + kkk
term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d)
temporary convfp(adj2)
and (term >= 1) do (temporary : ----------------------,
glob_h
array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))),
adj2, term
kkk : 1 + kkk))
(%o8) atomall() := (array_tmp1 : array_m1 array_const_2D0 ,
1 1 1
array_tmp1 array_tmp2
1 1
array_tmp2 : -----------, array_tmp3 : -----------,
1 array_x 1 array_x
1 1
array_tmp3
1
array_tmp4 : -----------, array_tmp5 : array_tmp4 + array_const_0D0 ,
1 array_x 1 1 1
1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp5 glob_h factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : ats(2, array_m1, array_const_2D0, 1),
2
array_tmp1 - ats(2, array_x, array_tmp2, 2)
2
array_tmp2 : --------------------------------------------,
2 array_x
1
array_tmp2 - ats(2, array_x, array_tmp3, 2)
2
array_tmp3 : --------------------------------------------,
2 array_x
1
array_tmp3 - ats(2, array_x, array_tmp4, 2)
2
array_tmp4 : --------------------------------------------,
2 array_x
1
array_tmp5 : array_tmp4 + array_const_0D0 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
1
then (temporary : array_tmp5 glob_h factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1 : ats(3, array_m1, array_const_2D0, 1),
3
array_tmp1 - ats(3, array_x, array_tmp2, 2)
3
array_tmp2 : --------------------------------------------,
3 array_x
1
array_tmp2 - ats(3, array_x, array_tmp3, 2)
3
array_tmp3 : --------------------------------------------,
3 array_x
1
array_tmp3 - ats(3, array_x, array_tmp4, 2)
3
array_tmp4 : --------------------------------------------,
3 array_x
1
array_tmp5 : array_tmp4 + array_const_0D0 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
1
then (temporary : array_tmp5 glob_h factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp1 : ats(4, array_m1, array_const_2D0, 1),
4
array_tmp1 - ats(4, array_x, array_tmp2, 2)
4
array_tmp2 : --------------------------------------------,
4 array_x
1
array_tmp2 - ats(4, array_x, array_tmp3, 2)
4
array_tmp3 : --------------------------------------------,
4 array_x
1
array_tmp3 - ats(4, array_x, array_tmp4, 2)
4
array_tmp4 : --------------------------------------------,
4 array_x
1
array_tmp5 : array_tmp4 + array_const_0D0 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
1
then (temporary : array_tmp5 glob_h factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp1 : ats(5, array_m1, array_const_2D0, 1),
5
array_tmp1 - ats(5, array_x, array_tmp2, 2)
5
array_tmp2 : --------------------------------------------,
5 array_x
1
array_tmp2 - ats(5, array_x, array_tmp3, 2)
5
array_tmp3 : --------------------------------------------,
5 array_x
1
array_tmp3 - ats(5, array_x, array_tmp4, 2)
5
array_tmp4 : --------------------------------------------,
5 array_x
1
array_tmp5 : array_tmp4 + array_const_0D0 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
1
then (temporary : array_tmp5 glob_h factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y_higher : temporary)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 :
kkk
ats(kkk, array_m1, array_const_2D0, 1),
array_tmp1 - ats(kkk, array_x, array_tmp2, 2)
kkk
array_tmp2 : ------------------------------------------------,
kkk array_x
1
array_tmp2 - ats(kkk, array_x, array_tmp3, 2)
kkk
array_tmp3 : ------------------------------------------------,
kkk array_x
1
array_tmp3 - ats(kkk, array_x, array_tmp4, 2)
kkk
array_tmp4 : ------------------------------------------------,
kkk array_x
1
array_tmp5 : array_tmp4 + array_const_0D0 , order_d : 1,
kkk kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
order_d
array_tmp5 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y : temporary, array_y_higher : temporary,
order_d + kkk 1, order_d + kkk
term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d)
temporary convfp(adj2)
and (term >= 1) do (temporary : ----------------------,
glob_h
array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))),
adj2, term
kkk : 1 + kkk))
log(x)
(%i9) log10(x) := ---------
log(10.0)
log(x)
(%o9) log10(x) := ---------
log(10.0)
(%i10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i11) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o11) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i12) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o12) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i13) 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))
(%o13) 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))
(%i14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i16) dump_series(iolevel, dump_label, series_name, array_series, numb) :=
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
(%o16) dump_series(iolevel, dump_label, series_name, array_series, numb) :=
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
(%i17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb,
subnum) := 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
(%o17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb,
subnum) := 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
(%i18) 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))
(%o18) 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))
(%i19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, "
"),
if secs >= 0.0 then (sec_in_millinium :
sec_in_min min_in_hour hours_in_day days_in_year years_in_century
secs
centuries_in_millinium, milliniums : ----------------,
sec_in_millinium
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) centuries_in_millinium,
cent_int : floor(centuries), years : (centuries - cent_int) years_in_century,
years_int : floor(years), days : (years - years_int) days_in_year,
days_int : floor(days), hours : (days - days_int) hours_in_day,
hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour,
minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min,
sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\
Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(fd,
"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif 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, " | "))
(%o19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""),
if secs >= 0.0 then (sec_in_millinium :
sec_in_min min_in_hour hours_in_day days_in_year years_in_century
secs
centuries_in_millinium, milliniums : ----------------,
sec_in_millinium
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) centuries_in_millinium,
cent_int : floor(centuries), years : (centuries - cent_int) years_in_century,
years_int : floor(years), days : (years - years_int) days_in_year,
days_int : floor(days), hours : (days - days_int) hours_in_day,
hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour,
minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min,
sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\
Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(fd,
"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif 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, " | "))
(%i20) omniout_timestr(secs_in) := (secs : convfloat(secs_in),
if secs >= convfloat(0.0) then (sec_in_millinium :
convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day)
convfloat(days_in_year) convfloat(years_in_century)
secs
convfloat(centuries_in_millinium), milliniums : ---------------------------,
convfloat(sec_in_millinium)
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) convfloat(centuries_in_millinium),
cent_int : floor(centuries), years : (centuries - cent_int)
convfloat(years_in_century), years_int : floor(years),
days : (years - years_int) convfloat(days_in_year), days_int : floor(days),
hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours),
minutes : (hours - hours_int) convfloat(min_in_hour),
minutes_int : floor(minutes), seconds :
(minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds),
if millinium_int > 0 then printf(true,
"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(true,
"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif 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~%"))
(%o20) omniout_timestr(secs_in) := (secs : convfloat(secs_in),
if secs >= convfloat(0.0) then (sec_in_millinium :
convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day)
convfloat(days_in_year) convfloat(years_in_century)
secs
convfloat(centuries_in_millinium), milliniums : ---------------------------,
convfloat(sec_in_millinium)
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) convfloat(centuries_in_millinium),
cent_int : floor(centuries), years : (centuries - cent_int)
convfloat(years_in_century), years_int : floor(years),
days : (years - years_int) convfloat(days_in_year), days_int : floor(days),
hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours),
minutes : (hours - hours_int) convfloat(min_in_hour),
minutes_int : floor(minutes), seconds :
(minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds),
if millinium_int > 0 then printf(true,
"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(true,
"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif 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~%"))
(%i21) mode_declare(ats, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o21) [ats]
(%i22) ats(mmm_ats, array_a, array_b, jjj_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 : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o22) ats(mmm_ats, array_a, array_b, jjj_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 : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i23) mode_declare(att, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o23) [att]
(%i24) att(mmm_att, array_aa, array_bb, jjj_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 : array_aa array_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o24) att(mmm_att, array_aa, array_bb, jjj_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 : array_aa array_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i25) 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
(%o25) 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
(%i26) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o26) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i27) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o27) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i28) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o28) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i29) log_revs(file, revs) := printf(file, revs)
(%o29) log_revs(file, revs) := printf(file, revs)
(%i30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i31) 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, " | "))
(%o31) 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, " | "))
(%i32) logstart(file) := printf(file, "")
(%o32) logstart(file) := printf(file, "
")
(%i33) logend(file) := printf(file, "
~%")
(%o33) logend(file) := printf(file, "~%")
(%i34) chk_data() := (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())
(%o34) chk_data() := (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())
(%i35) mode_declare(comp_expect_sec, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o35) [comp_expect_sec]
(%i36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) :=
(ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) :=
(ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i37) mode_declare(comp_percent, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o37) [comp_percent]
(%i38) comp_percent(t_end2, t_start2, t2) :=
(sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o38) comp_percent(t_end2, t_start2, t2) :=
(sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i39) factorial_1(nnn) := (if nnn <= glob_max_terms
then (if array_fact_1 = 0 then (ret : nnn!, array_fact_1 : ret)
nnn nnn
else ret : array_fact_1 ) else ret : nnn!, ret)
nnn
(%o39) factorial_1(nnn) := (if nnn <= glob_max_terms
then (if array_fact_1 = 0 then (ret : nnn!, array_fact_1 : ret)
nnn nnn
else ret : array_fact_1 ) else ret : nnn!, ret)
nnn
(%i40) factorial_3(mmm, nnn) := (if (nnn <= glob_max_terms)
and (mmm <= glob_max_terms) then (if array_fact_2 = 0
mmm, nnn
factorial_1(mmm)
then (ret : ----------------, array_fact_2 : ret)
factorial_1(nnn) mmm, nnn
mmm!
else ret : array_fact_2 ) else ret : ----, ret)
mmm, nnn nnn!
(%o40) factorial_3(mmm, nnn) := (if (nnn <= glob_max_terms)
and (mmm <= glob_max_terms) then (if array_fact_2 = 0
mmm, nnn
factorial_1(mmm)
then (ret : ----------------, array_fact_2 : ret)
factorial_1(nnn) mmm, nnn
mmm!
else ret : array_fact_2 ) else ret : ----, ret)
mmm, nnn nnn!
(%i41) convfp(mmm) := mmm
(%o41) convfp(mmm) := mmm
(%i42) convfloat(mmm) := mmm
(%o42) convfloat(mmm) := mmm
(%i43) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%o43) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%i44) arcsin(x) := asin(x)
(%o44) arcsin(x) := asin(x)
(%i45) arccos(x) := acos(x)
(%o45) arccos(x) := acos(x)
(%i46) arctan(x) := atan(x)
(%o46) arctan(x) := atan(x)
1.0
---
x
(%i47) exact_soln_y(x) := ---
x
1.0
---
x
(%o47) exact_soln_y(x) := ---
x
(%i48) mainprog() := (define_variable(glob_max_terms, 30, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(years_in_century, 100.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(days_in_year, 365.0, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_h, 0.1, float), define_variable(glob_initial_pass, true,
boolean), define_variable(glob_clock_start_sec, 0.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_log10normmin, 0.1, 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/sing3postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"),
omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : -1.0,"), omniout_str(ALWAYS, "x_end : -0.7,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.1,"), omniout_str(ALWAYS,
"glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 1000,"),
omniout_str(ALWAYS, "glob_max_minutes : 15,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := ("), omniout_str(ALWAYS, "1.0/x/x "),
omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_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, 1 + max_terms),
array(array_type_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_last_rel_error, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_init, 1 + max_terms), array(array_fact_1, 1 + max_terms),
array(array_norms, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher_work, 1 + 2,
1 + max_terms), array(array_poles, 1 + 1, 1 + 3),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
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 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_type_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_1st_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_y : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_last_rel_error : 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_m1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_fact_1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), ord : 1,
term
while ord <= 1 do (term : 1, while term <=
3 do (array_complex_pole : 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_work2 : 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 : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 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_set_initial : 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_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 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_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 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_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 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_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
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_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 1.0, x_end : - 0.7, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 0.1, glob_look_poles : true, glob_max_iter : 100000, glob_h : 0.001,
glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_log10_abserr glob_log10_relerr
glob_abserr : 10.0 , glob_relerr : 10.0 ,
chk_data(), array_y_set_initial : true, array_y_set_initial : false,
1, 1 1, 2
array_y_set_initial : false, array_y_set_initial : false,
1, 3 1, 4
array_y_set_initial : false, array_y_set_initial : false,
1, 5 1, 6
array_y_set_initial : false, array_y_set_initial : false,
1, 7 1, 8
array_y_set_initial : false, array_y_set_initial : false,
1, 9 1, 10
array_y_set_initial : false, array_y_set_initial : false,
1, 11 1, 12
array_y_set_initial : false, array_y_set_initial : false,
1, 13 1, 14
array_y_set_initial : false, array_y_set_initial : false,
1, 15 1, 16
array_y_set_initial : false, array_y_set_initial : false,
1, 17 1, 18
array_y_set_initial : false, array_y_set_initial : false,
1, 19 1, 20
array_y_set_initial : false, array_y_set_initial : false,
1, 21 1, 22
array_y_set_initial : false, array_y_set_initial : false,
1, 23 1, 24
array_y_set_initial : false, array_y_set_initial : false,
1, 25 1, 26
array_y_set_initial : false, array_y_set_initial : false,
1, 27 1, 28
array_y_set_initial : false, array_y_set_initial : false,
1, 29 1, 30
if glob_html_log then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, order_diff : 1, term_no : 1,
2
while term_no <= order_diff do (array_y :
term_no
term_no - 1
array_y_init glob_h
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,
term_no - 1
array_y_init glob_h
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(), start_array_y(),
if !array_y_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
1
convfloat(glob_max_sec)) do (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(),
if glob_look_poles then check_for_pole(), array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 1, 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
--------------------
calc_term - 1
glob_h
-------------------------------------, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 1, calc_term : 2, iii : glob_max_terms,
factorial_1(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 1, calc_term : 1, iii : glob_max_terms,
factorial_1(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, 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
calc_term - 1
temp_sum glob_h
----------------------------, 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
display_alot(current_iter)), 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 ) = m1 * 2.0 / x / x / x ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-06-18T00:57:08-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing3"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_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_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 092 | "), logitem_str(html_log_file, "sing3 diffeq.max"), logitem_str(html_log_file, "sing3 maxima results"),
logitem_str(html_log_file, "Mostly affecting speed of factorials"),
logend(html_log_file)), if glob_html_log then close(html_log_file))
(%o48) mainprog() := (define_variable(glob_max_terms, 30, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(years_in_century, 100.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(days_in_year, 365.0, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_h, 0.1, float), define_variable(glob_initial_pass, true,
boolean), define_variable(glob_clock_start_sec, 0.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_log10normmin, 0.1, 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/sing3postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"),
omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : -1.0,"), omniout_str(ALWAYS, "x_end : -0.7,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.1,"), omniout_str(ALWAYS,
"glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 1000,"),
omniout_str(ALWAYS, "glob_max_minutes : 15,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := ("), omniout_str(ALWAYS, "1.0/x/x "),
omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_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, 1 + max_terms),
array(array_type_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_last_rel_error, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_init, 1 + max_terms), array(array_fact_1, 1 + max_terms),
array(array_norms, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher_work, 1 + 2,
1 + max_terms), array(array_poles, 1 + 1, 1 + 3),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
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 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_type_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_1st_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_y : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_last_rel_error : 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_m1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_fact_1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), ord : 1,
term
while ord <= 1 do (term : 1, while term <=
3 do (array_complex_pole : 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_work2 : 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 : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 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_set_initial : 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_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 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_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 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_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 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_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
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_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 1.0, x_end : - 0.7, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 0.1, glob_look_poles : true, glob_max_iter : 100000, glob_h : 0.001,
glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_log10_abserr glob_log10_relerr
glob_abserr : 10.0 , glob_relerr : 10.0 ,
chk_data(), array_y_set_initial : true, array_y_set_initial : false,
1, 1 1, 2
array_y_set_initial : false, array_y_set_initial : false,
1, 3 1, 4
array_y_set_initial : false, array_y_set_initial : false,
1, 5 1, 6
array_y_set_initial : false, array_y_set_initial : false,
1, 7 1, 8
array_y_set_initial : false, array_y_set_initial : false,
1, 9 1, 10
array_y_set_initial : false, array_y_set_initial : false,
1, 11 1, 12
array_y_set_initial : false, array_y_set_initial : false,
1, 13 1, 14
array_y_set_initial : false, array_y_set_initial : false,
1, 15 1, 16
array_y_set_initial : false, array_y_set_initial : false,
1, 17 1, 18
array_y_set_initial : false, array_y_set_initial : false,
1, 19 1, 20
array_y_set_initial : false, array_y_set_initial : false,
1, 21 1, 22
array_y_set_initial : false, array_y_set_initial : false,
1, 23 1, 24
array_y_set_initial : false, array_y_set_initial : false,
1, 25 1, 26
array_y_set_initial : false, array_y_set_initial : false,
1, 27 1, 28
array_y_set_initial : false, array_y_set_initial : false,
1, 29 1, 30
if glob_html_log then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, order_diff : 1, term_no : 1,
2
while term_no <= order_diff do (array_y :
term_no
term_no - 1
array_y_init glob_h
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,
term_no - 1
array_y_init glob_h
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(), start_array_y(),
if !array_y_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
1
convfloat(glob_max_sec)) do (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(),
if glob_look_poles then check_for_pole(), array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 1, 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
--------------------
calc_term - 1
glob_h
-------------------------------------, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 1, calc_term : 2, iii : glob_max_terms,
factorial_1(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, 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
calc_term - 1
temp_sum glob_h
----------------------------, ord : 1, calc_term : 1, iii : glob_max_terms,
factorial_1(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, 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
calc_term - 1
temp_sum glob_h
----------------------------, 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
display_alot(current_iter)), 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 ) = m1 * 2.0 / x / x / x ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-06-18T00:57:08-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing3"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_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_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 092 | "), logitem_str(html_log_file, "sing3 diffeq.max"), logitem_str(html_log_file, "sing3 maxima results"),
logitem_str(html_log_file, "Mostly affecting speed of factorials"),
logend(html_log_file)), if glob_html_log then close(html_log_file))
(%i49) mainprog()
"##############ECHO OF PROBLEM#################"
"##############temp/sing3postode.ode#################"
"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 32,"
"max_terms : 30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : -1.0,"
"x_end : -0.7,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h : 0.1,"
"glob_look_poles : true,"
"glob_max_iter : 100000,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_h : 0.001 ,"
"glob_look_poles : true,"
"glob_max_iter : 1000,"
"glob_max_minutes : 15,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := ("
"1.0/x/x "
");"
""
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = -1. " "
y[1] (analytic) = 1. " "
y[1] (numeric) = 1. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0079971752221262 " "
Order of pole = 4.436743107446802 " "
x[1] = -0.999 " "
y[1] (analytic) = 1.002003004005006 " "
y[1] (numeric) = 1.0020030040050063 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.216007377597861400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0069891780469014 " "
Order of pole = 4.43674310744672 " "
x[1] = -0.998 " "
y[1] (analytic) = 1.0040120320801924 " "
y[1] (numeric) = 1.004012032080193 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63471944051252600000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0059811808716808 " "
Order of pole = 4.4367431074467625 " "
x[1] = -0.997 " "
y[1] (analytic) = 1.0060271084064631 " "
y[1] (numeric) = 1.006027108406464 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.82857342787701700000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0049731836964464 " "
Order of pole = 4.4367431074464 " "
x[1] = -0.996 " "
y[1] (analytic) = 1.0080482572861729 " "
y[1] (numeric) = 1.008048257286174 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10135900399654930000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0039651865212316 " "
Order of pole = 4.436743107446617 " "
x[1] = -0.995 " "
y[1] (analytic) = 1.01007550314386 " "
y[1] (numeric) = 1.0100755031438615 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.5388079699363288000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0029571893460016 " "
Order of pole = 4.4367431074463894 " "
x[1] = -0.994 " "
y[1] (analytic) = 1.0121088705269847 " "
y[1] (numeric) = 1.0121088705269867 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.97449256944537440000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0019491921707941 " "
Order of pole = 4.436743107446820 " "
x[1] = -0.993 " "
y[1] (analytic) = 1.014148384106672 " "
y[1] (numeric) = 1.0141483841066743 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.18946860641722220000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.000941194995562 " "
Order of pole = 4.436743107446521 " "
x[1] = -0.992 " "
y[1] (analytic) = 1.0161940686784598 " "
y[1] (numeric) = 1.0161940686784623 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.40356712311040640000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9999331978203396 " "
Order of pole = 4.436743107446514 " "
x[1] = -0.991 " "
y[1] (analytic) = 1.0182459491630527 " "
y[1] (numeric) = 1.0182459491630553 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.6167894517925560000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9989252006451197 " "
Order of pole = 4.436743107446588 " "
x[1] = -0.99 " "
y[1] (analytic) = 1.020304050607081 " "
y[1] (numeric) = 1.0203040506070837 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.6115110074442780000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9979172034698877 " "
Order of pole = 4.436743107446283 " "
x[1] = -0.989 " "
y[1] (analytic) = 1.022368398183865 " "
y[1] (numeric) = 1.0223683981838678 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.82342438318039460000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9969092062946808 " "
Order of pole = 4.436743107446741 " "
x[1] = -0.988 " "
y[1] (analytic) = 1.0244390171941844 " "
y[1] (numeric) = 1.0244390171941877 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.25121263244909640000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9959012091194513 " "
Order of pole = 4.436743107446521 " "
x[1] = -0.987 " "
y[1] (analytic) = 1.0265159330670552 " "
y[1] (numeric) = 1.0265159330670586 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.2446345610281920000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.994893211944227 " "
Order of pole = 4.436743107446453 " "
x[1] = -0.986 " "
y[1] (analytic) = 1.0285991713605076 " "
y[1] (numeric) = 1.0285991713605114 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.66980490440482750000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9938852147690105 " "
Order of pole = 4.43674310744662 " "
x[1] = -0.985 " "
y[1] (analytic) = 1.0306887577623747 " "
y[1] (numeric) = 1.030688757762379 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.09323130945438150000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9928772175937828 " "
Order of pole = 4.436743107446453 " "
x[1] = -0.984 " "
y[1] (analytic) = 1.0327847180910834 " "
y[1] (numeric) = 1.0327847180910878 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.2999204197258223000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9918692204185656 " "
Order of pole = 4.436743107446603 " "
x[1] = -0.983 " "
y[1] (analytic) = 1.0348870782964519 " "
y[1] (numeric) = 1.0348870782964565 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 4.50574444421647460000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.990861223243348 " "
Order of pole = 4.436743107446738 " "
x[1] = -0.982 " "
y[1] (analytic) = 1.0369958644604924 " "
y[1] (numeric) = 1.0369958644604977 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.1389505983934220000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9898532260681192 " "
Order of pole = 4.436743107446535 " "
x[1] = -0.981 " "
y[1] (analytic) = 1.0391111027982223 " "
y[1] (numeric) = 1.0391111027982278 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 5.3421767010064510000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9888452288928954 " "
Order of pole = 4.436743107446489 " "
x[1] = -0.98 " "
y[1] (analytic) = 1.0412328196584757 " "
y[1] (numeric) = 1.0412328196584815 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 5.5445426028200020000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.98783723171768 " "
Order of pole = 4.436743107446691 " "
x[1] = -0.979 " "
y[1] (analytic) = 1.043361041524726 " "
y[1] (numeric) = 1.0433610415247323 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 5.9588662892906540000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9868292345424472 " "
Order of pole = 4.436743107446368 " "
x[1] = -0.978 " "
y[1] (analytic) = 1.0454957950159125 " "
y[1] (numeric) = 1.045495795015919 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.1590812450162950000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9858212373672296 " "
Order of pole = 4.4367431074465 " "
x[1] = -0.977 " "
y[1] (analytic) = 1.0476371068872712 " "
y[1] (numeric) = 1.0476371068872778 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 6.3584404408345560000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9848132401920053 " "
Order of pole = 4.436743107446436 " "
x[1] = -0.976 " "
y[1] (analytic) = 1.0497850040311743 " "
y[1] (numeric) = 1.0497850040311814 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.7684595705941330000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9838052430167867 " "
Order of pole = 4.436743107446550 " "
x[1] = -0.975 " "
y[1] (analytic) = 1.0519395134779752 " "
y[1] (numeric) = 1.0519395134779823 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.7545968818194510000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9827972458415638 " "
Order of pole = 4.436743107446514 " "
x[1] = -0.974 " "
y[1] (analytic) = 1.0541006623968563 " "
y[1] (numeric) = 1.0541006623968638 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 7.1620451791432060000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.98178924866633 " "
Order of pole = 4.436743107446162 " "
x[1] = -0.973 " "
y[1] (analytic) = 1.0562684780966887 " "
y[1] (numeric) = 1.0562684780966967 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 7.5677784039385190000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9807812514911183 " "
Order of pole = 4.436743107446482 " "
x[1] = -0.972 " "
y[1] (analytic) = 1.0584429880268929 " "
y[1] (numeric) = 1.0584429880269013 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 7.971799220740650000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9797732543158909 " "
Order of pole = 4.436743107446322 " "
x[1] = -0.971 " "
y[1] (analytic) = 1.0606242197783085 " "
y[1] (numeric) = 1.0606242197783171 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.1647575367327350000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9787652571406842 " "
Order of pole = 4.436743107446787 " "
x[1] = -0.97 " "
y[1] (analytic) = 1.0628122010840686 " "
y[1] (numeric) = 1.0628122010840775 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.3568707509584770000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9777572599654536 " "
Order of pole = 4.436743107446535 " "
x[1] = -0.969 " "
y[1] (analytic) = 1.0650069598204825 " "
y[1] (numeric) = 1.0650069598204919 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 8.7566314199705160000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9767492627902332 " "
Order of pole = 4.436743107446581 " "
x[1] = -0.968 " "
y[1] (analytic) = 1.0672085240079232 " "
y[1] (numeric) = 1.0672085240079328 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 8.9466283270667170000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9757412656150092 " "
Order of pole = 4.4367431074465244 " "
x[1] = -0.967 " "
y[1] (analytic) = 1.0694169218117207 " "
y[1] (numeric) = 1.0694169218117306 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.3434160408634160000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9747332684397907 " "
Order of pole = 4.436743107446635 " "
x[1] = -0.966 " "
y[1] (analytic) = 1.0716321815430647 " "
y[1] (numeric) = 1.071632181543075 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 9.5313037462574330000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9737252712645655 " "
Order of pole = 4.436743107446546 " "
x[1] = -0.965 " "
y[1] (analytic) = 1.0738543316599105 " "
y[1] (numeric) = 1.073854331659921 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 9.7183538994016760000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9727172740893459 " "
Order of pole = 4.43674310744662 " "
x[1] = -0.964 " "
y[1] (analytic) = 1.0760834007678932 " "
y[1] (numeric) = 1.076083400767904 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.011091299574218100000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9717092769141257 " "
Order of pole = 4.436743107446680 " "
x[1] = -0.963 " "
y[1] (analytic) = 1.078319417621249 " "
y[1] (numeric) = 1.0783194176212603 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 1.050178144446079000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9707012797389015 " "
Order of pole = 4.436743107446617 " "
x[1] = -0.962 " "
y[1] (analytic) = 1.0805624111237417 " "
y[1] (numeric) = 1.0805624111237533 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 1.0685472062732515000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9696932825636813 " "
Order of pole = 4.436743107446677 " "
x[1] = -0.961 " "
y[1] (analytic) = 1.0828124103295975 " "
y[1] (numeric) = 1.0828124103296093 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.0868331346003399000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9686852853884511 " "
Order of pole = 4.436743107446421 " "
x[1] = -0.96 " "
y[1] (analytic) = 1.0850694444444446 " "
y[1] (numeric) = 1.0850694444444569 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1254996934439986000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9676772882132347 " "
Order of pole = 4.436743107446603 " "
x[1] = -0.959 " "
y[1] (analytic) = 1.0873335428262627 " "
y[1] (numeric) = 1.0873335428262754 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.1639981645217289000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9666692910380065 " "
Order of pole = 4.436743107446407 " "
x[1] = -0.958 " "
y[1] (analytic) = 1.0896047349863365 " "
y[1] (numeric) = 1.0896047349863496 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.2023288142870568000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9656612938627916 " "
Order of pole = 4.436743107446645 " "
x[1] = -0.957 " "
y[1] (analytic) = 1.0918830505902175 " "
y[1] (numeric) = 1.091883050590231 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2404919091935082000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9646532966875593 " "
Order of pole = 4.436743107446318 " "
x[1] = -0.956 " "
y[1] (analytic) = 1.094168519458693 " "
y[1] (numeric) = 1.094168519458707 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.2784877156946095000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9636452995123425 " "
Order of pole = 4.436743107446478 " "
x[1] = -0.955 " "
y[1] (analytic) = 1.0964611715687618 " "
y[1] (numeric) = 1.0964611715687762 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.316316500243886000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9626373023371204 " "
Order of pole = 4.436743107446485 " "
x[1] = -0.954 " "
y[1] (analytic) = 1.0987610370546173 " "
y[1] (numeric) = 1.098761037054632 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3337698945292686000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9616293051618989 " "
Order of pole = 4.436743107446507 " "
x[1] = -0.953 " "
y[1] (analytic) = 1.1010681462086371 " "
y[1] (numeric) = 1.101068146208652 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.351141487582197000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9606213079866752 " "
Order of pole = 4.436743107446464 " "
x[1] = -0.952 " "
y[1] (analytic) = 1.1033825294823814 " "
y[1] (numeric) = 1.1033825294823965 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.3684314126294336000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.959613310811445 " "
Order of pole = 4.436743107446201 " "
x[1] = -0.951 " "
y[1] (analytic) = 1.1057042174875968 " "
y[1] (numeric) = 1.1057042174876124 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.4057215391716227000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9586053136362435 " "
Order of pole = 4.436743107446844 " "
x[1] = -0.95 " "
y[1] (analytic) = 1.10803324099723 " "
y[1] (numeric) = 1.108033240997246 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.4428458428028532000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9575973164610109 " "
Order of pole = 4.436743107446521 " "
x[1] = -0.949 " "
y[1] (analytic) = 1.110369630946446 " "
y[1] (numeric) = 1.1103696309464621 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.4598072306526433000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.956589319285788 " "
Order of pole = 4.436743107446503 " "
x[1] = -0.948 " "
y[1] (analytic) = 1.1127134184336556 " "
y[1] (numeric) = 1.1127134184336722 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 1.49664280968409000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9555813221105711 " "
Order of pole = 4.436743107446663 " "
x[1] = -0.947 " "
y[1] (analytic) = 1.1150646347215518 " "
y[1] (numeric) = 1.1150646347215687 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.513400160746414000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9545733249353558 " "
Order of pole = 4.43674310744688 " "
x[1] = -0.946 " "
y[1] (analytic) = 1.1174233112381498 " "
y[1] (numeric) = 1.117423311238167 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.5499479033564967000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.953565327760122 " "
Order of pole = 4.43674310744651 " "
x[1] = -0.945 " "
y[1] (analytic) = 1.1197894795778396 " "
y[1] (numeric) = 1.1197894795778571 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.5665019281740908000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9525573305849078 " "
Order of pole = 4.436743107446755 " "
x[1] = -0.944 " "
y[1] (analytic) = 1.122163171502442 " "
y[1] (numeric) = 1.12216317150246 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 1.6027627225412286000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9515493334096853 " "
Order of pole = 4.436743107446741 " "
x[1] = -0.943 " "
y[1] (analytic) = 1.1245444189422762 " "
y[1] (numeric) = 1.1245444189422946 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.638859425945326800000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9505413362344524 " "
Order of pole = 4.436743107446404 " "
x[1] = -0.942 " "
y[1] (analytic) = 1.1269332539972323 " "
y[1] (numeric) = 1.1269332539972512 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.6747923048399113000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9495333390592366 " "
Order of pole = 4.436743107446603 " "
x[1] = -0.941 " "
y[1] (analytic) = 1.1293297089378542 " "
y[1] (numeric) = 1.1293297089378735 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.710561625678508000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9485253418840036 " "
Order of pole = 4.436743107446265 " "
x[1] = -0.94 " "
y[1] (analytic) = 1.1317338162064283 " "
y[1] (numeric) = 1.131733816206448 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.746167654914643000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9475173447087878 " "
Order of pole = 4.436743107446457 " "
x[1] = -0.939 " "
y[1] (analytic) = 1.1341456084180823 " "
y[1] (numeric) = 1.1341456084181025 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.7816106590018420000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9465093475335683 " "
Order of pole = 4.436743107446546 " "
x[1] = -0.938 " "
y[1] (analytic) = 1.1365651183618914 " "
y[1] (numeric) = 1.136565118361912 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 1.8168909043936310000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9455013503583464 " "
Order of pole = 4.436743107446546 " "
x[1] = -0.9369999999999999 " "
y[1] (analytic) = 1.1389923790019922 " "
y[1] (numeric) = 1.1389923790020131 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 1.832513829569393000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9444933531831284 " "
Order of pole = 4.436743107446677 " "
x[1] = -0.9359999999999999 " "
y[1] (analytic) = 1.1414274234787056 " "
y[1] (numeric) = 1.141427423478727 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.8675109458854422000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.943485356007909 " "
Order of pole = 4.436743107446766 " "
x[1] = -0.9349999999999999 " "
y[1] (analytic) = 1.1438702851096687 " "
y[1] (numeric) = 1.1438702851096905 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.9023460584577376000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9424773588326688 " "
Order of pole = 4.436743107446194 " "
x[1] = -0.9339999999999999 " "
y[1] (analytic) = 1.1463209973909736 " "
y[1] (numeric) = 1.1463209973909958 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 1.937019433739806000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9414693616574549 " "
Order of pole = 4.436743107446457 " "
x[1] = -0.9329999999999999 " "
y[1] (analytic) = 1.148779593998316 " "
y[1] (numeric) = 1.1487795939983387 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 1.9715313381851726000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9404613644822268 " "
Order of pole = 4.436743107446265 " "
x[1] = -0.9319999999999999 " "
y[1] (analytic) = 1.1512461087881525 " "
y[1] (numeric) = 1.1512461087881756 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 2.0058820382473636000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9394533673070125 " "
Order of pole = 4.436743107446514 " "
x[1] = -0.9309999999999999 " "
y[1] (analytic) = 1.1537205757988651 " "
y[1] (numeric) = 1.1537205757988886 " "
absolute error = 2.35367281220533200000000000000E-14 " "
relative error = 2.0400718003799054000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9384453701317934 " "
Order of pole = 4.436743107446603 " "
x[1] = -0.9299999999999999 " "
y[1] (analytic) = 1.156203029251937 " "
y[1] (numeric) = 1.1562030292519607 " "
absolute error = 2.37587727269783500000000000000E-14 " "
relative error = 2.0548962531563567000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9374373729565676 " "
Order of pole = 4.436743107446489 " "
x[1] = -0.9289999999999999 " "
y[1] (analytic) = 1.1586935035531336 " "
y[1] (numeric) = 1.1586935035531583 " "
absolute error = 2.464695114667847500000000000000E-14 " "
relative error = 2.127132936458053800000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9364293757813563 " "
Order of pole = 4.436743107446837 " "
x[1] = -0.9279999999999999 " "
y[1] (analytic) = 1.1611920332936982 " "
y[1] (numeric) = 1.1611920332937231 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 2.141678123734891000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9354213786061218 " "
Order of pole = 4.436743107446443 " "
x[1] = -0.9269999999999999 " "
y[1] (analytic) = 1.1636986532515488 " "
y[1] (numeric) = 1.163698653251574 " "
absolute error = 2.53130849614535700000000000000E-14 " "
relative error = 2.175226798684092900000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9344133814308989 " "
Order of pole = 4.436743107446414 " "
x[1] = -0.9259999999999999 " "
y[1] (analytic) = 1.1662133983924916 " "
y[1] (numeric) = 1.1662133983925174 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 2.208615867971275000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9334053842556839 " "
Order of pole = 4.436743107446642 " "
x[1] = -0.9249999999999999 " "
y[1] (analytic) = 1.1687363038714391 " "
y[1] (numeric) = 1.1687363038714653 " "
absolute error = 2.620126338115369400000000000000E-14 " "
relative error = 2.2418455980499627000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9323973870804645 " "
Order of pole = 4.4367431074467305 " "
x[1] = -0.9239999999999999 " "
y[1] (analytic) = 1.171267405033639 " "
y[1] (numeric) = 1.1712674050336656 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 2.2749162553736824000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9313893899052395 " "
Order of pole = 4.436743107446638 " "
x[1] = -0.9229999999999999 " "
y[1] (analytic) = 1.1738067374159116 " "
y[1] (numeric) = 1.1738067374159387 " "
absolute error = 2.70894418008538200000000000000E-14 " "
relative error = 2.307828106395959000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9303813927300139 " "
Order of pole = 4.436743107446528 " "
x[1] = -0.9219999999999999 " "
y[1] (analytic) = 1.176354336747898 " "
y[1] (numeric) = 1.1763543367479257 " "
absolute error = 2.775557561562891400000000000000E-14 " "
relative error = 2.3594570741636287000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9293733955547896 " "
Order of pole = 4.436743107446457 " "
x[1] = -0.9209999999999999 " "
y[1] (analytic) = 1.1789102389533164 " "
y[1] (numeric) = 1.1789102389533446 " "
absolute error = 2.819966482547897600000000000000E-14 " "
relative error = 2.3920111891229112000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9283653983795641 " "
Order of pole = 4.436743107446347 " "
x[1] = -0.9199999999999999 " "
y[1] (analytic) = 1.181474480151229 " "
y[1] (numeric) = 1.1814744801512573 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 2.405613486189395000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9273574012043468 " "
Order of pole = 4.436743107446507 " "
x[1] = -0.9189999999999999 " "
y[1] (analytic) = 1.1840470966573169 " "
y[1] (numeric) = 1.1840470966573458 " "
absolute error = 2.88657986402540700000000000000E-14 " "
relative error = 2.4378927765411612000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9263494040291294 " "
Order of pole = 4.436743107446649 " "
x[1] = -0.9179999999999999 " "
y[1] (analytic) = 1.1866281249851671 " "
y[1] (numeric) = 1.1866281249851967 " "
absolute error = 2.953193245502916400000000000000E-14 " "
relative error = 2.4887268246231997000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.925341406853911 " "
Order of pole = 4.436743107446773 " "
x[1] = -0.9169999999999999 " "
y[1] (analytic) = 1.1892176018475686 " "
y[1] (numeric) = 1.1892176018475984 " "
absolute error = 2.975397705995419500000000000000E-14 " "
relative error = 2.501979201596782000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9243334096786828 " "
Order of pole = 4.436743107446585 " "
x[1] = -0.9159999999999999 " "
y[1] (analytic) = 1.1918155641578156 " "
y[1] (numeric) = 1.1918155641578458 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 2.5337868692076876000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9233254125034671 " "
Order of pole = 4.436743107446787 " "
x[1] = -0.9149999999999999 " "
y[1] (analytic) = 1.1944220490310253 " "
y[1] (numeric) = 1.194422049031056 " "
absolute error = 3.06421554796543200000000000000E-14 " "
relative error = 2.5654378621453583000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9223174153282443 " "
Order of pole = 4.436743107446759 " "
x[1] = -0.9139999999999999 " "
y[1] (analytic) = 1.1970370937854624 " "
y[1] (numeric) = 1.1970370937854935 " "
absolute error = 3.10862446895043830000000000000E-14 " "
relative error = 2.59693244686332000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9213094181530237 " "
Order of pole = 4.436743107446816 " "
x[1] = -0.9129999999999999 " "
y[1] (analytic) = 1.1996607359438751 " "
y[1] (numeric) = 1.1996607359439069 " "
absolute error = 3.17523785042794770000000000000E-14 " "
relative error = 2.6467798397433734000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9203014209778035 " "
Order of pole = 4.436743107446876 " "
x[1] = -0.9119999999999999 " "
y[1] (analytic) = 1.2022930132348417 " "
y[1] (numeric) = 1.2022930132348737 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 2.6594534574542190000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9192934238025726 " "
Order of pole = 4.436743107446592 " "
x[1] = -0.9109999999999999 " "
y[1] (analytic) = 1.2049339635941254 " "
y[1] (numeric) = 1.204933963594158 " "
absolute error = 3.2640556923979600000000000000E-14 " "
relative error = 2.708908364290607000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9182854266273542 " "
Order of pole = 4.436743107446713 " "
x[1] = -0.9099999999999999 " "
y[1] (analytic) = 1.207583625166043 " "
y[1] (numeric) = 1.207583625166076 " "
absolute error = 3.308464613382966500000000000000E-14 " "
relative error = 2.739739546342434000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9172774294521229 " "
Order of pole = 4.436743107446410 " "
x[1] = -0.9089999999999999 " "
y[1] (analytic) = 1.2102420363048407 " "
y[1] (numeric) = 1.2102420363048745 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 2.7887628206713083000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9162694322769145 " "
Order of pole = 4.436743107446862 " "
x[1] = -0.9079999999999999 " "
y[1] (analytic) = 1.2129092355760835 " "
y[1] (numeric) = 1.2129092355761177 " "
absolute error = 3.41948691584548200000000000000E-14 " "
relative error = 2.8192438605856290000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9152614351016876 " "
Order of pole = 4.436743107446702 " "
x[1] = -0.9069999999999999 " "
y[1] (analytic) = 1.2155852617580525 " "
y[1] (numeric) = 1.2155852617580873 " "
absolute error = 3.486100297322991500000000000000E-14 " "
relative error = 2.867836923492461000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9142534379264642 " "
Order of pole = 4.436743107446663 " "
x[1] = -0.9059999999999999 " "
y[1] (analytic) = 1.2182701538431553 " "
y[1] (numeric) = 1.2182701538431906 " "
absolute error = 3.53050921830799800000000000000E-14 " "
relative error = 2.897969064719063000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9132454407512346 " "
Order of pole = 4.436743107446418 " "
x[1] = -0.9049999999999999 " "
y[1] (analytic) = 1.2209639510393457 " "
y[1] (numeric) = 1.2209639510393817 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 2.9461333372893245000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9122374435760137 " "
Order of pole = 4.436743107446457 " "
x[1] = -0.9039999999999999 " "
y[1] (analytic) = 1.2236666927715565 " "
y[1] (numeric) = 1.223666692771593 " "
absolute error = 3.641531520770513500000000000000E-14 " "
relative error = 2.975917823277995000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.911229446400799 " "
Order of pole = 4.436743107446702 " "
x[1] = -0.9029999999999999 " "
y[1] (analytic) = 1.2263784186831395 " "
y[1] (numeric) = 1.2263784186831768 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 3.0417604435228895000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9102214492255671 " "
Order of pole = 4.436743107446382 " "
x[1] = -0.9019999999999999 " "
y[1] (analytic) = 1.2290991686373227 " "
y[1] (numeric) = 1.2290991686373602 " "
absolute error = 3.75255382323302900000000000000E-14 " "
relative error = 3.0530928007976843000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9092134520503555 " "
Order of pole = 4.436743107446723 " "
x[1] = -0.9009999999999999 " "
y[1] (analytic) = 1.2318289827186715 " "
y[1] (numeric) = 1.2318289827187097 " "
absolute error = 3.819167204710538500000000000000E-14 " "
relative error = 3.1004037559512193000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9082054548751328 " "
Order of pole = 4.436743107446713 " "
x[1] = -0.8999999999999999 " "
y[1] (analytic) = 1.234567901234568 " "
y[1] (numeric) = 1.234567901234607 " "
absolute error = 3.88578058618804800000000000000E-14 " "
relative error = 3.1474822748123180000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9071974576999079 " "
Order of pole = 4.43674310744662 " "
x[1] = -0.8989999999999999 " "
y[1] (analytic) = 1.2373159647166982 " "
y[1] (numeric) = 1.2373159647167375 " "
absolute error = 3.93018950717305400000000000000E-14 " "
relative error = 3.1763830898867684000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9061894605246881 " "
Order of pole = 4.436743107446688 " "
x[1] = -0.8979999999999999 " "
y[1] (analytic) = 1.2400732139225503 " "
y[1] (numeric) = 1.24007321392259 " "
absolute error = 3.974598428158060400000000000000E-14 " "
relative error = 3.205132070860372000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9051814633494638 " "
Order of pole = 4.436743107446624 " "
x[1] = -0.8969999999999999 " "
y[1] (analytic) = 1.2428396898369274 " "
y[1] (numeric) = 1.2428396898369676 " "
absolute error = 4.019007349143066700000000000000E-14 " "
relative error = 3.233729484186652600000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9041734661742338 " "
Order of pole = 4.4367431074463575 " "
x[1] = -0.8959999999999999 " "
y[1] (analytic) = 1.2456154336734695 " "
y[1] (numeric) = 1.2456154336735106 " "
absolute error = 4.10782519111307900000000000000E-14 " "
relative error = 3.2978277886286380000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9031654689990247 " "
Order of pole = 4.436743107446791 " "
x[1] = -0.8949999999999999 " "
y[1] (analytic) = 1.2484004868761902 " "
y[1] (numeric) = 1.2484004868762317 " "
absolute error = 4.152234112098085500000000000000E-14 " "
relative error = 3.326043329643368000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9021574718237947 " "
Order of pole = 4.4367431074465316 " "
x[1] = -0.8939999999999999 " "
y[1] (analytic) = 1.2511948911210207 " "
y[1] (numeric) = 1.251194891121063 " "
absolute error = 4.24105195406809800000000000000E-14 " "
relative error = 3.38960139956157000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9011494746485633 " "
Order of pole = 4.4367431074462225 " "
x[1] = -0.8929999999999999 " "
y[1] (analytic) = 1.2539986883173724 " "
y[1] (numeric) = 1.2539986883174152 " "
absolute error = 4.28546087505310400000000000000E-14 " "
relative error = 3.417436489350222400000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.900141477473351 " "
Order of pole = 4.436743107446553 " "
x[1] = -0.8919999999999999 " "
y[1] (analytic) = 1.2568119206097048 " "
y[1] (numeric) = 1.2568119206097483 " "
absolute error = 4.352074256530613600000000000000E-14 " "
relative error = 3.4627888112481736000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8991334802981257 " "
Order of pole = 4.436743107446446 " "
x[1] = -0.8909999999999999 " "
y[1] (analytic) = 1.2596346303791126 " "
y[1] (numeric) = 1.2596346303791566 " "
absolute error = 4.3964831775156200000000000000E-14 " "
relative error = 3.4902844614492770000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8981254831229076 " "
Order of pole = 4.436743107446570 " "
x[1] = -0.8899999999999999 " "
y[1] (analytic) = 1.2624668602449187 " "
y[1] (numeric) = 1.2624668602449636 " "
absolute error = 4.485301019485632400000000000000E-14 " "
relative error = 3.552806937534569000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.897117485947691 " "
Order of pole = 4.436743107446759 " "
x[1] = -0.8889999999999999 " "
y[1] (analytic) = 1.2653086530662858 " "
y[1] (numeric) = 1.2653086530663313 " "
absolute error = 4.55191440096314200000000000000E-14 " "
relative error = 3.597473541283590600000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.896109488772456 " "
Order of pole = 4.436743107446333 " "
x[1] = -0.8879999999999999 " "
y[1] (analytic) = 1.2681600519438359 " "
y[1] (numeric) = 1.268160051943882 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 3.6419123716768803000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8951014915972436 " "
Order of pole = 4.436743107446649 " "
x[1] = -0.8869999999999999 " "
y[1] (analytic) = 1.271021100221285 " "
y[1] (numeric) = 1.2710211002213316 " "
absolute error = 4.662936703425657500000000000000E-14 " "
relative error = 3.6686540472175005000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8940934944220139 " "
Order of pole = 4.436743107446404 " "
x[1] = -0.8859999999999999 " "
y[1] (analytic) = 1.2738918414870906 " "
y[1] (numeric) = 1.2738918414871379 " "
absolute error = 4.72955008490316700000000000000E-14 " "
relative error = 3.712677898448646000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8930854972467909 " "
Order of pole = 4.436743107446372 " "
x[1] = -0.8849999999999999 " "
y[1] (analytic) = 1.2767723195761118 " "
y[1] (numeric) = 1.2767723195761598 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 3.756475130956004000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8920775000715677 " "
Order of pole = 4.43674310744634 " "
x[1] = -0.8839999999999999 " "
y[1] (analytic) = 1.2796625785712827 " "
y[1] (numeric) = 1.2796625785713311 " "
absolute error = 4.840572387365682500000000000000E-14 " "
relative error = 3.782694335541235700000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8910695028963591 " "
Order of pole = 4.436743107446791 " "
x[1] = -0.8829999999999999 " "
y[1] (analytic) = 1.2825626628052982 " "
y[1] (numeric) = 1.2825626628053475 " "
absolute error = 4.92939022933569500000000000000E-14 " "
relative error = 3.8433913385205190000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.890061505721127 " "
Order of pole = 4.43674310744645 " "
x[1] = -0.8819999999999999 " "
y[1] (analytic) = 1.285472616862316 " "
y[1] (numeric) = 1.2854726168623658 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 3.86923773021408000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.889053508545901 " "
Order of pole = 4.4367431074463255 " "
x[1] = -0.8809999999999999 " "
y[1] (analytic) = 1.2883924855796676 " "
y[1] (numeric) = 1.288392485579718 " "
absolute error = 5.04041253179821100000000000000E-14 " "
relative error = 3.912171631093029300000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8880455113706908 " "
Order of pole = 4.436743107446723 " "
x[1] = -0.8799999999999999 " "
y[1] (analytic) = 1.291322314049587 " "
y[1] (numeric) = 1.2913223140496384 " "
absolute error = 5.12923037376822300000000000000E-14 " "
relative error = 3.972076001446111000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8870375141954602 " "
Order of pole = 4.436743107446436 " "
x[1] = -0.8789999999999999 " "
y[1] (analytic) = 1.2942621476209524 " "
y[1] (numeric) = 1.2942621476210043 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 4.014521914896817000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8860295170202294 " "
Order of pole = 4.436743107446144 " "
x[1] = -0.8779999999999999 " "
y[1] (analytic) = 1.2972120319010387 " "
y[1] (numeric) = 1.2972120319010914 " "
absolute error = 5.26245713672324200000000000000E-14 " "
relative error = 4.0567440073857586000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8850215198450131 " "
Order of pole = 4.43674310744634 " "
x[1] = -0.8769999999999999 " "
y[1] (analytic) = 1.3001720127572882 " "
y[1] (numeric) = 1.3001720127573415 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 4.0987426785932246000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8840135226697942 " "
Order of pole = 4.43674310744645 " "
x[1] = -0.8759999999999999 " "
y[1] (analytic) = 1.303142136319093 " "
y[1] (numeric) = 1.303142136319147 " "
absolute error = 5.41788836017076400000000000000E-14 " "
relative error = 4.157557498274399000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8830055254945745 " "
Order of pole = 4.436743107446528 " "
x[1] = -0.8749999999999999 " "
y[1] (analytic) = 1.3061224489795922 " "
y[1] (numeric) = 1.306122448979647 " "
absolute error = 5.48450174164827300000000000000E-14 " "
relative error = 4.1990716459494587000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8819975283193504 " "
Order of pole = 4.4367431074464605 " "
x[1] = -0.8739999999999999 " "
y[1] (analytic) = 1.3091129973974835 " "
y[1] (numeric) = 1.3091129973975393 " "
absolute error = 5.57331958361828600000000000000E-14 " "
relative error = 4.257325070256000600000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8809895311441286 " "
Order of pole = 4.436743107446475 " "
x[1] = -0.8729999999999999 " "
y[1] (analytic) = 1.3121138284988503 " "
y[1] (numeric) = 1.3121138284989067 " "
absolute error = 5.63993296509579500000000000000E-14 " "
relative error = 4.2983564707554930000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8799815339688993 " "
Order of pole = 4.436743107446226 " "
x[1] = -0.8719999999999999 " "
y[1] (analytic) = 1.3151249894790005 " "
y[1] (numeric) = 1.3151249894790575 " "
absolute error = 5.70654634657330500000000000000E-14 " "
relative error = 4.339166537192794000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8789735367936868 " "
Order of pole = 4.4367431074465635 " "
x[1] = -0.8709999999999999 " "
y[1] (analytic) = 1.318146527804324 " "
y[1] (numeric) = 1.318146527804382 " "
absolute error = 5.79536418854331700000000000000E-14 " "
relative error = 4.39660088336069000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8779655396184669 " "
Order of pole = 4.436743107446631 " "
x[1] = -0.8699999999999999 " "
y[1] (analytic) = 1.3211784912141633 " "
y[1] (numeric) = 1.321178491214222 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 4.436930822748762500000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8769575424432413 " "
Order of pole = 4.436743107446517 " "
x[1] = -0.8689999999999999 " "
y[1] (analytic) = 1.324220927722698 " "
y[1] (numeric) = 1.3242209277227572 " "
absolute error = 5.92859095149833600000000000000E-14 " "
relative error = 4.477040671524433000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8759495452680226 " "
Order of pole = 4.436743107446631 " "
x[1] = -0.8679999999999999 " "
y[1] (analytic) = 1.327273885620846 " "
y[1] (numeric) = 1.327273885620906 " "
absolute error = 6.01740879346834800000000000000E-14 " "
relative error = 4.533660202810096000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8749415480927987 " "
Order of pole = 4.436743107446570 " "
x[1] = -0.8669999999999999 " "
y[1] (analytic) = 1.3303374134781807 " "
y[1] (numeric) = 1.3303374134782417 " "
absolute error = 6.10622663543836100000000000000E-14 " "
relative error = 4.589983393366025600000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8739335509175797 " "
Order of pole = 4.436743107446680 " "
x[1] = -0.8659999999999999 " "
y[1] (analytic) = 1.3334115601448622 " "
y[1] (numeric) = 1.333411560144924 " "
absolute error = 6.1728400169158700000000000000E-14 " "
relative error = 4.6293584077261574000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8729255537423554 " "
Order of pole = 4.436743107446599 " "
x[1] = -0.8649999999999999 " "
y[1] (analytic) = 1.3364963747535838 " "
y[1] (numeric) = 1.3364963747536462 " "
absolute error = 6.2394533983933800000000000000E-14 " "
relative error = 4.668515019012885500000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.871917556567138 " "
Order of pole = 4.43674310744677 " "
x[1] = -0.8639999999999999 " "
y[1] (analytic) = 1.339591906721537 " "
y[1] (numeric) = 1.3395919067216 " "
absolute error = 6.30606677987088900000000000000E-14 " "
relative error = 4.707453626906497000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8709095593919031 " "
Order of pole = 4.4367431074463255 " "
x[1] = -0.8629999999999999 " "
y[1] (analytic) = 1.3426982057523882 " "
y[1] (numeric) = 1.3426982057524521 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 4.762711824923825000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8699015622166872 " "
Order of pole = 4.436743107446539 " "
x[1] = -0.8619999999999999 " "
y[1] (analytic) = 1.3458153218382765 " "
y[1] (numeric) = 1.3458153218383413 " "
absolute error = 6.48370246381091400000000000000E-14 " "
relative error = 4.817676213519915000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8688935650414689 " "
Order of pole = 4.43674310744667 " "
x[1] = -0.8609999999999999 " "
y[1] (analytic) = 1.3489433052618236 " "
y[1] (numeric) = 1.348943305261889 " "
absolute error = 6.55031584528842400000000000000E-14 " "
relative error = 4.855886692745058000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8678855678662427 " "
Order of pole = 4.4367431074465316 " "
x[1] = -0.8599999999999999 " "
y[1] (analytic) = 1.3520822065981615 " "
y[1] (numeric) = 1.3520822065982279 " "
absolute error = 6.63913368725843600000000000000E-14 " "
relative error = 4.910303275096337700000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8668775706910086 " "
Order of pole = 4.436743107446112 " "
x[1] = -0.8589999999999999 " "
y[1] (analytic) = 1.3552320767169777 " "
y[1] (numeric) = 1.355232076717045 " "
absolute error = 6.72795152922844900000000000000E-14 " "
relative error = 4.964427602338616000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8658695735158017 " "
Order of pole = 4.436743107446638 " "
x[1] = -0.8579999999999999 " "
y[1] (analytic) = 1.3583929667845758 " "
y[1] (numeric) = 1.3583929667846435 " "
absolute error = 6.77236045021345500000000000000E-14 " "
relative error = 4.9855679584709356000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8648615763405799 " "
Order of pole = 4.4367431074466595 " "
x[1] = -0.8569999999999999 " "
y[1] (analytic) = 1.3615649282659523 " "
y[1] (numeric) = 1.361564928266021 " "
absolute error = 6.86117829218346700000000000000E-14 " "
relative error = 5.039185535515853000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8638535791653617 " "
Order of pole = 4.436743107446787 " "
x[1] = -0.8559999999999999 " "
y[1] (analytic) = 1.3647480129268936 " "
y[1] (numeric) = 1.3647480129269631 " "
absolute error = 6.9499961341534800000000000000E-14 " "
relative error = 5.092512367355083000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8628455819901318 " "
Order of pole = 4.436743107446521 " "
x[1] = -0.8549999999999999 " "
y[1] (analytic) = 1.3679422728360866 " "
y[1] (numeric) = 1.3679422728361572 " "
absolute error = 7.06101843661599600000000000000E-14 " "
relative error = 5.161781002627207000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8618375848149098 " "
Order of pole = 4.436743107446521 " "
x[1] = -0.8539999999999999 " "
y[1] (analytic) = 1.3711477603672486 " "
y[1] (numeric) = 1.37114776036732 " "
absolute error = 7.12763181809350500000000000000E-14 " "
relative error = 5.198295927044682000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.860829587639695 " "
Order of pole = 4.436743107446777 " "
x[1] = -0.8529999999999999 " "
y[1] (analytic) = 1.3743645282012735 " "
y[1] (numeric) = 1.3743645282013455 " "
absolute error = 7.19424519957101400000000000000E-14 " "
relative error = 5.234597555414664000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8598215904644657 " "
Order of pole = 4.436743107446528 " "
x[1] = -0.8519999999999999 " "
y[1] (analytic) = 1.3775926293283967 " "
y[1] (numeric) = 1.3775926293284695 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 5.286804594106795000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8588135932892413 " "
Order of pole = 4.436743107446453 " "
x[1] = -0.8509999999999999 " "
y[1] (analytic) = 1.3808321170503772 " "
y[1] (numeric) = 1.3808321170504512 " "
absolute error = 7.39408534400354300000000000000E-14 " "
relative error = 5.354804000212707000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8578055961140173 " "
Order of pole = 4.436743107446386 " "
x[1] = -0.8499999999999999 " "
y[1] (analytic) = 1.3840830449826995 " "
y[1] (numeric) = 1.3840830449827741 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 5.390354829160058000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8567975989387995 " "
Order of pole = 4.436743107446535 " "
x[1] = -0.8489999999999999 " "
y[1] (analytic) = 1.3873454670567886 " "
y[1] (numeric) = 1.3873454670568643 " "
absolute error = 7.57172102794356800000000000000E-14 " "
relative error = 5.45770408866274900000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8557896017635738 " "
Order of pole = 4.436743107446407 " "
x[1] = -0.8479999999999999 " "
y[1] (analytic) = 1.3906194375222505 " "
y[1] (numeric) = 1.3906194375223269 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 5.4927568271523320000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8547816045883534 " "
Order of pole = 4.4367431074464605 " "
x[1] = -0.8469999999999999 " "
y[1] (analytic) = 1.3939050109491242 " "
y[1] (numeric) = 1.3939050109492017 " "
absolute error = 7.74935671188359300000000000000E-14 " "
relative error = 5.559458249315695000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8537736074131316 " "
Order of pole = 4.436743107446482 " "
x[1] = -0.8459999999999999 " "
y[1] (analytic) = 1.3972022422301587 " "
y[1] (numeric) = 1.397202242230237 " "
absolute error = 7.83817455385360500000000000000E-14 " "
relative error = 5.609906938985886000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8527656102379018 " "
Order of pole = 4.436743107446205 " "
x[1] = -0.8449999999999999 " "
y[1] (analytic) = 1.4005111865831035 " "
y[1] (numeric) = 1.4005111865831825 " "
absolute error = 7.90478793533111500000000000000E-14 " "
relative error = 5.644216205524797000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.851757613062689 " "
Order of pole = 4.436743107446539 " "
x[1] = -0.8439999999999999 " "
y[1] (analytic) = 1.4038318995530203 " "
y[1] (numeric) = 1.4038318995531005 " "
absolute error = 8.0158102377936300000000000000E-14 " "
relative error = 5.709950201548962000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.850749615887468 " "
Order of pole = 4.436743107446578 " "
x[1] = -0.8429999999999999 " "
y[1] (analytic) = 1.4071644370146166 " "
y[1] (numeric) = 1.4071644370146978 " "
absolute error = 8.12683254025614600000000000000E-14 " "
relative error = 5.7753254179004890000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8497416187122481 " "
Order of pole = 4.436743107446656 " "
x[1] = -0.8419999999999999 " "
y[1] (analytic) = 1.4105088551745932 " "
y[1] (numeric) = 1.4105088551746754 " "
absolute error = 8.21565038222615800000000000000E-14 " "
relative error = 5.824600357584584000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8487336215370197 " "
Order of pole = 4.436743107446436 " "
x[1] = -0.8409999999999999 " "
y[1] (analytic) = 1.4138652105740157 " "
y[1] (numeric) = 1.4138652105740988 " "
absolute error = 8.30446822419617100000000000000E-14 " "
relative error = 5.87359259007769000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8477256243617975 " "
Order of pole = 4.4367431074464285 " "
x[1] = -0.8399999999999999 " "
y[1] (analytic) = 1.4172335600907033 " "
y[1] (numeric) = 1.4172335600907875 " "
absolute error = 8.41549052665868700000000000000E-14 " "
relative error = 5.937970115610368000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8467176271865804 " "
Order of pole = 4.436743107446606 " "
x[1] = -0.8389999999999999 " "
y[1] (analytic) = 1.4206139609416402 " "
y[1] (numeric) = 1.4206139609417252 " "
absolute error = 8.50430836862869900000000000000E-14 " "
relative error = 5.986361251153480000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8457096300113576 " "
Order of pole = 4.436743107446585 " "
x[1] = -0.8379999999999999 " "
y[1] (analytic) = 1.4240064706854032 " "
y[1] (numeric) = 1.4240064706854891 " "
absolute error = 8.59312621059871200000000000000E-14 " "
relative error = 6.03447132263567900000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8447016328361378 " "
Order of pole = 4.436743107446667 " "
x[1] = -0.8369999999999999 " "
y[1] (analytic) = 1.4274111472246136 " "
y[1] (numeric) = 1.4274111472247004 " "
absolute error = 8.68194405256872400000000000000E-14 " "
relative error = 6.0823008629640160000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8436936356609086 " "
Order of pole = 4.436743107446414 " "
x[1] = -0.8359999999999999 " "
y[1] (analytic) = 1.4308280488084069 " "
y[1] (numeric) = 1.4308280488084948 " "
absolute error = 8.7929663550312400000000000000E-14 " "
relative error = 6.1453690136659110000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8426856384856884 " "
Order of pole = 4.436743107446489 " "
x[1] = -0.8349999999999999 " "
y[1] (analytic) = 1.4342572340349244 " "
y[1] (numeric) = 1.4342572340350135 " "
absolute error = 8.90398865749375500000000000000E-14 " "
relative error = 6.208083491721083000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8416776413104605 " "
Order of pole = 4.436743107446283 " "
x[1] = -0.8339999999999999 " "
y[1] (analytic) = 1.4376987618538268 " "
y[1] (numeric) = 1.4376987618539168 " "
absolute error = 8.99280649946376800000000000000E-14 " "
relative error = 6.255000517541018000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8406696441352525 " "
Order of pole = 4.436743107446777 " "
x[1] = -0.8329999999999999 " "
y[1] (analytic) = 1.4411526915688249 " "
y[1] (numeric) = 1.441152691568916 " "
absolute error = 9.10382880192628400000000000000E-14 " "
relative error = 6.317046663539825000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8396616469600199 " "
Order of pole = 4.436743107446404 " "
x[1] = -0.8319999999999999 " "
y[1] (analytic) = 1.4446190828402372 " "
y[1] (numeric) = 1.4446190828403291 " "
absolute error = 9.19264664389629600000000000000E-14 " "
relative error = 6.363370630424467000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8386536497847985 " "
Order of pole = 4.436743107446432 " "
x[1] = -0.8309999999999998 " "
y[1] (analytic) = 1.4480979956875648 " "
y[1] (numeric) = 1.4480979956876576 " "
absolute error = 9.28146448586630900000000000000E-14 " "
relative error = 6.409417396824322000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8376456526095766 " "
Order of pole = 4.436743107446436 " "
x[1] = -0.8299999999999998 " "
y[1] (analytic) = 1.4515894904920894 " "
y[1] (numeric) = 1.4515894904921833 " "
absolute error = 9.39248678832882400000000000000E-14 " "
relative error = 6.470484148479725000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8366376554343519 " "
Order of pole = 4.436743107446343 " "
x[1] = -0.8289999999999998 " "
y[1] (analytic) = 1.455093627999494 " "
y[1] (numeric) = 1.4550936279995892 " "
absolute error = 9.52571355128384300000000000000E-14 " "
relative error = 6.546460906697859000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.835629658259136 " "
Order of pole = 4.436743107446570 " "
x[1] = -0.8279999999999998 " "
y[1] (analytic) = 1.4586104693225053 " "
y[1] (numeric) = 1.4586104693226012 " "
absolute error = 9.59232693276135300000000000000E-14 " "
relative error = 6.576345867870256000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8346216610839218 " "
Order of pole = 4.436743107446851 " "
x[1] = -0.8269999999999998 " "
y[1] (analytic) = 1.462140075943556 " "
y[1] (numeric) = 1.4621400759436531 " "
absolute error = 9.70334923522386800000000000000E-14 " "
relative error = 6.6364019390974230000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8336136639086914 " "
Order of pole = 4.436743107446556 " "
x[1] = -0.8259999999999998 " "
y[1] (analytic) = 1.4656825097174755 " "
y[1] (numeric) = 1.4656825097175739 " "
absolute error = 9.83657599817888700000000000000E-14 " "
relative error = 6.7112597257334960000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8326056667334649 " "
Order of pole = 4.4367431074463966 " "
x[1] = -0.8249999999999998 " "
y[1] (analytic) = 1.469237832874197 " "
y[1] (numeric) = 1.4692378328742965 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 6.770584093374052000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8315976695582445 " "
Order of pole = 4.436743107446468 " "
x[1] = -0.8239999999999998 " "
y[1] (analytic) = 1.4728061080214916 " "
y[1] (numeric) = 1.4728061080215924 " "
absolute error = 1.00808250635964210000000000000E-13 " "
relative error = 6.844638278380442000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8305896723830278 " "
Order of pole = 4.436743107446656 " "
x[1] = -0.8229999999999998 " "
y[1] (analytic) = 1.4763873981477251 " "
y[1] (numeric) = 1.4763873981478268 " "
absolute error = 1.01696429055664340000000000000E-13 " "
relative error = 6.888194059584404000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8295816752077951 " "
Order of pole = 4.436743107446276 " "
x[1] = -0.8219999999999998 " "
y[1] (analytic) = 1.4799817666246358 " "
y[1] (numeric) = 1.4799817666247388 " "
absolute error = 1.03028696685214530000000000000E-13 " "
relative error = 6.961484189105247000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.828573678032579 " "
Order of pole = 4.436743107446482 " "
x[1] = -0.8209999999999998 " "
y[1] (analytic) = 1.4835892772101407 " "
y[1] (numeric) = 1.4835892772102448 " "
absolute error = 1.04138919709839680000000000000E-13 " "
relative error = 7.019390158014002000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8275656808573587 " "
Order of pole = 4.436743107446556 " "
x[1] = -0.8199999999999998 " "
y[1] (analytic) = 1.4872099940511605 " "
y[1] (numeric) = 1.487209994051266 " "
absolute error = 1.05471187339389870000000000000E-13 " "
relative error = 7.0918826367005730000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8265576836821399 " "
Order of pole = 4.436743107446674 " "
x[1] = -0.8189999999999998 " "
y[1] (analytic) = 1.4908439816864731 " "
y[1] (numeric) = 1.4908439816865797 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 7.149065339717706000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8255496865069143 " "
Order of pole = 4.436743107446550 " "
x[1] = -0.8179999999999998 " "
y[1] (analytic) = 1.4944913050495878 " "
y[1] (numeric) = 1.4944913050496957 " "
absolute error = 1.07913677993565220000000000000E-13 " "
relative error = 7.22076318737663000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8245416893316945 " "
Order of pole = 4.436743107446635 " "
x[1] = -0.8169999999999998 " "
y[1] (analytic) = 1.4981520294716473 " "
y[1] (numeric) = 1.4981520294717565 " "
absolute error = 1.0924594562311540000000000000E-13 " "
relative error = 7.292046699802764000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.82353369215647 " "
Order of pole = 4.436743107446550 " "
x[1] = -0.8159999999999998 " "
y[1] (analytic) = 1.501826220684353 " "
y[1] (numeric) = 1.5018262206844633 " "
absolute error = 1.10356168647740560000000000000E-13 " "
relative error = 7.34813170311099000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8225256949812495 " "
Order of pole = 4.436743107446606 " "
x[1] = -0.8149999999999998 " "
y[1] (analytic) = 1.5055139448229145 " "
y[1] (numeric) = 1.5055139448230264 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 7.433373916398975000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8215176978060256 " "
Order of pole = 4.436743107446542 " "
x[1] = -0.8139999999999998 " "
y[1] (analytic) = 1.509215268429028 " "
y[1] (numeric) = 1.5092152684291413 " "
absolute error = 1.13242748511765970000000000000E-13 " "
relative error = 7.503419219290207000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8205097006308074 " "
Order of pole = 4.436743107446688 " "
x[1] = -0.8129999999999998 " "
y[1] (analytic) = 1.5129302584538766 " "
y[1] (numeric) = 1.512930258453991 " "
absolute error = 1.14352971536391120000000000000E-13 " "
relative error = 7.558376924343687000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8195017034555846 " "
Order of pole = 4.4367431074466595 " "
x[1] = -0.8119999999999998 " "
y[1] (analytic) = 1.5166589822611571 " "
y[1] (numeric) = 1.5166589822612728 " "
absolute error = 1.1568523916594131000000000000E-13 " "
relative error = 7.627636833262839000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8184937062803632 " "
Order of pole = 4.436743107446691 " "
x[1] = -0.8109999999999998 " "
y[1] (analytic) = 1.5204015076301356 " "
y[1] (numeric) = 1.5204015076302526 " "
absolute error = 1.1701750679549150000000000000E-13 " "
relative error = 7.696487158703743000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8174857091051301 " "
Order of pole = 4.436743107446283 " "
x[1] = -0.8099999999999998 " "
y[1] (analytic) = 1.5241579027587262 " "
y[1] (numeric) = 1.5241579027588448 " "
absolute error = 1.18571819029966720000000000000E-13 " "
relative error = 7.779497046556114000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8164777119299201 " "
Order of pole = 4.436743107446727 " "
x[1] = -0.8089999999999998 " "
y[1] (analytic) = 1.5279282362665998 " "
y[1] (numeric) = 1.5279282362667193 " "
absolute error = 1.19459997449666840000000000000E-13 " "
relative error = 7.818429859085537000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8154697147546965 " "
Order of pole = 4.436743107446674 " "
x[1] = -0.8079999999999998 " "
y[1] (analytic) = 1.5317125771983144 " "
y[1] (numeric) = 1.5317125771984355 " "
absolute error = 1.21014309684142060000000000000E-13 " "
relative error = 7.90058862776277000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8144617175794778 " "
Order of pole = 4.436743107446798 " "
x[1] = -0.8069999999999998 " "
y[1] (analytic) = 1.5355109950264807 " "
y[1] (numeric) = 1.5355109950266028 " "
absolute error = 1.22124532708767220000000000000E-13 " "
relative error = 7.95334798020519000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8134537204042506 " "
Order of pole = 4.43674310744661 " "
x[1] = -0.8059999999999998 " "
y[1] (analytic) = 1.5393235596549457 " "
y[1] (numeric) = 1.5393235596550696 " "
absolute error = 1.23900889548167470000000000000E-13 " "
relative error = 8.04904782825133000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8124457232290213 " "
Order of pole = 4.43674310744635 " "
x[1] = -0.8049999999999998 " "
y[1] (analytic) = 1.5431503414220138 " "
y[1] (numeric) = 1.5431503414221388 " "
absolute error = 1.25011112572792630000000000000E-13 " "
relative error = 8.10103262249839000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8114377260538028 " "
Order of pole = 4.436743107446489 " "
x[1] = -0.8039999999999998 " "
y[1] (analytic) = 1.5469914111036862 " "
y[1] (numeric) = 1.5469914111038128 " "
absolute error = 1.26565424807267850000000000000E-13 " "
relative error = 8.181391564221482000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8104297288785784 " "
Order of pole = 4.4367431074463966 " "
x[1] = -0.8029999999999998 " "
y[1] (analytic) = 1.5508468399169373 " "
y[1] (numeric) = 1.5508468399170652 " "
absolute error = 1.27897692436818030000000000000E-13 " "
relative error = 8.246958316249215000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8094217317033612 " "
Order of pole = 4.436743107446578 " "
x[1] = -0.8019999999999998 " "
y[1] (analytic) = 1.5547166995230135 " "
y[1] (numeric) = 1.554716699523143 " "
absolute error = 1.29452004671293250000000000000E-13 " "
relative error = 8.326404721259447000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8084137345281357 " "
Order of pole = 4.436743107446453 " "
x[1] = -0.8009999999999998 " "
y[1] (analytic) = 1.5586010620307644 " "
y[1] (numeric) = 1.5586010620308952 " "
absolute error = 1.30784272300843440000000000000E-13 " "
relative error = 8.39113198924934100000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8074057373529159 " "
Order of pole = 4.436743107446542 " "
x[1] = -0.7999999999999998 " "
y[1] (analytic) = 1.5625000000000007 " "
y[1] (numeric) = 1.562500000000133 " "
absolute error = 1.32338584535318660000000000000E-13 " "
relative error = 8.469669410260391000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8063977401776965 " "
Order of pole = 4.436743107446638 " "
x[1] = -0.7989999999999998 " "
y[1] (analytic) = 1.566413586444884 " "
y[1] (numeric) = 1.566413586445018 " "
absolute error = 1.33892896769793880000000000000E-13 " "
relative error = 8.547735919073315000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8053897430024787 " "
Order of pole = 4.436743107446798 " "
x[1] = -0.7979999999999998 " "
y[1] (analytic) = 1.5703418948373449 " "
y[1] (numeric) = 1.57034189483748 " "
absolute error = 1.35225164399344070000000000000E-13 " "
relative error = 8.611192559015984000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8043817458272485 " "
Order of pole = 4.436743107446503 " "
x[1] = -0.7969999999999998 " "
y[1] (analytic) = 1.5742849991105297 " "
y[1] (numeric) = 1.5742849991106667 " "
absolute error = 1.37001521238744320000000000000E-13 " "
relative error = 8.70245993045415000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8033737486520253 " "
Order of pole = 4.436743107446457 " "
x[1] = -0.7959999999999998 " "
y[1] (analytic) = 1.578242973662282 " "
y[1] (numeric) = 1.5782429736624204 " "
absolute error = 1.3833378886829450000000000000E-13 " "
relative error = 8.765050196757325000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8023657514768124 " "
Order of pole = 4.436743107446809 " "
x[1] = -0.7949999999999998 " "
y[1] (analytic) = 1.5822158933586496 " "
y[1] (numeric) = 1.5822158933587895 " "
absolute error = 1.39888101102769720000000000000E-13 " "
relative error = 8.841277709947798000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8013577543015878 " "
Order of pole = 4.436743107446710 " "
x[1] = -0.7939999999999998 " "
y[1] (analytic) = 1.5862038335374258 " "
y[1] (numeric) = 1.5862038335375672 " "
absolute error = 1.41442413337244940000000000000E-13 " "
relative error = 8.91703892946793000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.8003497571263534 " "
Order of pole = 4.436743107446251 " "
x[1] = -0.7929999999999998 " "
y[1] (analytic) = 1.5902068700117205 " "
y[1] (numeric) = 1.5902068700118637 " "
absolute error = 1.4321877017664520000000000000E-13 " "
relative error = 9.006298040681311000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7993417599511426 " "
Order of pole = 4.436743107446674 " "
x[1] = -0.7919999999999998 " "
y[1] (analytic) = 1.5942250790735648 " "
y[1] (numeric) = 1.5942250790737094 " "
absolute error = 1.44551037806195380000000000000E-13 " "
relative error = 9.067166217846528000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7983337627759195 " "
Order of pole = 4.436743107446645 " "
x[1] = -0.7909999999999998 " "
y[1] (analytic) = 1.5982585374975433 " "
y[1] (numeric) = 1.5982585374976896 " "
absolute error = 1.46327394645595630000000000000E-13 " "
relative error = 9.155427060925089000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7973257656006972 " "
Order of pole = 4.436743107446635 " "
x[1] = -0.7899999999999998 " "
y[1] (analytic) = 1.6023073225444648 " "
y[1] (numeric) = 1.6023073225446125 " "
absolute error = 1.47659662275145820000000000000E-13 " "
relative error = 9.215439522591846000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.796317768425468 " "
Order of pole = 4.436743107446368 " "
x[1] = -0.7889999999999998 " "
y[1] (analytic) = 1.606371511965059 " "
y[1] (numeric) = 1.6063715119652082 " "
absolute error = 1.49213974509621040000000000000E-13 " "
relative error = 9.288883262570375000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7953097712502512 " "
Order of pole = 4.43674310744656 " "
x[1] = -0.7879999999999998 " "
y[1] (analytic) = 1.6104511840037112 " "
y[1] (numeric) = 1.6104511840038622 " "
absolute error = 1.5099033134902130000000000000E-13 " "
relative error = 9.375654030918663000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7943017740750322 " "
Order of pole = 4.436743107446684 " "
x[1] = -0.7869999999999998 " "
y[1] (analytic) = 1.6145464174022277 " "
y[1] (numeric) = 1.6145464174023805 " "
absolute error = 1.52766688188421540000000000000E-13 " "
relative error = 9.461895089657443000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7932937768998027 " "
Order of pole = 4.436743107446410 " "
x[1] = -0.7859999999999998 " "
y[1] (analytic) = 1.6186572914036357 " "
y[1] (numeric) = 1.61865729140379 " "
absolute error = 1.54321000422896760000000000000E-13 " "
relative error = 9.533889677726388000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7922857797245788 " "
Order of pole = 4.436743107446336 " "
x[1] = -0.7849999999999998 " "
y[1] (analytic) = 1.6227838857560153 " "
y[1] (numeric) = 1.6227838857561712 " "
absolute error = 1.55875312657371980000000000000E-13 " "
relative error = 9.6054264542289000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7912777825493525 " "
Order of pole = 4.436743107446187 " "
x[1] = -0.7839999999999998 " "
y[1] (analytic) = 1.6269262807163691 " "
y[1] (numeric) = 1.6269262807165266 " "
absolute error = 1.5742962489184720000000000000E-13 " "
relative error = 9.676506351752318000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7902697853741429 " "
Order of pole = 4.436743107446656 " "
x[1] = -0.7829999999999998 " "
y[1] (analytic) = 1.631084557054523 " "
y[1] (numeric) = 1.6310845570546824 " "
absolute error = 1.59428026336172480000000000000E-13 " "
relative error = 9.77435692384176000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.789261788198921 " "
Order of pole = 4.43674310744667 " "
x[1] = -0.7819999999999998 " "
y[1] (analytic) = 1.6352587960570648 " "
y[1] (numeric) = 1.6352587960572258 " "
absolute error = 1.6098233857064770000000000000E-13 " "
relative error = 9.844456361207671000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7882537910236963 " "
Order of pole = 4.436743107446567 " "
x[1] = -0.7809999999999998 " "
y[1] (analytic) = 1.6394490795313152 " "
y[1] (numeric) = 1.6394490795314778 " "
absolute error = 1.62536650805122920000000000000E-13 " "
relative error = 9.914101806174352000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7872457938484771 " "
Order of pole = 4.436743107446674 " "
x[1] = -0.7799999999999998 " "
y[1] (analytic) = 1.6436554898093367 " "
y[1] (numeric) = 1.6436554898095013 " "
absolute error = 1.6453505224944820000000000000E-13 " "
relative error = 1.001031257885642400000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7862377966732532 " "
Order of pole = 4.436743107446606 " "
x[1] = -0.7789999999999998 " "
y[1] (analytic) = 1.6478781097519786 " "
y[1] (numeric) = 1.6478781097521449 " "
absolute error = 1.66311409088848450000000000000E-13 " "
relative error = 1.009245818028858400000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7852297994980395 " "
Order of pole = 4.436743107446926 " "
x[1] = -0.7779999999999998 " "
y[1] (analytic) = 1.6521170227529565 " "
y[1] (numeric) = 1.6521170227531246 " "
absolute error = 1.6808776592824870000000000000E-13 " "
relative error = 1.017408353121140400000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7842218023228074 " "
Order of pole = 4.436743107446542 " "
x[1] = -0.7769999999999998 " "
y[1] (analytic) = 1.65637231274297 " "
y[1] (numeric) = 1.6563723127431398 " "
absolute error = 1.69864122767648950000000000000E-13 " "
relative error = 1.025518969743898800000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7832138051475765 " "
Order of pole = 4.436743107446219 " "
x[1] = -0.7759999999999998 " "
y[1] (analytic) = 1.6606440641938578 " "
y[1] (numeric) = 1.6606440641940294 " "
absolute error = 1.7164047960704920000000000000E-13 " "
relative error = 1.033577774478544000000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7822058079723639 " "
Order of pole = 4.436743107446578 " "
x[1] = -0.7749999999999998 " "
y[1] (analytic) = 1.6649323621227896 " "
y[1] (numeric) = 1.664932362122963 " "
absolute error = 1.73416836446449450000000000000E-13 " "
relative error = 1.041584873906486600000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7811978107971439 " "
Order of pole = 4.436743107446656 " "
x[1] = -0.7739999999999998 " "
y[1] (analytic) = 1.6692372920964962 " "
y[1] (numeric) = 1.6692372920966714 " "
absolute error = 1.7519319328584970000000000000E-13 " "
relative error = 1.049540374609136400000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.780189813621926 " "
Order of pole = 4.436743107446820 " "
x[1] = -0.7729999999999998 " "
y[1] (analytic) = 1.6735589402355375 " "
y[1] (numeric) = 1.6735589402357147 " "
absolute error = 1.77191594730174980000000000000E-13 " "
relative error = 1.058771164075266900000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7791818164467038 " "
Order of pole = 4.436743107446816 " "
x[1] = -0.7719999999999998 " "
y[1] (analytic) = 1.6778973932186108 " "
y[1] (numeric) = 1.67789739321879 " "
absolute error = 1.79189996174500270000000000000E-13 " "
relative error = 1.067943706800633100000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7781738192714693 " "
Order of pole = 4.436743107446347 " "
x[1] = -0.7709999999999998 " "
y[1] (analytic) = 1.6822527382868955 " "
y[1] (numeric) = 1.6822527382870767 " "
absolute error = 1.81188397618825550000000000000E-13 " "
relative error = 1.077058122689322400000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7771658220962516 " "
Order of pole = 4.436743107446514 " "
x[1] = -0.7699999999999998 " "
y[1] (analytic) = 1.686625063248441 " "
y[1] (numeric) = 1.6866250632486237 " "
absolute error = 1.82742709853300770000000000000E-13 " "
relative error = 1.083481526720219600000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7761578249210312 " "
Order of pole = 4.436743107446578 " "
x[1] = -0.7689999999999998 " "
y[1] (analytic) = 1.6910144564825893 " "
y[1] (numeric) = 1.6910144564827743 " "
absolute error = 1.84963155902551080000000000000E-13 " "
relative error = 1.093799968376884500000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7751498277458091 " "
Order of pole = 4.436743107446578 " "
x[1] = -0.7679999999999998 " "
y[1] (analytic) = 1.6954210069444453 " "
y[1] (numeric) = 1.6954210069446323 " "
absolute error = 1.86961557346876360000000000000E-13 " "
relative error = 1.102744136005639500000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7741418305705857 " "
Order of pole = 4.436743107446528 " "
x[1] = -0.7669999999999998 " "
y[1] (analytic) = 1.6998448041693803 " "
y[1] (numeric) = 1.6998448041695693 " "
absolute error = 1.88959958791201640000000000000E-13 " "
relative error = 1.111630651973171700000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7731338333953593 " "
Order of pole = 4.436743107446365 " "
x[1] = -0.7659999999999998 " "
y[1] (analytic) = 1.7042859382775812 " "
y[1] (numeric) = 1.7042859382777724 " "
absolute error = 1.91180404840451960000000000000E-13 " "
relative error = 1.121762496225641700000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7721258362201401 " "
Order of pole = 4.436743107446482 " "
x[1] = -0.7649999999999998 " "
y[1] (analytic) = 1.7087444999786419 " "
y[1] (numeric) = 1.7087444999788348 " "
absolute error = 1.9295676167985220000000000000E-13 " "
relative error = 1.129231208540914400000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7711178390449159 " "
Order of pole = 4.436743107446393 " "
x[1] = -0.7639999999999998 " "
y[1] (analytic) = 1.7132205805761913 " "
y[1] (numeric) = 1.7132205805763865 " "
absolute error = 1.95177207729102520000000000000E-13 " "
relative error = 1.139241554426461700000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7701098418697051 " "
Order of pole = 4.43674310744683 " "
x[1] = -0.7629999999999998 " "
y[1] (analytic) = 1.7177142719725724 " "
y[1] (numeric) = 1.7177142719727698 " "
absolute error = 1.97397653778352830000000000000E-13 " "
relative error = 1.149187947024898300000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7691018446944748 " "
Order of pole = 4.436743107446517 " "
x[1] = -0.7619999999999998 " "
y[1] (analytic) = 1.7222256666735565 " "
y[1] (numeric) = 1.722225666673756 " "
absolute error = 1.99618099827603150000000000000E-13 " "
relative error = 1.159070519562987500000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.768093847519248 " "
Order of pole = 4.436743107446333 " "
x[1] = -0.7609999999999998 " "
y[1] (analytic) = 1.7267548577931047 " "
y[1] (numeric) = 1.7267548577933063 " "
absolute error = 2.01616501271928430000000000000E-13 " "
relative error = 1.167603498331004000000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7670858503440275 " "
Order of pole = 4.4367431074464 " "
x[1] = -0.7599999999999998 " "
y[1] (analytic) = 1.7313019390581728 " "
y[1] (numeric) = 1.7313019390583766 " "
absolute error = 2.03836947321178740000000000000E-13 " "
relative error = 1.177362207727127700000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7660778531688097 " "
Order of pole = 4.4367431074465635 " "
x[1] = -0.7589999999999998 " "
y[1] (analytic) = 1.7358670048135603 " "
y[1] (numeric) = 1.7358670048137663 " "
absolute error = 2.06057393370429050000000000000E-13 " "
relative error = 1.187057492302300600000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7650698559935847 " "
Order of pole = 4.43674310744645 " "
x[1] = -0.7579999999999998 " "
y[1] (analytic) = 1.740450150026804 " "
y[1] (numeric) = 1.7404501500270122 " "
absolute error = 2.08277839419679370000000000000E-13 " "
relative error = 1.196689485283285900000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7640618588183671 " "
Order of pole = 4.436743107446631 " "
x[1] = -0.7569999999999998 " "
y[1] (analytic) = 1.7450514702931175 " "
y[1] (numeric) = 1.7450514702933277 " "
absolute error = 2.10276240864004650000000000000E-13 " "
relative error = 1.204985895508769200000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7630538616431457 " "
Order of pole = 4.4367431074466595 " "
x[1] = -0.7559999999999998 " "
y[1] (analytic) = 1.7496710618403752 " "
y[1] (numeric) = 1.7496710618405877 " "
absolute error = 2.12496686913254960000000000000E-13 " "
relative error = 1.2144950645165400000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7620458644679272 " "
Order of pole = 4.436743107446798 " "
x[1] = -0.7549999999999998 " "
y[1] (analytic) = 1.7543090215341441 " "
y[1] (numeric) = 1.7543090215343593 " "
absolute error = 2.15161222172355340000000000000E-13 " "
relative error = 1.226472756687967800000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7610378672927004 " "
Order of pole = 4.436743107446613 " "
x[1] = -0.7539999999999998 " "
y[1] (analytic) = 1.7589654468827625 " "
y[1] (numeric) = 1.7589654468829798 " "
absolute error = 2.17381668221605650000000000000E-13 " "
relative error = 1.235849564906742900000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7600298701174814 " "
Order of pole = 4.436743107446734 " "
x[1] = -0.7529999999999998 " "
y[1] (analytic) = 1.7636404360424625 " "
y[1] (numeric) = 1.7636404360426823 " "
absolute error = 2.198241588757810000000000000E-13 " "
relative error = 1.246422764999976400000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7590218729422514 " "
Order of pole = 4.436743107446425 " "
x[1] = -0.7519999999999998 " "
y[1] (analytic) = 1.7683340878225453 " "
y[1] (numeric) = 1.7683340878227674 " "
absolute error = 2.2204460492503130000000000000E-13 " "
relative error = 1.255671122635248200000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7580138757670283 " "
Order of pole = 4.4367431074463894 " "
x[1] = -0.7509999999999998 " "
y[1] (analytic) = 1.7730465016906007 " "
y[1] (numeric) = 1.7730465016908254 " "
absolute error = 2.24709140184131680000000000000E-13 " "
relative error = 1.267361797729904000000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7570058785918056 " "
Order of pole = 4.436743107446365 " "
x[1] = -0.7499999999999998 " "
y[1] (analytic) = 1.7777777777777788 " "
y[1] (numeric) = 1.7777777777780057 " "
absolute error = 2.269295862333820000000000000E-13 " "
relative error = 1.276478922562773200000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7559978814165828 " "
Order of pole = 4.436743107446347 " "
x[1] = -0.7489999999999998 " "
y[1] (analytic) = 1.7825280168841064 " "
y[1] (numeric) = 1.7825280168843358 " "
absolute error = 2.29372076887557340000000000000E-13 " "
relative error = 1.286779645059964700000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7549898842413698 " "
Order of pole = 4.4367431074466985 " "
x[1] = -0.7479999999999998 " "
y[1] (analytic) = 1.7872973204838583 " "
y[1] (numeric) = 1.78729732048409 " "
absolute error = 2.3181456754173269000000000000E-13 " "
relative error = 1.297011777978695200000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.75398188706614 " "
Order of pole = 4.4367431074463966 " "
x[1] = -0.7469999999999998 " "
y[1] (analytic) = 1.792085790730975 " "
y[1] (numeric) = 1.7920857907312093 " "
absolute error = 2.34257058195908030000000000000E-13 " "
relative error = 1.307175467868403600000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7529738898909197 " "
Order of pole = 4.436743107446464 " "
x[1] = -0.7459999999999998 " "
y[1] (analytic) = 1.7968935304645341 " "
y[1] (numeric) = 1.7968935304647708 " "
absolute error = 2.36699548850083370000000000000E-13 " "
relative error = 1.31727086127852920000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7519658927157041 " "
Order of pole = 4.4367431074467305 " "
x[1] = -0.7449999999999998 " "
y[1] (analytic) = 1.801720643214271 " "
y[1] (numeric) = 1.80172064321451 " "
absolute error = 2.3914203950425872000000000000E-13 " "
relative error = 1.32729810475851080000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.750957895540478 " "
Order of pole = 4.436743107446574 " "
x[1] = -0.7439999999999998 " "
y[1] (analytic) = 1.806567233206152 " "
y[1] (numeric) = 1.806567233206394 " "
absolute error = 2.42028619368284130000000000000E-13 " "
relative error = 1.339715538506424700000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.749949898365256 " "
Order of pole = 4.436743107446574 " "
x[1] = -0.7429999999999998 " "
y[1] (analytic) = 1.8114334053680028 " "
y[1] (numeric) = 1.8114334053682475 " "
absolute error = 2.4469315462738450000000000000E-13 " "
relative error = 1.35082611318892900000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7489419011900348 " "
Order of pole = 4.43674310744661 " "
x[1] = -0.7419999999999998 " "
y[1] (analytic) = 1.8163192653351847 " "
y[1] (numeric) = 1.8163192653354319 " "
absolute error = 2.47135645281559850000000000000E-13 " "
relative error = 1.360639894087966300000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7479339040148159 " "
Order of pole = 4.436743107446738 " "
x[1] = -0.7409999999999998 " "
y[1] (analytic) = 1.8212249194563292 " "
y[1] (numeric) = 1.8212249194565788 " "
absolute error = 2.4957813593573520000000000000E-13 " "
relative error = 1.370386124577293300000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7469259068395846 " "
Order of pole = 4.436743107446375 " "
x[1] = -0.7399999999999998 " "
y[1] (analytic) = 1.8261504747991246 " "
y[1] (numeric) = 1.826150474799377 " "
absolute error = 2.5246471579976060000000000000E-13 " "
relative error = 1.382496783719488200000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7459179096643773 " "
Order of pole = 4.436743107446972 " "
x[1] = -0.7389999999999998 " "
y[1] (analytic) = 1.8310960391561588 " "
y[1] (numeric) = 1.8310960391564142 " "
absolute error = 2.553512956637860000000000000E-13 " "
relative error = 1.39452704939202400000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7449099124891393 " "
Order of pole = 4.4367431074463255 " "
x[1] = -0.7379999999999998 " "
y[1] (analytic) = 1.836061721050816 " "
y[1] (numeric) = 1.8360617210510741 " "
absolute error = 2.5801583092288640000000000000E-13 " "
relative error = 1.405267742171644200000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7439019153139217 " "
Order of pole = 4.436743107446507 " "
x[1] = -0.7369999999999998 " "
y[1] (analytic) = 1.8410476297432303 " "
y[1] (numeric) = 1.8410476297434912 " "
absolute error = 2.6090241078691180000000000000E-13 " "
relative error = 1.417141015647159800000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7428939181387 " "
Order of pole = 4.436743107446528 " "
x[1] = -0.7359999999999998 " "
y[1] (analytic) = 1.846053875236296 " "
y[1] (numeric) = 1.8460538752365598 " "
absolute error = 2.6378899065093720000000000000E-13 " "
relative error = 1.428934410796500000000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7418859209634813 " "
Order of pole = 4.436743107446663 " "
x[1] = -0.7349999999999998 " "
y[1] (analytic) = 1.8510805682817355 " "
y[1] (numeric) = 1.8510805682820022 " "
absolute error = 2.6667557051496260000000000000E-13 " "
relative error = 1.440648100814456000000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7408779237882486 " "
Order of pole = 4.436743107446237 " "
x[1] = -0.7339999999999998 " "
y[1] (analytic) = 1.8561278203862241 " "
y[1] (numeric) = 1.8561278203864937 " "
absolute error = 2.695621503789880000000000000E-13 " "
relative error = 1.452282258895819800000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7398699266130432 " "
Order of pole = 4.436743107446915 " "
x[1] = -0.7329999999999998 " "
y[1] (analytic) = 1.8611957438175744 " "
y[1] (numeric) = 1.8611957438178466 " "
absolute error = 2.7222668563808840000000000000E-13 " "
relative error = 1.462644036998027600000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7388619294378101 " "
Order of pole = 4.436743107446464 " "
x[1] = -0.7319999999999998 " "
y[1] (analytic) = 1.866284451610978 " "
y[1] (numeric) = 1.8662844516112533 " "
absolute error = 2.7533531010703880000000000000E-13 " "
relative error = 1.475312672027938600000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7378539322625888 " "
Order of pole = 4.436743107446503 " "
x[1] = -0.7309999999999998 " "
y[1] (analytic) = 1.871394057575311 " "
y[1] (numeric) = 1.8713940575755892 " "
absolute error = 2.78221889971064230000000000000E-13 " "
relative error = 1.486709273468277400000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.736845935087366 " "
Order of pole = 4.436743107446478 " "
x[1] = -0.7299999999999998 " "
y[1] (analytic) = 1.8765246762994945 " "
y[1] (numeric) = 1.876524676299776 " "
absolute error = 2.8155255904493970000000000000E-13 " "
relative error = 1.500393587150482800000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7358379379121515 " "
Order of pole = 4.43674310744678 " "
x[1] = -0.7289999999999998 " "
y[1] (analytic) = 1.881676423158922 " "
y[1] (numeric) = 1.8816764231592065 " "
absolute error = 2.8443913890896510000000000000E-13 " "
relative error = 1.51162620420919200000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7348299407369219 " "
Order of pole = 4.436743107446482 " "
x[1] = -0.7279999999999998 " "
y[1] (analytic) = 1.886849414321943 " "
y[1] (numeric) = 1.8868494143222305 " "
absolute error = 2.87547763377915540000000000000E-13 " "
relative error = 1.52395713826081080000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7338219435616993 " "
Order of pole = 4.436743107446457 " "
x[1] = -0.7269999999999998 " "
y[1] (analytic) = 1.892043766756414 " "
y[1] (numeric) = 1.8920437667567045 " "
absolute error = 2.90434343241940950000000000000E-13 " "
relative error = 1.53502972999319700000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7328139463864709 " "
Order of pole = 4.436743107446205 " "
x[1] = -0.7259999999999998 " "
y[1] (analytic) = 1.8972595982363085 " "
y[1] (numeric) = 1.8972595982366025 " "
absolute error = 2.93987056920741450000000000000E-13 " "
relative error = 1.549535220135566000000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7318059492112643 " "
Order of pole = 4.436743107446840 " "
x[1] = -0.7249999999999998 " "
y[1] (analytic) = 1.902497027348396 " "
y[1] (numeric) = 1.902497027348693 " "
absolute error = 2.96873636784766860000000000000E-13 " "
relative error = 1.560442053349930000000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7307979520360337 " "
Order of pole = 4.436743107446489 " "
x[1] = -0.7239999999999998 " "
y[1] (analytic) = 1.9077561734989787 " "
y[1] (numeric) = 1.907756173499279 " "
absolute error = 3.00204305858642330000000000000E-13 " "
relative error = 1.57359892227759600000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7297899548608155 " "
Order of pole = 4.436743107446649 " "
x[1] = -0.7229999999999998 " "
y[1] (analytic) = 1.9130371569207 " "
y[1] (numeric) = 1.9130371569210036 " "
absolute error = 3.0353497493251780000000000000E-13 " "
relative error = 1.58666533911500000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7287819576855857 " "
Order of pole = 4.436743107446336 " "
x[1] = -0.7219999999999998 " "
y[1] (analytic) = 1.9183400986794161 " "
y[1] (numeric) = 1.9183400986797228 " "
absolute error = 3.06643599401468240000000000000E-13 " "
relative error = 1.598484020703948300000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7277739605103732 " "
Order of pole = 4.436743107446738 " "
x[1] = -0.7209999999999998 " "
y[1] (analytic) = 1.9236651206811326 " "
y[1] (numeric) = 1.9236651206814428 " "
absolute error = 3.10196313080268740000000000000E-13 " "
relative error = 1.61252761587959900000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7267659633351483 " "
Order of pole = 4.43674310744662 " "
x[1] = -0.7199999999999998 " "
y[1] (analytic) = 1.9290123456790136 " "
y[1] (numeric) = 1.9290123456793271 " "
absolute error = 3.1352698215414420000000000000E-13 " "
relative error = 1.625323875487082700000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7257579661599309 " "
Order of pole = 4.436743107446809 " "
x[1] = -0.7189999999999998 " "
y[1] (analytic) = 1.934381897280454 " "
y[1] (numeric) = 1.9343818972807707 " "
absolute error = 3.16635606623094650000000000000E-13 " "
relative error = 1.636882598354815000000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7247499689847015 " "
Order of pole = 4.43674310744651 " "
x[1] = -0.7179999999999997 " "
y[1] (analytic) = 1.9397738999542227 " "
y[1] (numeric) = 1.939773899954543 " "
absolute error = 3.2041036490682020000000000000E-13 " "
relative error = 1.651792329582234500000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7237419718094731 " "
Order of pole = 4.436743107446254 " "
x[1] = -0.7169999999999997 " "
y[1] (analytic) = 1.9451884790376779 " "
y[1] (numeric) = 1.9451884790380016 " "
absolute error = 3.23741033980695650000000000000E-13 " "
relative error = 1.664317044181017000000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7227339746342605 " "
Order of pole = 4.436743107446642 " "
x[1] = -0.7159999999999997 " "
y[1] (analytic) = 1.950625760744048 " "
y[1] (numeric) = 1.9506257607443755 " "
absolute error = 3.2751579226442120000000000000E-13 " "
relative error = 1.6790293599910900000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7217259774590393 " "
Order of pole = 4.436743107446684 " "
x[1] = -0.7149999999999997 " "
y[1] (analytic) = 1.9560858721697898 " "
y[1] (numeric) = 1.9560858721701206 " "
absolute error = 3.30846461338296650000000000000E-13 " "
relative error = 1.691369821976705700000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7207179802838181 " "
Order of pole = 4.436743107446713 " "
x[1] = -0.7139999999999997 " "
y[1] (analytic) = 1.9615689413020125 " "
y[1] (numeric) = 1.961568941302347 " "
absolute error = 3.34399175017097150000000000000E-13 " "
relative error = 1.704753618270159200000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7197099831085932 " "
Order of pole = 4.43674310744661 " "
x[1] = -0.7129999999999997 " "
y[1] (analytic) = 1.9670750970259805 " "
y[1] (numeric) = 1.9670750970263187 " "
absolute error = 3.3817393330082270000000000000E-13 " "
relative error = 1.71917144298205820000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7187019859333679 " "
Order of pole = 4.436743107446468 " "
x[1] = -0.7119999999999997 " "
y[1] (analytic) = 1.9726044691326867 " "
y[1] (numeric) = 1.9726044691330284 " "
absolute error = 3.4172664697962320000000000000E-13 " "
relative error = 1.732362733264379600000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7176939887581502 " "
Order of pole = 4.436743107446656 " "
x[1] = -0.7109999999999997 " "
y[1] (analytic) = 1.9781571883265001 " "
y[1] (numeric) = 1.9781571883268456 " "
absolute error = 3.4550140526334870000000000000E-13 " "
relative error = 1.74658215890133200000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.716685991582926 " "
Order of pole = 4.436743107446567 " "
x[1] = -0.7099999999999997 " "
y[1] (analytic) = 1.9837333862328919 " "
y[1] (numeric) = 1.983733386233241 " "
absolute error = 3.4905411894214920000000000000E-13 " "
relative error = 1.759581813587372800000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.715677994407709 " "
Order of pole = 4.436743107446787 " "
x[1] = -0.7089999999999997 " "
y[1] (analytic) = 1.9893331954062332 " "
y[1] (numeric) = 1.9893331954065863 " "
absolute error = 3.5305092183079980000000000000E-13 " "
relative error = 1.774719904368281300000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7146699972324774 " "
Order of pole = 4.436743107446386 " "
x[1] = -0.7079999999999997 " "
y[1] (analytic) = 1.9949567493376759 " "
y[1] (numeric) = 1.9949567493380327 " "
absolute error = 3.5682568011452530000000000000E-13 " "
relative error = 1.788638677169272800000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7136620000572569 " "
Order of pole = 4.43674310744645 " "
x[1] = -0.7069999999999997 " "
y[1] (analytic) = 2.000604182463105 " "
y[1] (numeric) = 2.000604182463466 " "
absolute error = 3.6104452760810090000000000000E-13 " "
relative error = 1.80467746080381520000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7126540028820341 " "
Order of pole = 4.436743107446425 " "
x[1] = -0.7059999999999997 " "
y[1] (analytic) = 2.006275630171177 " "
y[1] (numeric) = 2.0062756301715416 " "
absolute error = 3.6459724128690140000000000000E-13 " "
relative error = 1.817283905580778200000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.711646005706815 " "
Order of pole = 4.436743107446556 " "
x[1] = -0.7049999999999997 " "
y[1] (analytic) = 2.0119712288114293 " "
y[1] (numeric) = 2.0119712288117984 " "
absolute error = 3.69038133385402030000000000000E-13 " "
relative error = 1.834211782458793300000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7106380085315966 " "
Order of pole = 4.436743107446713 " "
x[1] = -0.7039999999999997 " "
y[1] (analytic) = 2.017691115702481 " "
y[1] (numeric) = 2.0176911157028536 " "
absolute error = 3.72590847064202530000000000000E-13 " "
relative error = 1.846619852585716400000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7096300113563698 " "
Order of pole = 4.436743107446521 " "
x[1] = -0.7029999999999997 " "
y[1] (analytic) = 2.0234354291403047 " "
y[1] (numeric) = 2.0234354291406813 " "
absolute error = 3.7658764995285310000000000000E-13 " "
relative error = 1.86113005895549400000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7086220141811482 " "
Order of pole = 4.436743107446535 " "
x[1] = -0.7019999999999997 " "
y[1] (analytic) = 2.029204308406589 " "
y[1] (numeric) = 2.02920430840697 " "
absolute error = 3.8102854205135370000000000000E-13 " "
relative error = 1.877723896370751500000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7076140170059305 " "
Order of pole = 4.436743107446723 " "
x[1] = -0.7009999999999997 " "
y[1] (analytic) = 2.0349978937771813 " "
y[1] (numeric) = 2.034997893777567 " "
absolute error = 3.85469434149854350000000000000E-13 " "
relative error = 1.894200654106724700000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.7066060198307029 " "
Order of pole = 4.4367431074464925 " "
x[1] = -0.6999999999999997 " "
y[1] (analytic) = 2.0408163265306136 " "
y[1] (numeric) = 2.0408163265310035 " "
absolute error = 3.899103262483550000000000000E-13 " "
relative error = 1.91056059861693800000000000E-11 "%"
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"
Iterations = 300
"Total Elapsed Time "= 3 Minutes 46 Seconds
"Elapsed Time(since restart) "= 3 Minutes 46 Seconds
"Time to Timeout "= 11 Minutes 13 Seconds
Percent Done = 100.3333333333334 "%"
(%o49) true
(%o49) diffeq.max