(%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) mode_declare(factorial_1, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o39) [factorial_1]
(%i40) factorial_1(nnn) := nnn!
(%o40) factorial_1(nnn) := nnn!
(%i41) mode_declare(factorial_3, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o41) [factorial_3]
mmm2!
(%i42) factorial_3(mmm2, nnn2) := -----
nnn2!
mmm2!
(%o42) factorial_3(mmm2, nnn2) := -----
nnn2!
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%i46) arcsin(x) := asin(x)
(%o46) arcsin(x) := asin(x)
(%i47) arccos(x) := acos(x)
(%o47) arccos(x) := acos(x)
(%i48) arctan(x) := atan(x)
(%o48) arctan(x) := atan(x)
1.0
---
x
(%i49) exact_soln_y(x) := ---
x
1.0
---
x
(%o49) exact_soln_y(x) := ---
x
(%i50) mainprog() := (define_variable(glob_iolevel, 5, fixnum),
define_variable(INFO, 2, fixnum), define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(glob_unchanged_h_cnt, 0,
fixnum), define_variable(glob_large_float, 9.0E+100, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(days_in_year, 365.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_max_hours, 0.0, float),
define_variable(years_in_century, 100.0, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10abserr, 0.0, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_hmax, 1.0, 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(glob_html_log, true, boolean),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_dump, false, boolean),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(djd_debug, true, boolean), 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 : 100,"),
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 : 0.0001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 100,"),
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 : 100, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_last_rel_error, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_init, 1 + max_terms),
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher_work2, 1 + 2,
1 + max_terms), 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_complex_pole, 1 + 1, 1 + 3),
array(array_y_higher, 1 + 2, 1 + max_terms), term : 1,
while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_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_tmp0 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_1st_rel_error : 0.0,
term
term : 1 + 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_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_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_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 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), 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_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_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_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, x_start : - 1.0, x_end : - 0.7,
1
array_y_init : exact_soln_y(x_start), glob_h : 0.1,
1 + 0
glob_look_poles : true, glob_max_iter : 100000, glob_h : 1.0E-4,
glob_look_poles : true, glob_max_iter : 100, 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,
convfp(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,
convfp(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,
convfp(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,
"2012-06-13T04:05:24-05:00"), 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, " 090 | "), logitem_str(html_log_file, "sing3 diffeq.max"), logitem_str(html_log_file, "sing3 maxima results"),
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs"),
logend(html_log_file)), if glob_html_log then close(html_log_file))
(%o50) mainprog() := (define_variable(glob_iolevel, 5, fixnum),
define_variable(INFO, 2, fixnum), define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(glob_unchanged_h_cnt, 0,
fixnum), define_variable(glob_large_float, 9.0E+100, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(days_in_year, 365.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_max_hours, 0.0, float),
define_variable(years_in_century, 100.0, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10abserr, 0.0, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_hmax, 1.0, 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(glob_html_log, true, boolean),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_dump, false, boolean),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(djd_debug, true, boolean), 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 : 100,"),
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 : 0.0001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 100,"),
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 : 100, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_last_rel_error, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_init, 1 + max_terms),
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher_work2, 1 + 2,
1 + max_terms), 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_complex_pole, 1 + 1, 1 + 3),
array(array_y_higher, 1 + 2, 1 + max_terms), term : 1,
while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_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_tmp0 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_1st_rel_error : 0.0,
term
term : 1 + 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_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_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_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 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), 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_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_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_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, x_start : - 1.0, x_end : - 0.7,
1
array_y_init : exact_soln_y(x_start), glob_h : 0.1,
1 + 0
glob_look_poles : true, glob_max_iter : 100000, glob_h : 1.0E-4,
glob_look_poles : true, glob_max_iter : 100, 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,
convfp(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,
convfp(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,
convfp(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,
"2012-06-13T04:05:24-05:00"), 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, " 090 | "), logitem_str(html_log_file, "sing3 diffeq.max"), logitem_str(html_log_file, "sing3 maxima results"),
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs"),
logend(html_log_file)), if glob_html_log then close(html_log_file))
(%i51) mainprog()
"##############ECHO OF PROBLEM#################"
"##############temp/sing3postode.ode#################"
"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 100,"
"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 : 0.0001 ,"
"glob_look_poles : true,"
"glob_max_iter : 100,"
"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 = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.007997175222113 " "
Order of pole = 4.436743107446407 " "
x[1] = -0.9999 " "
y[1] (analytic) = 1.0002000300040004 " "
y[1] (numeric) = 1.0002000300040006 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.22000198224492380000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.007896375504586 " "
Order of pole = 4.4367431074462615 " "
x[1] = -0.9998 " "
y[1] (analytic) = 1.0004001200320078 " "
y[1] (numeric) = 1.000400120032008 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.219557959648455200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.007795575787081 " "
Order of pole = 4.436743107446773 " "
x[1] = -0.9997 " "
y[1] (analytic) = 1.0006002701080403 " "
y[1] (numeric) = 1.0006002701080405 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.219113981460907600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0076947760695423 " "
Order of pole = 4.436743107446286 " "
x[1] = -0.9996 " "
y[1] (analytic) = 1.000800480256128 " "
y[1] (numeric) = 1.0008004802561281 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21867004768228100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0075939763520312 " "
Order of pole = 4.436743107446617 " "
x[1] = -0.9995 " "
y[1] (analytic) = 1.0010007505003125 " "
y[1] (numeric) = 1.0010007505003127 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.218226158312575600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0074931766345057 " "
Order of pole = 4.436743107446517 " "
x[1] = -0.9994000000000001 " "
y[1] (analytic) = 1.0012010808646483 " "
y[1] (numeric) = 1.0012010808646485 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.217782313351790700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0073923769169835 " "
Order of pole = 4.43674310744651 " "
x[1] = -0.9993000000000001 " "
y[1] (analytic) = 1.0014014713732013 " "
y[1] (numeric) = 1.0014014713732016 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.217338512799927000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0072915771994535 " "
Order of pole = 4.436743107446283 " "
x[1] = -0.9992000000000001 " "
y[1] (analytic) = 1.0016019220500498 " "
y[1] (numeric) = 1.00160192205005 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.216894756656984400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0071907774819295 " "
Order of pole = 4.436743107446237 " "
x[1] = -0.9991000000000001 " "
y[1] (analytic) = 1.0018024329192838 " "
y[1] (numeric) = 1.001802432919284 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.216451044922962700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0070899777644189 " "
Order of pole = 4.436743107446578 " "
x[1] = -0.9990000000000001 " "
y[1] (analytic) = 1.0020030040050059 " "
y[1] (numeric) = 1.002003004005006 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21600737759786200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.006989178046896 " "
Order of pole = 4.43674310744656 " "
x[1] = -0.9989000000000001 " "
y[1] (analytic) = 1.00220363533133 " "
y[1] (numeric) = 1.0022036353313302 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.215563754681682500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0068883783293778 " "
Order of pole = 4.436743107446674 " "
x[1] = -0.9988000000000001 " "
y[1] (analytic) = 1.0024043269223826 " "
y[1] (numeric) = 1.002404326922383 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.43024035234884800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0067875786118432 " "
Order of pole = 4.436743107446308 " "
x[1] = -0.9987000000000001 " "
y[1] (analytic) = 1.0026050788023024 " "
y[1] (numeric) = 1.0026050788023029 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.429353284152172700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0066867788943357 " "
Order of pole = 4.436743107446738 " "
x[1] = -0.9986000000000002 " "
y[1] (analytic) = 1.00280589099524 " "
y[1] (numeric) = 1.0028058909952404 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.42846630477333860000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0065859791768086 " "
Order of pole = 4.436743107446599 " "
x[1] = -0.9985000000000002 " "
y[1] (analytic) = 1.003006763525358 " "
y[1] (numeric) = 1.0030067635253583 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.42757941421234760000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0064851794592753 " "
Order of pole = 4.436743107446265 " "
x[1] = -0.9984000000000002 " "
y[1] (analytic) = 1.0032076964168306 " "
y[1] (numeric) = 1.0032076964168313 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.64003891870379800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0063843797417642 " "
Order of pole = 4.4367431074465955 " "
x[1] = -0.9983000000000002 " "
y[1] (analytic) = 1.0034086896938457 " "
y[1] (numeric) = 1.0034086896938461 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.425805899543890000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0062835800242405 " "
Order of pole = 4.436743107446550 " "
x[1] = -0.9982000000000002 " "
y[1] (analytic) = 1.0036097433806013 " "
y[1] (numeric) = 1.003609743380602 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63737891315463700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0061827803067156 " "
Order of pole = 4.436743107446475 " "
x[1] = -0.9981000000000002 " "
y[1] (analytic) = 1.003810857501309 " "
y[1] (numeric) = 1.0038108575013098 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.84806548029360300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0060819805891994 " "
Order of pole = 4.436743107446652 " "
x[1] = -0.9980000000000002 " "
y[1] (analytic) = 1.004012032080192 " "
y[1] (numeric) = 1.0040120320801929 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.8462925873500400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.005981180871686 " "
Order of pole = 4.436743107446922 " "
x[1] = -0.9979000000000002 " "
y[1] (analytic) = 1.0042132671414858 " "
y[1] (numeric) = 1.0042132671414865 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.63338990403161900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0058803811541375 " "
Order of pole = 4.436743107446137 " "
x[1] = -0.9978000000000002 " "
y[1] (analytic) = 1.0044145627094374 " "
y[1] (numeric) = 1.0044145627094383 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.84274733436996600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0057795814366408 " "
Order of pole = 4.43674310744689 " "
x[1] = -0.9977000000000003 " "
y[1] (analytic) = 1.0046159188083073 " "
y[1] (numeric) = 1.004615918808308 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.6307312307500900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0056787817191142 " "
Order of pole = 4.436743107446752 " "
x[1] = -0.9976000000000003 " "
y[1] (analytic) = 1.0048173354623666 " "
y[1] (numeric) = 1.0048173354623673 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.62940209394946900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0055779820015838 " "
Order of pole = 4.436743107446517 " "
x[1] = -0.9975000000000003 " "
y[1] (analytic) = 1.0050188126958997 " "
y[1] (numeric) = 1.0050188126959003 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.62807309037561100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.005477182284061 " "
Order of pole = 4.4367431074464925 " "
x[1] = -0.9974000000000003 " "
y[1] (analytic) = 1.0052203505332025 " "
y[1] (numeric) = 1.0052203505332031 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.62674422002851600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0053763825665323 " "
Order of pole = 4.436743107446300 " "
x[1] = -0.9973000000000003 " "
y[1] (analytic) = 1.0054219489985836 " "
y[1] (numeric) = 1.0054219489985843 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.62541548290818500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0052755828490139 " "
Order of pole = 4.436743107446410 " "
x[1] = -0.9972000000000003 " "
y[1] (analytic) = 1.0056236081163634 " "
y[1] (numeric) = 1.005623608116364 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.62408687901461700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0051747831314977 " "
Order of pole = 4.436743107446599 " "
x[1] = -0.9971000000000003 " "
y[1] (analytic) = 1.0058253279108746 " "
y[1] (numeric) = 1.0058253279108755 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.83034454446374700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0050739834139784 " "
Order of pole = 4.436743107446680 " "
x[1] = -0.9970000000000003 " "
y[1] (analytic) = 1.0060271084064625 " "
y[1] (numeric) = 1.0060271084064634 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.82857342787702300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0049731836964526 " "
Order of pole = 4.436743107446578 " "
x[1] = -0.9969000000000003 " "
y[1] (analytic) = 1.0062289496274839 " "
y[1] (numeric) = 1.0062289496274848 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.82680248892598200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.004872383978924 " "
Order of pole = 4.436743107446386 " "
x[1] = -0.9968000000000004 " "
y[1] (analytic) = 1.0064308515983083 " "
y[1] (numeric) = 1.0064308515983091 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.82503172761062700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.004771584261412 " "
Order of pole = 4.436743107446695 " "
x[1] = -0.9967000000000004 " "
y[1] (analytic) = 1.006632814343317 " "
y[1] (numeric) = 1.006632814343318 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10290764299136940000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.004670784543886 " "
Order of pole = 4.436743107446570 " "
x[1] = -0.9966000000000004 " "
y[1] (analytic) = 1.0068348378869043 " "
y[1] (numeric) = 1.0068348378869054 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10268634223587080000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.004569984826361 " "
Order of pole = 4.436743107446485 " "
x[1] = -0.9965000000000004 " "
y[1] (analytic) = 1.0070369222534759 " "
y[1] (numeric) = 1.0070369222534772 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32295807642179960000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0044691851088419 " "
Order of pole = 4.436743107446581 " "
x[1] = -0.9964000000000004 " "
y[1] (analytic) = 1.0072390674674505 " "
y[1] (numeric) = 1.0072390674674516 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10224380733825540000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0043683853913095 " "
Order of pole = 4.436743107446280 " "
x[1] = -0.9963000000000004 " "
y[1] (analytic) = 1.0074412735532583 " "
y[1] (numeric) = 1.0074412735532596 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.3224270878353660000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0042675856737953 " "
Order of pole = 4.436743107446514 " "
x[1] = -0.9962000000000004 " "
y[1] (analytic) = 1.0076435405353426 " "
y[1] (numeric) = 1.0076435405353437 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10180136125848180000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0041667859562764 " "
Order of pole = 4.43674310744662 " "
x[1] = -0.9961000000000004 " "
y[1] (analytic) = 1.0078458684381577 " "
y[1] (numeric) = 1.007845868438159 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.3218962058303430000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0040659862387542 " "
Order of pole = 4.436743107446613 " "
x[1] = -0.9960000000000004 " "
y[1] (analytic) = 1.008048257286172 " "
y[1] (numeric) = 1.008048257286173 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10135900399655010000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0039651865212238 " "
Order of pole = 4.436743107446372 " "
x[1] = -0.9959000000000005 " "
y[1] (analytic) = 1.0082507071038644 " "
y[1] (numeric) = 1.0082507071038656 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10113785867227520000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.003864386803713 " "
Order of pole = 4.436743107446713 " "
x[1] = -0.9958000000000005 " "
y[1] (analytic) = 1.008453217915727 " "
y[1] (numeric) = 1.0084532179157284 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32110008266295300000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0037635870861872 " "
Order of pole = 4.43674310744661 " "
x[1] = -0.9957000000000005 " "
y[1] (analytic) = 1.0086557897462645 " "
y[1] (numeric) = 1.0086557897462658 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32083476156452770000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0036627873686617 " "
Order of pole = 4.436743107446507 " "
x[1] = -0.9956000000000005 " "
y[1] (analytic) = 1.008858422619993 " "
y[1] (numeric) = 1.0088584226199944 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32056946711145570000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.003561987651137 " "
Order of pole = 4.436743107446436 " "
x[1] = -0.9955000000000005 " "
y[1] (analytic) = 1.0090611165614416 " "
y[1] (numeric) = 1.009061116561443 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.3203041993037360000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0034611879336162 " "
Order of pole = 4.436743107446475 " "
x[1] = -0.9954000000000005 " "
y[1] (analytic) = 1.0092638715951514 " "
y[1] (numeric) = 1.0092638715951527 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32003895814136880000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0033603882161002 " "
Order of pole = 4.436743107446656 " "
x[1] = -0.9953000000000005 " "
y[1] (analytic) = 1.009466687745676 " "
y[1] (numeric) = 1.0094666877456773 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.31977374362435420000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0032595884985793 " "
Order of pole = 4.4367431074466985 " "
x[1] = -0.9952000000000005 " "
y[1] (analytic) = 1.009669565037581 " "
y[1] (numeric) = 1.0096695650375824 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.31950855575269250000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0031587887810551 " "
Order of pole = 4.436743107446638 " "
x[1] = -0.9951000000000005 " "
y[1] (analytic) = 1.0098725034954452 " "
y[1] (numeric) = 1.0098725034954465 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.3192433945263832000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0030579890635318 " "
Order of pole = 4.436743107446606 " "
x[1] = -0.9950000000000006 " "
y[1] (analytic) = 1.0100755031438589 " "
y[1] (numeric) = 1.0100755031438602 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.31897825994542600000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0029571893460112 " "
Order of pole = 4.436743107446656 " "
x[1] = -0.9949000000000006 " "
y[1] (analytic) = 1.0102785640074248 " "
y[1] (numeric) = 1.010278564007426 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.31871315200982220000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0028563896284808 " "
Order of pole = 4.436743107446407 " "
x[1] = -0.9948000000000006 " "
y[1] (analytic) = 1.0104816861107584 " "
y[1] (numeric) = 1.0104816861107597 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.31844807071957030000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0027555899109646 " "
Order of pole = 4.436743107446585 " "
x[1] = -0.9947000000000006 " "
y[1] (analytic) = 1.0106848694784871 " "
y[1] (numeric) = 1.0106848694784887 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.53788018542045020000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.002654790193442 " "
Order of pole = 4.436743107446574 " "
x[1] = -0.9946000000000006 " "
y[1] (analytic) = 1.0108881141352513 " "
y[1] (numeric) = 1.0108881141352528 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.53757098608764600000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0025539904759202 " "
Order of pole = 4.436743107446588 " "
x[1] = -0.9945000000000006 " "
y[1] (analytic) = 1.0110914201057033 " "
y[1] (numeric) = 1.0110914201057049 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.53726181784108660000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0024531907584007 " "
Order of pole = 4.436743107446667 " "
x[1] = -0.9944000000000006 " "
y[1] (analytic) = 1.011294787414508 " "
y[1] (numeric) = 1.0112947874145095 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.53695268068077180000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0023523910408743 " "
Order of pole = 4.436743107446535 " "
x[1] = -0.9943000000000006 " "
y[1] (analytic) = 1.0114982160863424 " "
y[1] (numeric) = 1.011498216086344 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.53664357460670170000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0022515913233643 " "
Order of pole = 4.436743107446905 " "
x[1] = -0.9942000000000006 " "
y[1] (analytic) = 1.0117017061458964 " "
y[1] (numeric) = 1.011701706145898 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.53633449961887630000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0021507916058403 " "
Order of pole = 4.436743107446851 " "
x[1] = -0.9941000000000006 " "
y[1] (analytic) = 1.0119052576178718 " "
y[1] (numeric) = 1.0119052576178735 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75545766367690950000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0020499918883048 " "
Order of pole = 4.436743107446464 " "
x[1] = -0.9940000000000007 " "
y[1] (analytic) = 1.0121088705269834 " "
y[1] (numeric) = 1.0121088705269852 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75510450617366840000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0019491921707846 " "
Order of pole = 4.436743107446517 " "
x[1] = -0.9939000000000007 " "
y[1] (analytic) = 1.0123125448979582 " "
y[1] (numeric) = 1.0123125448979597 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.53540746117286820000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0018483924532693 " "
Order of pole = 4.43674310744672 " "
x[1] = -0.9938000000000007 " "
y[1] (analytic) = 1.012516280755535 " "
y[1] (numeric) = 1.0125162807555368 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75439829774859640000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.001747592735747 " "
Order of pole = 4.436743107446723 " "
x[1] = -0.9937000000000007 " "
y[1] (analytic) = 1.012720078124466 " "
y[1] (numeric) = 1.0127200781244678 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75404524682676600000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.001646793018226 " "
Order of pole = 4.436743107446755 " "
x[1] = -0.9936000000000007 " "
y[1] (analytic) = 1.0129239370295158 " "
y[1] (numeric) = 1.0129239370295173 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.53448070250306240000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.001545993300699 " "
Order of pole = 4.436743107446606 " "
x[1] = -0.9935000000000007 " "
y[1] (analytic) = 1.0131278574954605 " "
y[1] (numeric) = 1.013127857495462 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.534171845118949800000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0014451935831699 " "
Order of pole = 4.436743107446407 " "
x[1] = -0.9934000000000007 " "
y[1] (analytic) = 1.0133318395470894 " "
y[1] (numeric) = 1.0133318395470912 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7529863072240942000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0013443938656588 " "
Order of pole = 4.436743107446738 " "
x[1] = -0.9933000000000007 " "
y[1] (analytic) = 1.0135358832092047 " "
y[1] (numeric) = 1.0135358832092063 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.5335542236094588000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.001243594148131 " "
Order of pole = 4.436743107446570 " "
x[1] = -0.9932000000000007 " "
y[1] (analytic) = 1.01373998850662 " "
y[1] (numeric) = 1.0137399885066216 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.53324545948408050000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0011427944306113 " "
Order of pole = 4.436743107446645 " "
x[1] = -0.9931000000000008 " "
y[1] (analytic) = 1.0139441554641622 " "
y[1] (numeric) = 1.013944155464164 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75192768736565360000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0010419947130786 " "
Order of pole = 4.436743107446333 " "
x[1] = -0.9930000000000008 " "
y[1] (analytic) = 1.0141483841066707 " "
y[1] (numeric) = 1.0141483841066723 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.53262802449205760000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.000941194995567 " "
Order of pole = 4.436743107446652 " "
x[1] = -0.9929000000000008 " "
y[1] (analytic) = 1.0143526744589968 " "
y[1] (numeric) = 1.0143526744589983 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.53231935362541320000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0008403952780391 " "
Order of pole = 4.436743107446475 " "
x[1] = -0.9928000000000008 " "
y[1] (analytic) = 1.0145570265460047 " "
y[1] (numeric) = 1.0145570265460064 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75086938725144410000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.000739595560516 " "
Order of pole = 4.436743107446453 " "
x[1] = -0.9927000000000008 " "
y[1] (analytic) = 1.0147614403925713 " "
y[1] (numeric) = 1.014761440392573 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.75051669160098150000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0006387958430043 " "
Order of pole = 4.4367431074467625 " "
x[1] = -0.9926000000000008 " "
y[1] (analytic) = 1.014965916023586 " "
y[1] (numeric) = 1.0149659160235878 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7501640314776550000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.000537996125474 " "
Order of pole = 4.436743107446517 " "
x[1] = -0.9925000000000008 " "
y[1] (analytic) = 1.0151704534639503 " "
y[1] (numeric) = 1.015170453463952 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7498114068814660000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0004371964079535 " "
Order of pole = 4.436743107446578 " "
x[1] = -0.9924000000000008 " "
y[1] (analytic) = 1.0153750527385785 " "
y[1] (numeric) = 1.0153750527385803 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74945881781241350000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.000336396690431 " "
Order of pole = 4.436743107446567 " "
x[1] = -0.9923000000000008 " "
y[1] (analytic) = 1.0155797138723976 " "
y[1] (numeric) = 1.0155797138723994 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74910626427049770000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0002355969729144 " "
Order of pole = 4.436743107446738 " "
x[1] = -0.9922000000000009 " "
y[1] (analytic) = 1.0157844368903473 " "
y[1] (numeric) = 1.015784436890349 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74875374625571870000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.0001347972553876 " "
Order of pole = 4.436743107446592 " "
x[1] = -0.9921000000000009 " "
y[1] (analytic) = 1.0159892218173794 " "
y[1] (numeric) = 1.015989221817381 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.52985110579706650000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 1.000033997537863 " "
Order of pole = 4.4367431074465244 " "
x[1] = -0.9920000000000009 " "
y[1] (analytic) = 1.016194068678458 " "
y[1] (numeric) = 1.0161940686784598 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74804881680757100000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9999331978203431 " "
Order of pole = 4.436743107446599 " "
x[1] = -0.9919000000000009 " "
y[1] (analytic) = 1.0163989774985611 " "
y[1] (numeric) = 1.016398977498563 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74769640537420280000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9998323981028236 " "
Order of pole = 4.436743107446674 " "
x[1] = -0.9918000000000009 " "
y[1] (analytic) = 1.016603948302678 " "
y[1] (numeric) = 1.0166039483026799 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7473440294679710000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9997315983852944 " "
Order of pole = 4.4367431074464605 " "
x[1] = -0.9917000000000009 " "
y[1] (analytic) = 1.0168089811158116 " "
y[1] (numeric) = 1.0168089811158132 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.52861772795276630000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9996307986677692 " "
Order of pole = 4.436743107446375 " "
x[1] = -0.9916000000000009 " "
y[1] (analytic) = 1.0170140759629762 " "
y[1] (numeric) = 1.0170140759629778 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.52830946120730280000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9995299989502513 " "
Order of pole = 4.436743107446503 " "
x[1] = -0.9915000000000009 " "
y[1] (analytic) = 1.0172192328691996 " "
y[1] (numeric) = 1.0172192328692014 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74628711491209650000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.999429199232725 " "
Order of pole = 4.436743107446379 " "
x[1] = -0.991400000000001 " "
y[1] (analytic) = 1.0174244518595223 " "
y[1] (numeric) = 1.017424451859524 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.527693020975110200000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9993283995151944 " "
Order of pole = 4.4367431074461265 " "
x[1] = -0.991300000000001 " "
y[1] (analytic) = 1.017629732958997 " "
y[1] (numeric) = 1.0176297329589985 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.52738484748838080000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9992275997976916 " "
Order of pole = 4.436743107446706 " "
x[1] = -0.991200000000001 " "
y[1] (analytic) = 1.0178350761926889 " "
y[1] (numeric) = 1.0178350761926906 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7452305201004528000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9991268000801609 " "
Order of pole = 4.436743107446453 " "
x[1] = -0.991100000000001 " "
y[1] (analytic) = 1.0180404815856767 " "
y[1] (numeric) = 1.0180404815856783 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.5267685937736558000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9990260003626396 " "
Order of pole = 4.436743107446482 " "
x[1] = -0.991000000000001 " "
y[1] (analytic) = 1.018245949163051 " "
y[1] (numeric) = 1.0182459491630524 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.52646051354566050000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9989252006451198 " "
Order of pole = 4.436743107446550 " "
x[1] = -0.990900000000001 " "
y[1] (analytic) = 1.0184514789499146 " "
y[1] (numeric) = 1.0184514789499164 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74417424503304020000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9988244009276007 " "
Order of pole = 4.436743107446645 " "
x[1] = -0.990800000000001 " "
y[1] (analytic) = 1.0186570709713845 " "
y[1] (numeric) = 1.0186570709713862 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74382222439817630000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9987236012100752 " "
Order of pole = 4.436743107446553 " "
x[1] = -0.990700000000001 " "
y[1] (analytic) = 1.018862725252589 " "
y[1] (numeric) = 1.0188627252525908 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.74347023929044910000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9986228014925518 " "
Order of pole = 4.43674310744651 " "
x[1] = -0.990600000000001 " "
y[1] (analytic) = 1.0190684418186697 " "
y[1] (numeric) = 1.0190684418186717 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.96100807592359120000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9985220017750281 " "
Order of pole = 4.436743107446468 " "
x[1] = -0.990500000000001 " "
y[1] (analytic) = 1.019274220694781 " "
y[1] (numeric) = 1.019274220694783 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.9606121726134560000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9984212020575134 " "
Order of pole = 4.436743107446688 " "
x[1] = -0.9904000000000011 " "
y[1] (analytic) = 1.0194800619060895 " "
y[1] (numeric) = 1.0194800619060915 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.96021630927134950000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.998320402339993 " "
Order of pole = 4.436743107446745 " "
x[1] = -0.9903000000000011 " "
y[1] (analytic) = 1.0196859654777748 " "
y[1] (numeric) = 1.019685965477777 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.1775783176636360000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9982196026224681 " "
Order of pole = 4.436743107446663 " "
x[1] = -0.9902000000000011 " "
y[1] (analytic) = 1.0198919314350294 " "
y[1] (numeric) = 1.0198919314350314 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.95942470249122340000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9981188029049292 " "
Order of pole = 4.436743107446162 " "
x[1] = -0.9901000000000011 " "
y[1] (analytic) = 1.0200979598030582 " "
y[1] (numeric) = 1.0200979598030602 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.95902895905320370000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Real estimate of pole used"
Radius of convergence = 0.9980180031874168 " "
Order of pole = 4.436743107446457 " "
x[1] = -0.9900000000000011 " "
y[1] (analytic) = 1.0203040506070786 " "
y[1] (numeric) = 1.0203040506070808 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.17625917287023660000000000000E-13 "%"
h = 1.0000E-4 " "
"Finished!"
"Maximum Iterations Reached before Solution Completed!"
"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"
Iterations = 100
"Total Elapsed Time "= 2 Minutes 13 Seconds
"Elapsed Time(since restart) "= 2 Minutes 12 Seconds
"Expected Time Remaining "= 1 Hours 3 Minutes 44 Seconds
"Optimized Time Remaining "= 1 Hours 3 Minutes 30 Seconds
"Time to Timeout "= 12 Minutes 46 Seconds
Percent Done = 3.3666666666662954 "%"
(%o51) true
(%o51) diffeq.max