(%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_tmp2 : array_tmp1 array_x , array_tmp3 : array_x array_x ,
1 1 1 1 1 1
array_tmp2
1
array_tmp4 : array_const_1D0 + array_tmp3 , array_tmp5 : -----------,
1 1 1 1 array_tmp4
1
array_tmp6 : array_x array_x , array_tmp7 : array_const_1D0 + array_tmp6 ,
1 1 1 1 1 1
array_tmp5
1
array_tmp8 : -----------, array_tmp9 : array_tmp8 + array_const_0D0 ,
1 array_tmp7 1 1 1
1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp9 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_tmp2 : ats(2, array_tmp1, array_x, 1),
2
array_tmp3 : ats(2, array_x, array_x, 1),
2
array_tmp4 : array_const_1D0 + array_tmp3 ,
2 2 2
array_tmp2 - ats(2, array_tmp4, array_tmp5, 2)
2
array_tmp5 : -----------------------------------------------,
2 array_tmp4
1
array_tmp6 : ats(2, array_x, array_x, 1),
2
array_tmp7 : array_const_1D0 + array_tmp6 ,
2 2 2
array_tmp5 - ats(2, array_tmp7, array_tmp8, 2)
2
array_tmp8 : -----------------------------------------------,
2 array_tmp7
1
array_tmp9 : array_tmp8 + array_const_0D0 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
1
then (temporary : array_tmp9 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_tmp2 : ats(3, array_tmp1, array_x, 1),
3
array_tmp3 : ats(3, array_x, array_x, 1),
3
array_tmp4 : array_const_1D0 + array_tmp3 ,
3 3 3
array_tmp2 - ats(3, array_tmp4, array_tmp5, 2)
3
array_tmp5 : -----------------------------------------------,
3 array_tmp4
1
array_tmp6 : ats(3, array_x, array_x, 1),
3
array_tmp7 : array_const_1D0 + array_tmp6 ,
3 3 3
array_tmp5 - ats(3, array_tmp7, array_tmp8, 2)
3
array_tmp8 : -----------------------------------------------,
3 array_tmp7
1
array_tmp9 : array_tmp8 + array_const_0D0 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
1
then (temporary : array_tmp9 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_tmp2 : ats(4, array_tmp1, array_x, 1),
4
array_tmp3 : ats(4, array_x, array_x, 1),
4
array_tmp4 : array_const_1D0 + array_tmp3 ,
4 4 4
array_tmp2 - ats(4, array_tmp4, array_tmp5, 2)
4
array_tmp5 : -----------------------------------------------,
4 array_tmp4
1
array_tmp6 : ats(4, array_x, array_x, 1),
4
array_tmp7 : array_const_1D0 + array_tmp6 ,
4 4 4
array_tmp5 - ats(4, array_tmp7, array_tmp8, 2)
4
array_tmp8 : -----------------------------------------------,
4 array_tmp7
1
array_tmp9 : array_tmp8 + array_const_0D0 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
1
then (temporary : array_tmp9 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_tmp2 : ats(5, array_tmp1, array_x, 1),
5
array_tmp3 : ats(5, array_x, array_x, 1),
5
array_tmp4 : array_const_1D0 + array_tmp3 ,
5 5 5
array_tmp2 - ats(5, array_tmp4, array_tmp5, 2)
5
array_tmp5 : -----------------------------------------------,
5 array_tmp4
1
array_tmp6 : ats(5, array_x, array_x, 1),
5
array_tmp7 : array_const_1D0 + array_tmp6 ,
5 5 5
array_tmp5 - ats(5, array_tmp7, array_tmp8, 2)
5
array_tmp8 : -----------------------------------------------,
5 array_tmp7
1
array_tmp9 : array_tmp8 + array_const_0D0 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
1
then (temporary : array_tmp9 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_tmp2 : ats(kkk, array_tmp1, array_x, 1),
kkk
array_tmp3 : ats(kkk, array_x, array_x, 1),
kkk
array_tmp4 : array_const_1D0 + array_tmp3 ,
kkk kkk kkk
array_tmp2 - ats(kkk, array_tmp4, array_tmp5, 2)
kkk
array_tmp5 : ---------------------------------------------------,
kkk array_tmp4
1
array_tmp6 : ats(kkk, array_x, array_x, 1),
kkk
array_tmp7 : array_const_1D0 + array_tmp6 ,
kkk kkk kkk
array_tmp5 - ats(kkk, array_tmp7, array_tmp8, 2)
kkk
array_tmp8 : ---------------------------------------------------,
kkk array_tmp7
1
array_tmp9 : array_tmp8 + 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_tmp9 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_tmp2 : array_tmp1 array_x , array_tmp3 : array_x array_x ,
1 1 1 1 1 1
array_tmp2
1
array_tmp4 : array_const_1D0 + array_tmp3 , array_tmp5 : -----------,
1 1 1 1 array_tmp4
1
array_tmp6 : array_x array_x , array_tmp7 : array_const_1D0 + array_tmp6 ,
1 1 1 1 1 1
array_tmp5
1
array_tmp8 : -----------, array_tmp9 : array_tmp8 + array_const_0D0 ,
1 array_tmp7 1 1 1
1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp9 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_tmp2 : ats(2, array_tmp1, array_x, 1),
2
array_tmp3 : ats(2, array_x, array_x, 1),
2
array_tmp4 : array_const_1D0 + array_tmp3 ,
2 2 2
array_tmp2 - ats(2, array_tmp4, array_tmp5, 2)
2
array_tmp5 : -----------------------------------------------,
2 array_tmp4
1
array_tmp6 : ats(2, array_x, array_x, 1),
2
array_tmp7 : array_const_1D0 + array_tmp6 ,
2 2 2
array_tmp5 - ats(2, array_tmp7, array_tmp8, 2)
2
array_tmp8 : -----------------------------------------------,
2 array_tmp7
1
array_tmp9 : array_tmp8 + array_const_0D0 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
1
then (temporary : array_tmp9 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_tmp2 : ats(3, array_tmp1, array_x, 1),
3
array_tmp3 : ats(3, array_x, array_x, 1),
3
array_tmp4 : array_const_1D0 + array_tmp3 ,
3 3 3
array_tmp2 - ats(3, array_tmp4, array_tmp5, 2)
3
array_tmp5 : -----------------------------------------------,
3 array_tmp4
1
array_tmp6 : ats(3, array_x, array_x, 1),
3
array_tmp7 : array_const_1D0 + array_tmp6 ,
3 3 3
array_tmp5 - ats(3, array_tmp7, array_tmp8, 2)
3
array_tmp8 : -----------------------------------------------,
3 array_tmp7
1
array_tmp9 : array_tmp8 + array_const_0D0 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
1
then (temporary : array_tmp9 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_tmp2 : ats(4, array_tmp1, array_x, 1),
4
array_tmp3 : ats(4, array_x, array_x, 1),
4
array_tmp4 : array_const_1D0 + array_tmp3 ,
4 4 4
array_tmp2 - ats(4, array_tmp4, array_tmp5, 2)
4
array_tmp5 : -----------------------------------------------,
4 array_tmp4
1
array_tmp6 : ats(4, array_x, array_x, 1),
4
array_tmp7 : array_const_1D0 + array_tmp6 ,
4 4 4
array_tmp5 - ats(4, array_tmp7, array_tmp8, 2)
4
array_tmp8 : -----------------------------------------------,
4 array_tmp7
1
array_tmp9 : array_tmp8 + array_const_0D0 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
1
then (temporary : array_tmp9 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_tmp2 : ats(5, array_tmp1, array_x, 1),
5
array_tmp3 : ats(5, array_x, array_x, 1),
5
array_tmp4 : array_const_1D0 + array_tmp3 ,
5 5 5
array_tmp2 - ats(5, array_tmp4, array_tmp5, 2)
5
array_tmp5 : -----------------------------------------------,
5 array_tmp4
1
array_tmp6 : ats(5, array_x, array_x, 1),
5
array_tmp7 : array_const_1D0 + array_tmp6 ,
5 5 5
array_tmp5 - ats(5, array_tmp7, array_tmp8, 2)
5
array_tmp8 : -----------------------------------------------,
5 array_tmp7
1
array_tmp9 : array_tmp8 + array_const_0D0 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
1
then (temporary : array_tmp9 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_tmp2 : ats(kkk, array_tmp1, array_x, 1),
kkk
array_tmp3 : ats(kkk, array_x, array_x, 1),
kkk
array_tmp4 : array_const_1D0 + array_tmp3 ,
kkk kkk kkk
array_tmp2 - ats(kkk, array_tmp4, array_tmp5, 2)
kkk
array_tmp5 : ---------------------------------------------------,
kkk array_tmp4
1
array_tmp6 : ats(kkk, array_x, array_x, 1),
kkk
array_tmp7 : array_const_1D0 + array_tmp6 ,
kkk kkk kkk
array_tmp5 - ats(kkk, array_tmp7, array_tmp8, 2)
kkk
array_tmp8 : ---------------------------------------------------,
kkk array_tmp7
1
array_tmp9 : array_tmp8 + 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_tmp9 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
(%i49) exact_soln_y(x) := ---------
1.0 + x x
1.0
(%o49) exact_soln_y(x) := ---------
1.0 + x x
(%i50) mainprog() := (define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(glob_max_minutes, 0.0,
float), define_variable(glob_log10abserr, 0.0, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(years_in_century, 100.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_dump, false, boolean),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(djd_debug, true, boolean),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_h, 0.1, float), define_variable(glob_reached_optimal_h,
false, boolean), define_variable(glob_initial_pass, true, boolean),
define_variable(hours_in_day, 24.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3,
DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/sing4postode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 50,"),
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 : -2.0,"), omniout_str(ALWAYS, "x_end : 1.0,"),
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 : 50,"),
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 + 1.0) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 50, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms),
array(array_tmp8, 1 + max_terms), array(array_tmp9, 1 + max_terms),
array(array_type_pole, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y, 1 + max_terms), array(array_x, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_y_init, 1 + max_terms),
array(array_norms, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher_work, 1 + 2,
1 + max_terms), term : 1, while term <= max_terms do (array_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp5 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp6 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp7 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp8 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp9 : 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_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_1st_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_y : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_y_init : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_norms : 0.0, term : 1 + term), ord : 1,
term
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 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 <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), array(array_tmp9, 1 + 1 + max_terms),
term : 1, while term <= 1 + max_terms do (array_tmp9 : 0.0,
term
term : 1 + term), array(array_tmp8, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term),
term
array(array_tmp7, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_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_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_const_1D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_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 : - 2.0, x_end : 1.0,
1
array_y_init : exact_soln_y(x_start), glob_h : 0.1,
1 + 0
glob_look_poles : true, glob_max_iter : 50, 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 + 1.0) /( x * x + 1.0);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-06-13T04:07:51-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing4"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_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, "sing4 diffeq.max"), logitem_str(html_log_file, "sing4 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(DEBUGMASSIVE, 4, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(glob_max_minutes, 0.0,
float), define_variable(glob_log10abserr, 0.0, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(years_in_century, 100.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_dump, false, boolean),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(djd_debug, true, boolean),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_h, 0.1, float), define_variable(glob_reached_optimal_h,
false, boolean), define_variable(glob_initial_pass, true, boolean),
define_variable(hours_in_day, 24.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3,
DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/sing4postode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 50,"),
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 : -2.0,"), omniout_str(ALWAYS, "x_end : 1.0,"),
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 : 50,"),
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 + 1.0) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 50, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms),
array(array_tmp8, 1 + max_terms), array(array_tmp9, 1 + max_terms),
array(array_type_pole, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y, 1 + max_terms), array(array_x, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_y_init, 1 + max_terms),
array(array_norms, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher_work, 1 + 2,
1 + max_terms), term : 1, while term <= max_terms do (array_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp5 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp6 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp7 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp8 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp9 : 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_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_1st_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_y : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_y_init : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_norms : 0.0, term : 1 + term), ord : 1,
term
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 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 <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), array(array_tmp9, 1 + 1 + max_terms),
term : 1, while term <= 1 + max_terms do (array_tmp9 : 0.0,
term
term : 1 + term), array(array_tmp8, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term),
term
array(array_tmp7, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_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_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_const_1D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_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 : - 2.0, x_end : 1.0,
1
array_y_init : exact_soln_y(x_start), glob_h : 0.1,
1 + 0
glob_look_poles : true, glob_max_iter : 50, 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 + 1.0) /( x * x + 1.0);"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-06-13T04:07:51-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing4"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_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, "sing4 diffeq.max"), logitem_str(html_log_file, "sing4 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/sing4postode.ode#################"
"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 50,"
"max_terms : 30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : -2.0,"
"x_end : 1.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h : 0.1,"
"glob_look_poles : true,"
"glob_max_iter : 50,"
"/* 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 + 1.0) "
");"
""
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = -2. " "
y[1] (analytic) = 0.2 " "
y[1] (numeric) = 0.2 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2590374448964488 " "
Order of pole = 3.5716028840313676 " "
x[1] = -1.9999 " "
y[1] (analytic) = 0.2000160008800384 " "
y[1] (numeric) = 0.2000160008800384 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2589443147775454 " "
Order of pole = 3.571562794485928 " "
x[1] = -1.9998 " "
y[1] (analytic) = 0.20003200352030723 " "
y[1] (numeric) = 0.20003200352030723 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2588511841606955 " "
Order of pole = 3.571522687492916 " "
x[1] = -1.9997 " "
y[1] (analytic) = 0.2000480079210369 " "
y[1] (numeric) = 0.2000480079210369 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2587580530494344 " "
Order of pole = 3.571482563098428 " "
x[1] = -1.9996 " "
y[1] (analytic) = 0.20006401408245794 " "
y[1] (numeric) = 0.20006401408245794 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258664921447164 " "
Order of pole = 3.571442421346635 " "
x[1] = -1.9995 " "
y[1] (analytic) = 0.2000800220048008 " "
y[1] (numeric) = 0.20008002200480082 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.387223738658072400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2585717893574135 " "
Order of pole = 3.5714022622835806 " "
x[1] = -1.9994 " "
y[1] (analytic) = 0.2000960316882961 " "
y[1] (numeric) = 0.2000960316882961 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258478656783206 " "
Order of pole = 3.571362085948028 " "
x[1] = -1.9993 " "
y[1] (analytic) = 0.20011204313317432 " "
y[1] (numeric) = 0.20011204313317435 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.387001760666528900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2583855237283452 " "
Order of pole = 3.5713218923899106 " "
x[1] = -1.9992 " "
y[1] (analytic) = 0.20012805633966618 " "
y[1] (numeric) = 0.20012805633966618 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2582923901957823 " "
Order of pole = 3.571281681647008 " "
x[1] = -1.9991 " "
y[1] (analytic) = 0.20014407130800219 " "
y[1] (numeric) = 0.2001440713080022 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.386779804879445800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.258199256189261 " "
Order of pole = 3.5712414537683763 " "
x[1] = -1.999 " "
y[1] (analytic) = 0.2001600880384131 " "
y[1] (numeric) = 0.20016008803841312 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.386668835312577000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2581061217124256 " "
Order of pole = 3.571201208801682 " "
x[1] = -1.9989000000000001 " "
y[1] (analytic) = 0.2001761065311296 " "
y[1] (numeric) = 0.2001761065311296 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2580129867681973 " "
Order of pole = 3.5711609467842536 " "
x[1] = -1.9988000000000001 " "
y[1] (analytic) = 0.20019212678638237 " "
y[1] (numeric) = 0.2001921267863824 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.386446912832184600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.25791985135981 " "
Order of pole = 3.5711206677578957 " "
x[1] = -1.9987000000000001 " "
y[1] (analytic) = 0.20020814880440224 " "
y[1] (numeric) = 0.20020814880440227 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.386335959918661200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.257826715491365 " "
Order of pole = 3.5710803717768087 " "
x[1] = -1.9986000000000002 " "
y[1] (analytic) = 0.20022417258541997 " "
y[1] (numeric) = 0.20022417258542 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.386225012556252800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2577335791657847 " "
Order of pole = 3.571040058878328 " "
x[1] = -1.9985000000000002 " "
y[1] (analytic) = 0.2002401981296664 " "
y[1] (numeric) = 0.20024019812966642 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.386114070744959600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2576404423869283 " "
Order of pole = 3.570999729113197 " "
x[1] = -1.9984000000000002 " "
y[1] (analytic) = 0.20025622543737237 " "
y[1] (numeric) = 0.2002562254373724 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.386003134484781500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.257547305157139 " "
Order of pole = 3.5709593825105053 " "
x[1] = -1.9983000000000002 " "
y[1] (analytic) = 0.2002722545087688 " "
y[1] (numeric) = 0.20027225450876882 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.385892203775718500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.257454167481154 " "
Order of pole = 3.570919019133516 " "
x[1] = -1.9982000000000002 " "
y[1] (analytic) = 0.20028828534408655 " "
y[1] (numeric) = 0.20028828534408658 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.385781278617770600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.257361029361915 " "
Order of pole = 3.570878639019874 " "
x[1] = -1.9981000000000002 " "
y[1] (analytic) = 0.20030431794355663 " "
y[1] (numeric) = 0.20030431794355663 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.257267890802185 " "
Order of pole = 3.5708382422046547 " "
x[1] = -1.9980000000000002 " "
y[1] (analytic) = 0.20032035230740997 " "
y[1] (numeric) = 0.20032035230741 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.385559444955220300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2571747518062675 " "
Order of pole = 3.5707978287449293 " "
x[1] = -1.9979000000000002 " "
y[1] (analytic) = 0.20033638843587764 " "
y[1] (numeric) = 0.20033638843587764 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.257081612377275 " "
Order of pole = 3.5707573986808008 " "
x[1] = -1.9978000000000002 " "
y[1] (analytic) = 0.20035242632919065 " "
y[1] (numeric) = 0.20035242632919065 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.256988472518681 " "
Order of pole = 3.5707169520574773 " "
x[1] = -1.9977000000000003 " "
y[1] (analytic) = 0.2003684659875801 " "
y[1] (numeric) = 0.2003684659875801 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2568953322337797 " "
Order of pole = 3.570676488917634 " "
x[1] = -1.9976000000000003 " "
y[1] (analytic) = 0.20038450741127706 " "
y[1] (numeric) = 0.20038450741127709 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.385115844243501300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.256802191525822 " "
Order of pole = 3.5706360093033354 " "
x[1] = -1.9975000000000003 " "
y[1] (analytic) = 0.20040055060051273 " "
y[1] (numeric) = 0.20040055060051273 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.256709050398781 " "
Order of pole = 3.5705955132669693 " "
x[1] = -1.9974000000000003 " "
y[1] (analytic) = 0.20041659555551825 " "
y[1] (numeric) = 0.20041659555551825 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2566159088555766 " "
Order of pole = 3.570555000845836 " "
x[1] = -1.9973000000000003 " "
y[1] (analytic) = 0.2004326422765248 " "
y[1] (numeric) = 0.20043264227652483 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.384783201996420700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2565227668998 " "
Order of pole = 3.570514472086849 " "
x[1] = -1.9972000000000003 " "
y[1] (analytic) = 0.20044869076376365 " "
y[1] (numeric) = 0.20044869076376368 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.38467233234962400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.256429624534799 " "
Order of pole = 3.570473927033472 " "
x[1] = -1.9971000000000003 " "
y[1] (analytic) = 0.20046474101746606 " "
y[1] (numeric) = 0.20046474101746609 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.384561468253942600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2563364817643596 " "
Order of pole = 3.5704333657354077 " "
x[1] = -1.9970000000000003 " "
y[1] (analytic) = 0.20048079303786334 " "
y[1] (numeric) = 0.20048079303786337 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.38445060970937600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.256243338591613 " "
Order of pole = 3.5703927882329936 " "
x[1] = -1.9969000000000003 " "
y[1] (analytic) = 0.20049684682518681 " "
y[1] (numeric) = 0.20049684682518684 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.384339756715924600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.25615019501973 " "
Order of pole = 3.570352194567157 " "
x[1] = -1.9968000000000004 " "
y[1] (analytic) = 0.20051290237966782 " "
y[1] (numeric) = 0.20051290237966785 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.384228909273588800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.256057051052886 " "
Order of pole = 3.5703115847931635 " "
x[1] = -1.9967000000000004 " "
y[1] (analytic) = 0.20052895970153778 " "
y[1] (numeric) = 0.2005289597015378 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.384118067382367500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.255963906694132 " "
Order of pole = 3.570270958950225 " "
x[1] = -1.9966000000000004 " "
y[1] (analytic) = 0.2005450187910281 " "
y[1] (numeric) = 0.20054501879102812 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.384007231042261600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2558707619466123 " "
Order of pole = 3.5702303170788774 " "
x[1] = -1.9965000000000004 " "
y[1] (analytic) = 0.20056107964837022 " "
y[1] (numeric) = 0.20056107964837028 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.76779280050654200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.255777616814318 " "
Order of pole = 3.5701896592317617 " "
x[1] = -1.9964000000000004 " "
y[1] (analytic) = 0.20057714227379572 " "
y[1] (numeric) = 0.20057714227379575 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.383785575015395200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2556844712999125 " "
Order of pole = 3.5701489854425574 " "
x[1] = -1.9963000000000004 " "
y[1] (analytic) = 0.20059320666753597 " "
y[1] (numeric) = 0.20059320666753605 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 4.15102426598590500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.255591325408067 " "
Order of pole = 3.5701082957736148 " "
x[1] = -1.9962000000000004 " "
y[1] (analytic) = 0.20060927282982266 " "
y[1] (numeric) = 0.20060927282982272 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.76712788238597900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.255498179140897 " "
Order of pole = 3.570067590250794 " "
x[1] = -1.9961000000000004 " "
y[1] (analytic) = 0.2006253407608873 " "
y[1] (numeric) = 0.20062534076088737 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.766906265216918000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2554050325027983 " "
Order of pole = 3.5700268689325156 " "
x[1] = -1.9960000000000004 " "
y[1] (analytic) = 0.2006414104609615 " "
y[1] (numeric) = 0.2006414104609616 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 4.150026988725132300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.255311885496508 " "
Order of pole = 3.569986131853497 " "
x[1] = -1.9959000000000005 " "
y[1] (analytic) = 0.200657481930277 " "
y[1] (numeric) = 0.20065748193027705 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.76646306418548760000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2552187381258384 " "
Order of pole = 3.5699453790638493 " "
x[1] = -1.9958000000000005 " "
y[1] (analytic) = 0.20067355516906538 " "
y[1] (numeric) = 0.2006735551690654 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.38312074016155900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2551255903946297 " "
Order of pole = 3.5699046106140635 " "
x[1] = -1.9957000000000005 " "
y[1] (analytic) = 0.20068963017755834 " "
y[1] (numeric) = 0.2006896301775584 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.766019907562979000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2550324423060197 " "
Order of pole = 3.5698638265445872 " "
x[1] = -1.9956000000000005 " "
y[1] (analytic) = 0.2007057069559877 " "
y[1] (numeric) = 0.20070570695598774 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.76579834590506900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2549392938627446 " "
Order of pole = 3.5698230268901447 " "
x[1] = -1.9955000000000005 " "
y[1] (analytic) = 0.20072178550458517 " "
y[1] (numeric) = 0.20072178550458522 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.7655767953493900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2548461450692643 " "
Order of pole = 3.569782211710077 " "
x[1] = -1.9954000000000005 " "
y[1] (analytic) = 0.20073786582358252 " "
y[1] (numeric) = 0.20073786582358263 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 5.53071051179188400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.254752995928889 " "
Order of pole = 3.569741381047333 " "
x[1] = -1.9953000000000005 " "
y[1] (analytic) = 0.20075394791321172 " "
y[1] (numeric) = 0.2007539479132118 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 4.147700591317084500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2546598464446372 " "
Order of pole = 3.5697005349406616 " "
x[1] = -1.9952000000000005 " "
y[1] (analytic) = 0.2007700317737045 " "
y[1] (numeric) = 0.20077003177370462 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 5.5298244205914690000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.254566696620408 " "
Order of pole = 3.5696596734413966 " "
x[1] = -1.9951000000000005 " "
y[1] (analytic) = 0.2007861174052929 " "
y[1] (numeric) = 0.20078611740529298 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 4.147036056223464000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.254473546459299 " "
Order of pole = 3.569618796589431 " "
x[1] = -1.9950000000000006 " "
y[1] (analytic) = 0.2008022048082087 " "
y[1] (numeric) = 0.20080220480820882 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 5.52893841820889700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2543803959649518 " "
Order of pole = 3.5695779044324247 " "
x[1] = -1.9949000000000006 " "
y[1] (analytic) = 0.20081829398268397 " "
y[1] (numeric) = 0.20081829398268408 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 5.52849545032430200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.254287245140483 " "
Order of pole = 3.569536997010548 " "
x[1] = -1.9948000000000006 " "
y[1] (analytic) = 0.20083438492895064 " "
y[1] (numeric) = 0.20083438492895075 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 5.52805250464416800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2541940939900877 " "
Order of pole = 3.569496074379366 " "
x[1] = -1.9947000000000006 " "
y[1] (analytic) = 0.2008504776472408 " "
y[1] (numeric) = 0.2008504776472409 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 5.52760958116849300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.254100942517016 " "
Order of pole = 3.5694551365809737 " "
x[1] = -1.9946000000000006 " "
y[1] (analytic) = 0.20086657213778641 " "
y[1] (numeric) = 0.20086657213778655 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 6.90895834987160100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2540077907242217 " "
Order of pole = 3.56941418365318 " "
x[1] = -1.9945000000000006 " "
y[1] (analytic) = 0.2008826684008197 " "
y[1] (numeric) = 0.2008826684008198 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 5.526723800830526000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.253914638615238 " "
Order of pole = 3.5693732156421376 " "
x[1] = -1.9944000000000006 " "
y[1] (analytic) = 0.20089876643657267 " "
y[1] (numeric) = 0.20089876643657278 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 5.526280943968234000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.253821486194329 " "
Order of pole = 3.5693322326043955 " "
x[1] = -1.9943000000000006 " "
y[1] (analytic) = 0.20091486624527752 " "
y[1] (numeric) = 0.20091486624527763 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 5.52583810931040100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2537283334643217 " "
Order of pole = 3.569291234575985 " "
x[1] = -1.9942000000000006 " "
y[1] (analytic) = 0.2009309678271664 " "
y[1] (numeric) = 0.20093096782716655 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 6.90674412107128800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2536351804288333 " "
Order of pole = 3.5692502216042463 " "
x[1] = -1.9941000000000006 " "
y[1] (analytic) = 0.2009470711824716 " "
y[1] (numeric) = 0.20094707118247174 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 6.90619063326014900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.253542027091171 " "
Order of pole = 3.56920919373205 " "
x[1] = -1.9940000000000007 " "
y[1] (analytic) = 0.2009631763114253 " "
y[1] (numeric) = 0.20096317631142543 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 6.90563717320458500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2534488734550213 " "
Order of pole = 3.569168151007741 " "
x[1] = -1.9939000000000007 " "
y[1] (analytic) = 0.2009792832142598 " "
y[1] (numeric) = 0.20097928321425995 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 6.90508374090459700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2533557195238525 " "
Order of pole = 3.569127093476485 " "
x[1] = -1.9938000000000007 " "
y[1] (analytic) = 0.2009953918912074 " "
y[1] (numeric) = 0.20099539189120758 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 8.28543640363222300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.253262565301109 " "
Order of pole = 3.569086021183182 " "
x[1] = -1.9937000000000007 " "
y[1] (analytic) = 0.20101150234250048 " "
y[1] (numeric) = 0.20101150234250065 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 8.2847723514856200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2531694107902625 " "
Order of pole = 3.5690449341730535 " "
x[1] = -1.9936000000000007 " "
y[1] (analytic) = 0.20102761456837143 " "
y[1] (numeric) = 0.20102761456837157 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 6.90342361053808800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2530762559946083 " "
Order of pole = 3.569003832488864 " "
x[1] = -1.9935000000000007 " "
y[1] (analytic) = 0.20104372856905256 " "
y[1] (numeric) = 0.20104372856905273 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 8.28344434711248200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2529831009181627 " "
Order of pole = 3.568962716183602 " "
x[1] = -1.9934000000000007 " "
y[1] (analytic) = 0.20105984434477636 " "
y[1] (numeric) = 0.20105984434477656 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 9.6632437940336100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2528899455639286 " "
Order of pole = 3.5689215852958647 " "
x[1] = -1.9933000000000007 " "
y[1] (analytic) = 0.20107596189577534 " "
y[1] (numeric) = 0.20107596189577553 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 9.66246922196046200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2527967899352355 " "
Order of pole = 3.568880439868863 " "
x[1] = -1.9932000000000007 " "
y[1] (analytic) = 0.20109208122228198 " "
y[1] (numeric) = 0.20109208122228214 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 8.28145259035295900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2527036340365147 " "
Order of pole = 3.5688392799615585 " "
x[1] = -1.9931000000000008 " "
y[1] (analytic) = 0.20110820232452872 " "
y[1] (numeric) = 0.20110820232452895 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.10410516507286690000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2526104778699647 " "
Order of pole = 3.568798105601026 " "
x[1] = -1.9930000000000008 " "
y[1] (analytic) = 0.20112432520274826 " "
y[1] (numeric) = 0.20112432520274848 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.10401665587289780000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2525173214399303 " "
Order of pole = 3.5687569168450075 " "
x[1] = -1.9929000000000008 " "
y[1] (analytic) = 0.20114044985717316 " "
y[1] (numeric) = 0.20114044985717336 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 9.6593713222459300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.252424164749769 " "
Order of pole = 3.568715713737113 " "
x[1] = -1.9928000000000008 " "
y[1] (analytic) = 0.20115657628803604 " "
y[1] (numeric) = 0.2011565762880362 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 8.27879738096726500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2523310078029994 " "
Order of pole = 3.5686744963232826 " "
x[1] = -1.9927000000000008 " "
y[1] (analytic) = 0.2011727044955695 " "
y[1] (numeric) = 0.20117270449556968 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 8.2781336618875690000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.252237850603072 " "
Order of pole = 3.568633264648483 " "
x[1] = -1.9926000000000008 " "
y[1] (analytic) = 0.2011888344800063 " "
y[1] (numeric) = 0.2011888344800065 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 9.65704830546699200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2521446931532174 " "
Order of pole = 3.568592018754533 " "
x[1] = -1.9925000000000008 " "
y[1] (analytic) = 0.20120496624157913 " "
y[1] (numeric) = 0.20120496624157932 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 9.65627404425629100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2520515354572486 " "
Order of pole = 3.5685507586915755 " "
x[1] = -1.9924000000000008 " "
y[1] (analytic) = 0.20122109978052077 " "
y[1] (numeric) = 0.20122109978052097 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 9.65549982190339700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.251958377518809 " "
Order of pole = 3.568509484507313 " "
x[1] = -1.9923000000000008 " "
y[1] (analytic) = 0.20123723509706398 " "
y[1] (numeric) = 0.2012372350970642 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.10339721581809240000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2518652193408264 " "
Order of pole = 3.5684681962392766 " "
x[1] = -1.9922000000000009 " "
y[1] (analytic) = 0.20125337219144165 " "
y[1] (numeric) = 0.20125337219144185 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 9.65395149377102400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2517720609275984 " "
Order of pole = 3.568426893944519 " "
x[1] = -1.9921000000000009 " "
y[1] (analytic) = 0.20126951106388652 " "
y[1] (numeric) = 0.20126951106388674 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.10322027291331980000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2516789022816996 " "
Order of pole = 3.5683855776554765 " "
x[1] = -1.9920000000000009 " "
y[1] (analytic) = 0.20128565171463156 " "
y[1] (numeric) = 0.20128565171463178 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.10313180812227140000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.251585743407272 " "
Order of pole = 3.5683442474270137 " "
x[1] = -1.991900000000001 " "
y[1] (analytic) = 0.20130179414390964 " "
y[1] (numeric) = 0.20130179414390986 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.10304334777211550000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2514925843076874 " "
Order of pole = 3.5683029033029925 " "
x[1] = -1.991800000000001 " "
y[1] (analytic) = 0.20131793835195372 " "
y[1] (numeric) = 0.20131793835195394 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.10295489186285140000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2513994249863587 " "
Order of pole = 3.5682615453278217 " "
x[1] = -1.991700000000001 " "
y[1] (analytic) = 0.20133408433899674 " "
y[1] (numeric) = 0.201334084338997 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.24072474544378970000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2513062654468174 " "
Order of pole = 3.568220173547651 " "
x[1] = -1.991600000000001 " "
y[1] (analytic) = 0.2013502321052718 " "
y[1] (numeric) = 0.20135023210527203 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.10277799336699980000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2512131056929876 " "
Order of pole = 3.5681787880142117 " "
x[1] = -1.991500000000001 " "
y[1] (analytic) = 0.2013663816510119 " "
y[1] (numeric) = 0.2013663816510121 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 9.64853356932860600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.251119945727694 " "
Order of pole = 3.5681373887635353 " "
x[1] = -1.991400000000001 " "
y[1] (analytic) = 0.20138253297645003 " "
y[1] (numeric) = 0.20138253297645026 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.10260111263471660000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2510267855550206 " "
Order of pole = 3.5680959758496584 " "
x[1] = -1.991300000000001 " "
y[1] (analytic) = 0.2013986860818194 " "
y[1] (numeric) = 0.20139868608181963 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.1025126789299130000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2509336251780794 " "
Order of pole = 3.5680545493127127 " "
x[1] = -1.991200000000001 " "
y[1] (analytic) = 0.2014148409673531 " "
y[1] (numeric) = 0.20141484096735335 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.2402272808742520000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.250840464600652 " "
Order of pole = 3.5680131092024254 " "
x[1] = -1.991100000000001 " "
y[1] (analytic) = 0.20143099763328431 " "
y[1] (numeric) = 0.20143099763328456 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.2401278029483550000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2507473038260954 " "
Order of pole = 3.5679716555624275 " "
x[1] = -1.991000000000001 " "
y[1] (analytic) = 0.20144715607984626 " "
y[1] (numeric) = 0.20144715607984648 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.10224740446085500000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2506541428578903 " "
Order of pole = 3.567930188438133 " "
x[1] = -1.990900000000001 " "
y[1] (analytic) = 0.20146331630727213 " "
y[1] (numeric) = 0.20146331630727235 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.10215898851962000000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.250560981699891 " "
Order of pole = 3.567888707880293 " "
x[1] = -1.990800000000001 " "
y[1] (analytic) = 0.20147947831579516 " "
y[1] (numeric) = 0.2014794783157954 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.23982939914668670000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2504678203550643 " "
Order of pole = 3.5678472139270063 " "
x[1] = -1.990700000000001 " "
y[1] (analytic) = 0.20149564210564871 " "
y[1] (numeric) = 0.20149564210564896 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.23972994120480450000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.250374658827274 " "
Order of pole = 3.567805706629116 " "
x[1] = -1.990600000000001 " "
y[1] (analytic) = 0.2015118076770661 " "
y[1] (numeric) = 0.20151180767706636 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.23963048825892580000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.250281497120496 " "
Order of pole = 3.567764186039174 " "
x[1] = -1.990500000000001 " "
y[1] (analytic) = 0.20152797503028066 " "
y[1] (numeric) = 0.20152797503028094 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 1.37725671145450100000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2501883352371768 " "
Order of pole = 3.5677226521877685 " "
x[1] = -1.990400000000001 " "
y[1] (analytic) = 0.20154414416552582 " "
y[1] (numeric) = 0.20154414416552607 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.23943159735517950000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.25009517318182 " "
Order of pole = 3.56768110513498 " "
x[1] = -1.990300000000001 " "
y[1] (analytic) = 0.20156031508303493 " "
y[1] (numeric) = 0.2015603150830352 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 1.37703573266367980000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2500020109574996 " "
Order of pole = 3.5676395449203966 " "
x[1] = -1.990200000000001 " "
y[1] (analytic) = 0.20157648778304155 " "
y[1] (numeric) = 0.2015764877830418 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.23923272643544730000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.2499088485679204 " "
Order of pole = 3.5675979715926545 " "
x[1] = -1.990100000000001 " "
y[1] (analytic) = 0.20159266226577907 " "
y[1] (numeric) = 0.20159266226577932 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.23913329846958690000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"Complex estimate of poles used"
Radius of convergence = 2.249815686016328 " "
Order of pole = 3.5675563851938144 " "
x[1] = -1.990000000000001 " "
y[1] (analytic) = 0.20160883853148104 " "
y[1] (numeric) = 0.20160883853148132 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 1.3767043061108110000000000000E-13 "%"
h = 1.0000E-4 " "
"Finished!"
"Maximum Iterations Reached before Solution Completed!"
"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"
Iterations = 100
"Total Elapsed Time "= 3 Minutes 9 Seconds
"Elapsed Time(since restart) "= 3 Minutes 8 Seconds
"Expected Time Remaining "= 15 Hours 32 Minutes 34 Seconds
"Optimized Time Remaining "= 15 Hours 29 Minutes 9 Seconds
"Time to Timeout "= 11 Minutes 50 Seconds
Percent Done = 0.3366666666666296 "%"
(%o51) true
(%o51) diffeq.max