(%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 - 3 + 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 - 3 + 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 - 3 + 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 - 3 + 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_y_higher ,
1 2, 1
array_tmp2 : array_m1 array_tmp1 , array_tmp3 :
1 1 1 1
array_tmp2 + array_const_0D0 , if not array_y_set_initial
1 1 1, 4
then (if 1 <= glob_max_terms then (temporary :
3
array_tmp3 glob_h factorial_3(0, 3), array_y : temporary,
1 4
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
temporary 3.0
array_y_higher : temporary, temporary : -------------,
2, 3 glob_h
temporary 4.0
array_y_higher : temporary, temporary : -------------,
3, 2 glob_h
array_y_higher : temporary)), kkk : 2, array_tmp1 : array_y_higher ,
4, 1 2 2, 2
array_tmp2 : ats(2, array_m1, array_tmp1, 1),
2
array_tmp3 : array_tmp2 + array_const_0D0 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 5
3
then (temporary : array_tmp3 glob_h factorial_3(1, 4),
2
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 3
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 3,
glob_h 4, 2
array_tmp1 : array_y_higher , array_tmp2 :
3 2, 3 3
ats(3, array_m1, array_tmp1, 1), array_tmp3 : array_tmp2 + array_const_0D0 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 6
3
then (temporary : array_tmp3 glob_h factorial_3(2, 5),
3
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 5
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 4
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 4,
glob_h 4, 3
array_tmp1 : array_y_higher , array_tmp2 :
4 2, 4 4
ats(4, array_m1, array_tmp1, 1), array_tmp3 : array_tmp2 + array_const_0D0 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 7
3
then (temporary : array_tmp3 glob_h factorial_3(3, 6),
4
array_y : temporary, array_y_higher : temporary,
7 1, 7
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 6
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 5,
glob_h 4, 4
array_tmp1 : array_y_higher , array_tmp2 :
5 2, 5 5
ats(5, array_m1, array_tmp1, 1), array_tmp3 : array_tmp2 + array_const_0D0 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 8
3
then (temporary : array_tmp3 glob_h factorial_3(4, 7),
5
array_y : temporary, array_y_higher : temporary,
8 1, 8
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 7
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 6
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 6,
glob_h 4, 5
while kkk <= glob_max_terms do (array_tmp1 : array_y_higher ,
kkk 2, kkk
array_tmp2 : ats(kkk, array_m1, array_tmp1, 1),
kkk
array_tmp3 : array_tmp2 + array_const_0D0 , order_d : 3,
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_tmp3 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_y_higher ,
1 2, 1
array_tmp2 : array_m1 array_tmp1 , array_tmp3 :
1 1 1 1
array_tmp2 + array_const_0D0 , if not array_y_set_initial
1 1 1, 4
then (if 1 <= glob_max_terms then (temporary :
3
array_tmp3 glob_h factorial_3(0, 3), array_y : temporary,
1 4
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
temporary 3.0
array_y_higher : temporary, temporary : -------------,
2, 3 glob_h
temporary 4.0
array_y_higher : temporary, temporary : -------------,
3, 2 glob_h
array_y_higher : temporary)), kkk : 2, array_tmp1 : array_y_higher ,
4, 1 2 2, 2
array_tmp2 : ats(2, array_m1, array_tmp1, 1),
2
array_tmp3 : array_tmp2 + array_const_0D0 ,
2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 5
3
then (temporary : array_tmp3 glob_h factorial_3(1, 4),
2
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 3
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 3,
glob_h 4, 2
array_tmp1 : array_y_higher , array_tmp2 :
3 2, 3 3
ats(3, array_m1, array_tmp1, 1), array_tmp3 : array_tmp2 + array_const_0D0 ,
3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 6
3
then (temporary : array_tmp3 glob_h factorial_3(2, 5),
3
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 5
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 4
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 4,
glob_h 4, 3
array_tmp1 : array_y_higher , array_tmp2 :
4 2, 4 4
ats(4, array_m1, array_tmp1, 1), array_tmp3 : array_tmp2 + array_const_0D0 ,
4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 7
3
then (temporary : array_tmp3 glob_h factorial_3(3, 6),
4
array_y : temporary, array_y_higher : temporary,
7 1, 7
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 6
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 5,
glob_h 4, 4
array_tmp1 : array_y_higher , array_tmp2 :
5 2, 5 5
ats(5, array_m1, array_tmp1, 1), array_tmp3 : array_tmp2 + array_const_0D0 ,
5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 8
3
then (temporary : array_tmp3 glob_h factorial_3(4, 7),
5
array_y : temporary, array_y_higher : temporary,
8 1, 8
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 7
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 3, 6
temporary 4.0
temporary : -------------, array_y_higher : temporary)), kkk : 6,
glob_h 4, 5
while kkk <= glob_max_terms do (array_tmp1 : array_y_higher ,
kkk 2, kkk
array_tmp2 : ats(kkk, array_m1, array_tmp1, 1),
kkk
array_tmp3 : array_tmp2 + array_const_0D0 , order_d : 3,
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_tmp3 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)
(%i49) exact_soln_y(x) := 2.0 - cos(x)
(%o49) exact_soln_y(x) := 2.0 - cos(x)
(%i50) exact_soln_yp(x) := sin(x)
(%o50) exact_soln_yp(x) := sin(x)
(%i51) exact_soln_ypp(x) := cos(x)
(%o51) exact_soln_ypp(x) := cos(x)
(%i52) exact_soln_yppp(x) := - sin(x)
(%o52) exact_soln_yppp(x) := - sin(x)
(%i53) mainprog() := (define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(INFO, 2, fixnum), define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_h, 0.1, float), define_variable(glob_not_yet_start_msg,
true, boolean), define_variable(glob_initial_pass, true, boolean),
define_variable(djd_debug, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_done, false, boolean),
define_variable(years_in_century, 100.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_hmax, 1.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(days_in_year, 365.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_dump, false, boolean),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_hmin, 1.0E-11, 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/diff2postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"),
omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 5.0 ,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "array_y_init[1 + 1] : exact_soln_yp(x_start),"),
omniout_str(ALWAYS, "array_y_init[2 + 1] : exact_soln_ypp(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
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, "2.0 - cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_yp (x) := ("), omniout_str(ALWAYS, "sin(x)"),
omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_ypp (x) := ("),
omniout_str(ALWAYS, "cos(x)"), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_yppp (x) := ("),
omniout_str(ALWAYS, "-sin(x)"), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_norms, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_type_pole, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_last_rel_error, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_init, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3),
array(array_y_higher_work2, 1 + 4, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_y_higher_work, 1 + 4,
1 + max_terms), array(array_y_higher, 1 + 4, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_real_pole, 1 + 1, 1 + 3), term : 1,
while term <= max_terms do (array_norms : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_type_pole : 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_last_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y_init : 0.0,
term
term : 1 + 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 <= 4 do (term : 1,
while term <= max_terms do (array_y_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 4 do (term : 1, while term <=
max_terms do (array_y_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 4 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, 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_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_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_3, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3 : 0.0, term : 1 + term),
term
array_const_3 : 3, 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 : 0.1, x_end : 5.0,
1
array_y_init : exact_soln_y(x_start),
1 + 0
array_y_init : exact_soln_yp(x_start),
1 + 1
array_y_init : exact_soln_ypp(x_start), glob_h : 0.001,
1 + 2
glob_look_poles : true, 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 : true,
1, 1 1, 2
array_y_set_initial : true, 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 : 3, 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 : 3, ord : 4, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
4, iii
array_y_higher
4, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, 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 : 3, calc_term : 2, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
3, iii
array_y_higher
3, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, 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 : 3, calc_term : 1, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
3, iii
array_y_higher
3, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, 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 : 2, calc_term : 3, iii : glob_max_terms,
convfp(calc_term - 1)!
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 : 3, 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 : 2, calc_term : 2, iii : glob_max_terms,
convfp(calc_term - 1)!
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 : 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 : 2, calc_term : 1, iii : glob_max_terms,
convfp(calc_term - 1)!
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 : 4, 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 : 4, 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 : 3, 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 : 3, 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 , 3 ) = m1 * diff ( y , x , 1 ) ;"),
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,
"2012-06-13T01:34:20-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "diff2"),
logitem_str(html_log_file, "diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;"),
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, "diff2 diffeq.max"), logitem_str(html_log_file, "diff2 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))
(%o53) mainprog() := (define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(INFO, 2, fixnum), define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_h, 0.1, float), define_variable(glob_not_yet_start_msg,
true, boolean), define_variable(glob_initial_pass, true, boolean),
define_variable(djd_debug, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_done, false, boolean),
define_variable(years_in_century, 100.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_hmax, 1.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(days_in_year, 365.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_dump, false, boolean),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_hmin, 1.0E-11, 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/diff2postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"),
omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 5.0 ,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "array_y_init[1 + 1] : exact_soln_yp(x_start),"),
omniout_str(ALWAYS, "array_y_init[2 + 1] : exact_soln_ypp(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
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, "2.0 - cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_yp (x) := ("), omniout_str(ALWAYS, "sin(x)"),
omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_ypp (x) := ("),
omniout_str(ALWAYS, "cos(x)"), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_yppp (x) := ("),
omniout_str(ALWAYS, "-sin(x)"), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_norms, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_type_pole, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_last_rel_error, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_init, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3),
array(array_y_higher_work2, 1 + 4, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_y_higher_work, 1 + 4,
1 + max_terms), array(array_y_higher, 1 + 4, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_real_pole, 1 + 1, 1 + 3), term : 1,
while term <= max_terms do (array_norms : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_type_pole : 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_last_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y_init : 0.0,
term
term : 1 + 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 <= 4 do (term : 1,
while term <= max_terms do (array_y_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 4 do (term : 1, while term <=
max_terms do (array_y_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 4 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, 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_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_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_3, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3 : 0.0, term : 1 + term),
term
array_const_3 : 3, 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 : 0.1, x_end : 5.0,
1
array_y_init : exact_soln_y(x_start),
1 + 0
array_y_init : exact_soln_yp(x_start),
1 + 1
array_y_init : exact_soln_ypp(x_start), glob_h : 0.001,
1 + 2
glob_look_poles : true, 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 : true,
1, 1 1, 2
array_y_set_initial : true, 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 : 3, 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 : 3, ord : 4, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
4, iii
array_y_higher
4, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, 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 : 3, calc_term : 2, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
3, iii
array_y_higher
3, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, 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 : 3, calc_term : 1, iii : glob_max_terms,
convfp(calc_term - 1)!
while iii >= calc_term do (array_y_higher_work :
3, iii
array_y_higher
3, iii
--------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, 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 : 2, calc_term : 3, iii : glob_max_terms,
convfp(calc_term - 1)!
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 : 3, 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 : 2, calc_term : 2, iii : glob_max_terms,
convfp(calc_term - 1)!
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 : 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 : 2, calc_term : 1, iii : glob_max_terms,
convfp(calc_term - 1)!
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 : 4, 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 : 4, 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 : 3, 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 : 3, 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 , 3 ) = m1 * diff ( y , x , 1 ) ;"),
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,
"2012-06-13T01:34:20-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "diff2"),
logitem_str(html_log_file, "diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;"),
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, "diff2 diffeq.max"), logitem_str(html_log_file, "diff2 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))
(%i54) mainprog()
"##############ECHO OF PROBLEM#################"
"##############temp/diff2postode.ode#################"
"diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 32,"
"max_terms : 30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : 0.1,"
"x_end : 5.0 ,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"array_y_init[1 + 1] : exact_soln_yp(x_start),"
"array_y_init[2 + 1] : exact_soln_ypp(x_start),"
"glob_h : 0.001 ,"
"glob_look_poles : true,"
"/* 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) := ("
"2.0 - cos(x) "
");"
"exact_soln_yp (x) := ("
"sin(x)"
");"
"exact_soln_ypp (x) := ("
"cos(x)"
");"
"exact_soln_yppp (x) := ("
"-sin(x)"
");"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = 0.1 " "
y[1] (analytic) = 1.0049958347219743 " "
y[1] (numeric) = 1.0049958347219743 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10010000000000001 " "
y[1] (analytic) = 1.0050058230386432 " "
y[1] (numeric) = 1.0050058230386432 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10020000000000001 " "
y[1] (analytic) = 1.0050158213052538 " "
y[1] (numeric) = 1.0050158213052538 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10030000000000001 " "
y[1] (analytic) = 1.0050258295217063 " "
y[1] (numeric) = 1.0050258295217063 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10040000000000002 " "
y[1] (analytic) = 1.0050358476879002 " "
y[1] (numeric) = 1.0050358476879004 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.209320248982642700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10050000000000002 " "
y[1] (analytic) = 1.0050458758037357 " "
y[1] (numeric) = 1.0050458758037362 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.418596409789994000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10060000000000002 " "
y[1] (analytic) = 1.0050559138691129 " "
y[1] (numeric) = 1.005055913869113 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20927613937653920000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10070000000000003 " "
y[1] (analytic) = 1.0050659618839304 " "
y[1] (numeric) = 1.0050659618839308 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.4185081048575800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10080000000000003 " "
y[1] (analytic) = 1.0050760198480884 " "
y[1] (numeric) = 1.0050760198480888 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41846388810653600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10090000000000003 " "
y[1] (analytic) = 1.0050860877614864 " "
y[1] (numeric) = 1.0050860877614867 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.209209814251492700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10100000000000003 " "
y[1] (analytic) = 1.0050961656240234 " "
y[1] (numeric) = 1.0050961656240236 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.209187663024988500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10110000000000004 " "
y[1] (analytic) = 1.0051062534355988 " "
y[1] (numeric) = 1.005106253435599 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20916549037527800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10120000000000004 " "
y[1] (analytic) = 1.0051163511961114 " "
y[1] (numeric) = 1.0051163511961119 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41828659260777400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10130000000000004 " "
y[1] (analytic) = 1.0051264589054607 " "
y[1] (numeric) = 1.0051264589054612 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41824216162468300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10140000000000005 " "
y[1] (analytic) = 1.0051365765635454 " "
y[1] (numeric) = 1.0051365765635458 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.4181976878043400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10150000000000005 " "
y[1] (analytic) = 1.0051467041702642 " "
y[1] (numeric) = 1.0051467041702646 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41815317114980340000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10160000000000005 " "
y[1] (analytic) = 1.0051568417255161 " "
y[1] (numeric) = 1.0051568417255166 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.418108611664135000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10170000000000005 " "
y[1] (analytic) = 1.0051669892291994 " "
y[1] (numeric) = 1.0051669892292 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41806400935039900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10180000000000006 " "
y[1] (analytic) = 1.0051771466812132 " "
y[1] (numeric) = 1.0051771466812134 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.209009682105831400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10190000000000006 " "
y[1] (analytic) = 1.005187314081455 " "
y[1] (numeric) = 1.0051873140814553 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41797467625099800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10200000000000006 " "
y[1] (analytic) = 1.0051974914298238 " "
y[1] (numeric) = 1.0051974914298243 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41792994547147600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10210000000000007 " "
y[1] (analytic) = 1.0052076787262179 " "
y[1] (numeric) = 1.0052076787262183 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.417885171876173600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10220000000000007 " "
y[1] (analytic) = 1.005217875970535 " "
y[1] (numeric) = 1.0052178759705355 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41784035546816900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10230000000000007 " "
y[1] (analytic) = 1.0052280831626734 " "
y[1] (numeric) = 1.0052280831626739 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.417795496250544500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10240000000000007 " "
y[1] (analytic) = 1.0052383003025311 " "
y[1] (numeric) = 1.0052383003025314 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208875297113191400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10250000000000008 " "
y[1] (analytic) = 1.0052485273900056 " "
y[1] (numeric) = 1.0052485273900058 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20885282469938720000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10260000000000008 " "
y[1] (analytic) = 1.0052587644249948 " "
y[1] (numeric) = 1.005258764424995 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208830330885403200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10270000000000008 " "
y[1] (analytic) = 1.0052690114073966 " "
y[1] (numeric) = 1.0052690114073968 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208807815672786400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10280000000000009 " "
y[1] (analytic) = 1.005279268337108 " "
y[1] (numeric) = 1.0052792683371083 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.417570558126170400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10290000000000009 " "
y[1] (analytic) = 1.0052895352140268 " "
y[1] (numeric) = 1.0052895352140272 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41752544211569600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10300000000000009 " "
y[1] (analytic) = 1.00529981203805 " "
y[1] (numeric) = 1.0052998120380505 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.417480283317253000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1031000000000001 " "
y[1] (analytic) = 1.0053100988090755 " "
y[1] (numeric) = 1.0053100988090757 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208717540866971300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1032000000000001 " "
y[1] (analytic) = 1.0053203955269998 " "
y[1] (numeric) = 1.005320395527 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208694918684437300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1033000000000001 " "
y[1] (analytic) = 1.0053307021917202 " "
y[1] (numeric) = 1.0053307021917204 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20867227511257900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1034000000000001 " "
y[1] (analytic) = 1.0053410188031333 " "
y[1] (numeric) = 1.0053410188031338 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.417299220305906400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1035000000000001 " "
y[1] (analytic) = 1.0053513453611367 " "
y[1] (numeric) = 1.005351345361137 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208626923807116300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10360000000000011 " "
y[1] (analytic) = 1.0053616818656264 " "
y[1] (numeric) = 1.0053616818656266 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20860421607662900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10370000000000011 " "
y[1] (analytic) = 1.005372028316499 " "
y[1] (numeric) = 1.0053720283164993 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208581486963051800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10380000000000011 " "
y[1] (analytic) = 1.0053823847136516 " "
y[1] (numeric) = 1.0053823847136518 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208558736467946300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10390000000000012 " "
y[1] (analytic) = 1.0053927510569802 " "
y[1] (numeric) = 1.0053927510569804 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20853596459287600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10400000000000012 " "
y[1] (analytic) = 1.0054031273463815 " "
y[1] (numeric) = 1.0054031273463815 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10410000000000012 " "
y[1] (analytic) = 1.0054135135817512 " "
y[1] (numeric) = 1.0054135135817512 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10420000000000013 " "
y[1] (analytic) = 1.0054239097629862 " "
y[1] (numeric) = 1.005423909762986 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20846752070353120000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10430000000000013 " "
y[1] (analytic) = 1.0054343158899819 " "
y[1] (numeric) = 1.0054343158899817 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208444663324264400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10440000000000013 " "
y[1] (analytic) = 1.0054447319626343 " "
y[1] (numeric) = 1.005444731962634 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.208421784572871500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10450000000000013 " "
y[1] (analytic) = 1.0054551579808395 " "
y[1] (numeric) = 1.005455157980839 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41679776890184700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10460000000000014 " "
y[1] (analytic) = 1.005465593944493 " "
y[1] (numeric) = 1.0054655939444925 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.416751925919990600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10470000000000014 " "
y[1] (analytic) = 1.0054760398534905 " "
y[1] (numeric) = 1.00547603985349 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.416706040203320400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10480000000000014 " "
y[1] (analytic) = 1.0054864957077276 " "
y[1] (numeric) = 1.0054864957077272 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41666011175499100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10490000000000015 " "
y[1] (analytic) = 1.0054969615071 " "
y[1] (numeric) = 1.0054969615070994 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.62492121086723200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10500000000000015 " "
y[1] (analytic) = 1.0055074372515027 " "
y[1] (numeric) = 1.005507437251502 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.62485219001395700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10510000000000015 " "
y[1] (analytic) = 1.0055179229408306 " "
y[1] (numeric) = 1.0055179229408302 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.416522070051604000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10520000000000015 " "
y[1] (analytic) = 1.0055284185749798 " "
y[1] (numeric) = 1.005528418574979 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.62471395606231600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10530000000000016 " "
y[1] (analytic) = 1.0055389241538446 " "
y[1] (numeric) = 1.0055389241538437 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.83285965729792500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10540000000000016 " "
y[1] (analytic) = 1.0055494396773201 " "
y[1] (numeric) = 1.0055494396773192 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.83276728775405500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10550000000000016 " "
y[1] (analytic) = 1.0055599651453013 " "
y[1] (numeric) = 1.0055599651453002 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10408435409889410000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10560000000000017 " "
y[1] (analytic) = 1.005570500557683 " "
y[1] (numeric) = 1.0055705005576816 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32488734386233570000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10570000000000017 " "
y[1] (analytic) = 1.0055810459143593 " "
y[1] (numeric) = 1.005581045914358 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.324873449995049900000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10580000000000017 " "
y[1] (analytic) = 1.0055916012152253 " "
y[1] (numeric) = 1.0055916012152237 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54566946720406440000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10590000000000017 " "
y[1] (analytic) = 1.005602166460175 " "
y[1] (numeric) = 1.0056021664601735 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.5456532278033580000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10600000000000018 " "
y[1] (analytic) = 1.0056127416491036 " "
y[1] (numeric) = 1.0056127416491016 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.98724753730556800000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10610000000000018 " "
y[1] (analytic) = 1.0056233267819046 " "
y[1] (numeric) = 1.0056233267819024 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.20802957739252430000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10620000000000018 " "
y[1] (analytic) = 1.005633921858472 " "
y[1] (numeric) = 1.0056339218584698 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.2080063142130240000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10630000000000019 " "
y[1] (analytic) = 1.0056445268787004 " "
y[1] (numeric) = 1.005644526878698 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.42878133266065530000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10640000000000019 " "
y[1] (analytic) = 1.0056551418424835 " "
y[1] (numeric) = 1.0056551418424808 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.64955166859547950000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10650000000000019 " "
y[1] (analytic) = 1.0056657667497153 " "
y[1] (numeric) = 1.0056657667497122 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.091110955280330000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1066000000000002 " "
y[1] (analytic) = 1.0056764016002893 " "
y[1] (numeric) = 1.005676401600286 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.3118695721362460000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1067000000000002 " "
y[1] (analytic) = 1.0056870463940992 " "
y[1] (numeric) = 1.0056870463940957 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.53262348514758240000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1068000000000002 " "
y[1] (analytic) = 1.0056977011310386 " "
y[1] (numeric) = 1.0056977011310348 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.75337268791638150000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1069000000000002 " "
y[1] (analytic) = 1.0057083658110013 " "
y[1] (numeric) = 1.005708365810997 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.1949014614922930000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.1070000000000002 " "
y[1] (analytic) = 1.0057190404338798 " "
y[1] (numeric) = 1.0057190404338756 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.19485693713776250000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10710000000000021 " "
y[1] (analytic) = 1.0057297249995685 " "
y[1] (numeric) = 1.0057297249995636 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.8571511678774190000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10720000000000021 " "
y[1] (analytic) = 1.0057404195079596 " "
y[1] (numeric) = 1.0057404195079545 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 5.0778767704038790000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10730000000000021 " "
y[1] (analytic) = 1.0057511239589465 " "
y[1] (numeric) = 1.005751123958941 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 5.5193725275442720000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10740000000000022 " "
y[1] (analytic) = 1.0057618383524223 " "
y[1] (numeric) = 1.0057618383524163 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.9608588279674880000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10750000000000022 " "
y[1] (analytic) = 1.0057725626882794 " "
y[1] (numeric) = 1.0057725626882732 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 6.1815654637496790000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10760000000000022 " "
y[1] (analytic) = 1.0057832969664111 " "
y[1] (numeric) = 1.0057832969664044 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 6.6230351685522170000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10770000000000023 " "
y[1] (analytic) = 1.00579404118671 " "
y[1] (numeric) = 1.0057940411867026 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 7.2852608610412340000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10780000000000023 " "
y[1] (analytic) = 1.005804795349068 " "
y[1] (numeric) = 1.0058047953490603 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 7.7267092067093880000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10790000000000023 " "
y[1] (analytic) = 1.0058155594533784 " "
y[1] (numeric) = 1.00581555945337 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.3889087893378270000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10800000000000023 " "
y[1] (analytic) = 1.0058263334995332 " "
y[1] (numeric) = 1.005826333499524 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 9.0510941091109430000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10810000000000024 " "
y[1] (analytic) = 1.0058371174874245 " "
y[1] (numeric) = 1.0058371174874148 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.7132651468526930000000000000E-13 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10820000000000024 " "
y[1] (analytic) = 1.0058479114169447 " "
y[1] (numeric) = 1.0058479114169343 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 1.0375421883388984000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10830000000000024 " "
y[1] (analytic) = 1.0058587152879856 " "
y[1] (numeric) = 1.0058587152879748 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.0816813013556727000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10840000000000025 " "
y[1] (analytic) = 1.0058695291004396 " "
y[1] (numeric) = 1.005869529100428 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 1.1478943463400897000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10850000000000025 " "
y[1] (analytic) = 1.0058803528541982 " "
y[1] (numeric) = 1.005880352854186 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.2141059556659728000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10860000000000025 " "
y[1] (analytic) = 1.0058911865491533 " "
y[1] (numeric) = 1.0058911865491402 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.302390543406623000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10870000000000025 " "
y[1] (analytic) = 1.0059020301851964 " "
y[1] (numeric) = 1.0059020301851826 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.3685990377032387000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10880000000000026 " "
y[1] (analytic) = 1.0059128837622193 " "
y[1] (numeric) = 1.0059128837622047 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.4568800302309523000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10890000000000026 " "
y[1] (analytic) = 1.0059237472801135 " "
y[1] (numeric) = 1.005923747280098 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.5451591024447695000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10900000000000026 " "
y[1] (analytic) = 1.00593462073877 " "
y[1] (numeric) = 1.0059346207387536 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 1.6334362517899007000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10910000000000027 " "
y[1] (analytic) = 1.0059455041380803 " "
y[1] (numeric) = 1.005945504138063 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.7217114757118193000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10920000000000027 " "
y[1] (analytic) = 1.0059563974779355 " "
y[1] (numeric) = 1.0059563974779173 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 1.8099847716562617000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10930000000000027 " "
y[1] (analytic) = 1.0059673007582268 " "
y[1] (numeric) = 1.0059673007582075 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.9203288828491022000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10940000000000027 " "
y[1] (analytic) = 1.0059782139788451 " "
y[1] (numeric) = 1.0059782139788247 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 2.0306705820502455000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10950000000000028 " "
y[1] (analytic) = 1.0059891371396814 " "
y[1] (numeric) = 1.0059891371396597 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 2.163082132728004000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10960000000000028 " "
y[1] (analytic) = 1.006000070240626 " "
y[1] (numeric) = 1.0060000702406033 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 2.251346731709061000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10970000000000028 " "
y[1] (analytic) = 1.00601101328157 " "
y[1] (numeric) = 1.006011013281546 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 2.3837529624729314000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10980000000000029 " "
y[1] (analytic) = 1.006021966262404 " "
y[1] (numeric) = 1.0060219662623786 " "
absolute error = 2.53130849614535700000000000000E-14 " "
relative error = 2.5161562878688754000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.10990000000000029 " "
y[1] (analytic) = 1.0060329291830183 " "
y[1] (numeric) = 1.0060329291829915 " "
absolute error = 2.686739719592879000000000000000E-14 " "
relative error = 2.6706280099347574000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
x[1] = 0.11000000000000029 " "
y[1] (analytic) = 1.0060439020433032 " "
y[1] (numeric) = 1.006043902043275 " "
absolute error = 2.819966482547897600000000000000E-14 " "
relative error = 2.8030252723767496000000000000E-12 "%"
h = 1.0000E-4 " "
"Finished!"
"Maximum Iterations Reached before Solution Completed!"
"diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;"
Iterations = 100
"Total Elapsed Time "= 41 Seconds
"Elapsed Time(since restart) "= 40 Seconds
"Expected Time Remaining "= 5 Hours 31 Minutes 53 Seconds
"Optimized Time Remaining "= 5 Hours 30 Minutes 26 Seconds
"Time to Timeout "= 14 Minutes 18 Seconds
Percent Done = 0.20612244897959772 "%"
(%o54) true
(%o54) diffeq.max