(%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_y2(ind_var),
omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y2 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y2[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, " "), analytic_val_y : exact_soln_y1(ind_var),
omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y1 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y1[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
2
else array_last_rel_error : relerr, omniout_float(ALWAYS,
2
"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_y2(ind_var),
omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y2 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y2[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, " "), analytic_val_y : exact_soln_y1(ind_var),
omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y1 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y1[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
2
else array_last_rel_error : relerr, omniout_float(ALWAYS,
2
"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_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_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_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_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 - 4 + n,
while (m >= 10) and ((!array_y2_higher ! < glob_small_float)
! 1, m!
or (!array_y2_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y2_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y2_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y2_higher
1, m - 1
array_y2_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y2_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : glob_max_terms, m : - 1 - 1 + n,
1, 2
while (m >= 10) and ((!array_y1_higher ! < glob_small_float)
! 1, m!
or (!array_y1_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y1_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y1_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y1_higher
1, m - 1
array_y1_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y1_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
2, 1 2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float))
2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float), n : - 1 - 4 + glob_max_terms,
2, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y2_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_y2_higher ! >= glob_large_float)
! 1, m!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y2_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_y2_higher array_y2_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y2_higher array_y2_higher
1, m - 1 1, m - 2
array_y2_higher array_y2_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y2_higher array_y2_higher
1, m - 3 1, m - 4
array_y2_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y2_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), n : - 1 - 1 + glob_max_terms, cnt : 0,
1, 2
while (cnt < 5) and (n >= 10) do (if !array_y1_higher ! > glob_small_float
! 1, n!
then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
elseif (!array_y1_higher ! >= glob_large_float)
! 1, m!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 5!
then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
array_y1_higher array_y1_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y1_higher array_y1_higher
1, m - 1 1, m - 2
array_y1_higher array_y1_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y1_higher array_y1_higher
1, m - 3 1, m - 4
array_y1_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y1_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 :
2, 1
glob_large_float, array_complex_pole : glob_large_float)
2, 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,
2, 1
array_complex_pole : ord_no), found : false,
2, 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")), found : false,
if (not found) and ((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
2, 1 2, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
2, 1 2, 2
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
2, 2 2, 2 2
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)
2, 1 2, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
2, 1 2, 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)))
2, 1 2, 2 2, 1 2, 2
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
2, 1 2, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
2, 1 2, 2
found : true, array_type_pole : 3, if glob_display_flag
2
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
2, 1 2, 1
and (array_real_pole > 0.0) and (array_real_pole >
2, 1 2, 2
0.0))
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
2, 1
and (array_complex_pole # glob_large_float)
2, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
2, 1 2, 2
0.0))
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
2, 2 2, 2 2
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,
2, 1 2, 2
array_type_pole : 3, if glob_display_flag
2
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
if array_pole > array_poles then (array_pole : array_poles ,
1 2, 1 1 2, 1
array_pole : array_poles ), display_pole())
2 2, 2
(%o6) check_for_pole() := (n : glob_max_terms, m : - 1 - 4 + n,
while (m >= 10) and ((!array_y2_higher ! < glob_small_float)
! 1, m!
or (!array_y2_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y2_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y2_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y2_higher
1, m - 1
array_y2_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y2_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : glob_max_terms, m : - 1 - 1 + n,
1, 2
while (m >= 10) and ((!array_y1_higher ! < glob_small_float)
! 1, m!
or (!array_y1_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y1_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y1_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y1_higher
1, m - 1
array_y1_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y1_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
2, 1 2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float))
2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float), n : - 1 - 4 + glob_max_terms,
2, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y2_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_y2_higher ! >= glob_large_float)
! 1, m!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y2_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_y2_higher array_y2_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y2_higher array_y2_higher
1, m - 1 1, m - 2
array_y2_higher array_y2_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y2_higher array_y2_higher
1, m - 3 1, m - 4
array_y2_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y2_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), n : - 1 - 1 + glob_max_terms, cnt : 0,
1, 2
while (cnt < 5) and (n >= 10) do (if !array_y1_higher ! > glob_small_float
! 1, n!
then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
elseif (!array_y1_higher ! >= glob_large_float)
! 1, m!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 5!
then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
array_y1_higher array_y1_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y1_higher array_y1_higher
1, m - 1 1, m - 2
array_y1_higher array_y1_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y1_higher array_y1_higher
1, m - 3 1, m - 4
array_y1_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y1_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 :
2, 1
glob_large_float, array_complex_pole : glob_large_float)
2, 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,
2, 1
array_complex_pole : ord_no), found : false,
2, 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")), found : false,
if (not found) and ((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
2, 1 2, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
2, 1 2, 2
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
2, 2 2, 2 2
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)
2, 1 2, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
2, 1 2, 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)))
2, 1 2, 2 2, 1 2, 2
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
2, 1 2, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
2, 1 2, 2
found : true, array_type_pole : 3, if glob_display_flag
2
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
2, 1 2, 1
and (array_real_pole > 0.0) and (array_real_pole >
2, 1 2, 2
0.0))
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
2, 1
and (array_complex_pole # glob_large_float)
2, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
2, 1 2, 2
0.0))
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
2, 2 2, 2 2
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,
2, 1 2, 2
array_type_pole : 3, if glob_display_flag
2
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
if array_pole > array_poles then (array_pole : array_poles ,
1 2, 1 1 2, 1
array_pole : array_poles ), display_pole())
2 2, 2
(%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_y2 ! > array_norms
! iii! iii
then array_norms : !array_y2 !, iii : 1 + iii), iii : 1,
iii ! iii!
while iii <= glob_max_terms do (if !array_y1 ! > array_norms
! iii! iii
then array_norms : !array_y1 !, 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_y2 ! > array_norms
! iii! iii
then array_norms : !array_y2 !, iii : 1 + iii), iii : 1,
iii ! iii!
while iii <= glob_max_terms do (if !array_y1 ! > array_norms
! iii! iii
then array_norms : !array_y1 !, iii : 1 + iii))
iii ! iii!
(%i8) atomall() := (array_tmp1 : array_y1 + array_const_0D0 ,
1 1 1
array_tmp2 : array_tmp1 - array_const_1D0 ,
1 1 1
if not array_y2_set_initial then (if 1 <= glob_max_terms
1, 5
4
then (temporary : array_tmp2 glob_h factorial_3(0, 4),
1
array_y2 : temporary, array_y2_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 4
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 3
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 2
temporary 5.0
temporary : -------------, array_y2_higher : temporary)), kkk : 2,
glob_h 5, 1
array_tmp4 : array_y2_higher , array_tmp5 : array_m1 array_tmp4 ,
1 4, 1 1 1 1
if not array_y1_set_initial then (if 1 <= glob_max_terms
2, 2
1
then (temporary : array_tmp5 glob_h factorial_3(0, 1),
1
array_y1 : temporary, array_y1_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_y1 + array_const_0D0 ,
2 2 2
array_tmp2 : array_tmp1 - array_const_1D0 ,
2 2 2
if not array_y2_set_initial then (if 2 <= glob_max_terms
1, 6
4
then (temporary : array_tmp2 glob_h factorial_3(1, 5),
2
array_y2 : temporary, array_y2_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 5
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 4
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 3
temporary 5.0
temporary : -------------, array_y2_higher : temporary)), kkk : 3,
glob_h 5, 2
array_tmp4 : array_y2_higher , array_tmp5 :
2 4, 2 2
ats(2, array_m1, array_tmp4, 1), if not array_y1_set_initial
2, 3
then (if 2 <= glob_max_terms then (temporary :
1
array_tmp5 glob_h factorial_3(1, 2), array_y1 : temporary,
2 3
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y1_higher : temporary)), kkk : 3,
2, 2
array_tmp1 : array_y1 + array_const_0D0 ,
3 3 3
array_tmp2 : array_tmp1 - array_const_1D0 ,
3 3 3
if not array_y2_set_initial then (if 3 <= glob_max_terms
1, 7
4
then (temporary : array_tmp2 glob_h factorial_3(2, 6),
3
array_y2 : temporary, array_y2_higher : temporary,
7 1, 7
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 6
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 5
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 4
temporary 5.0
temporary : -------------, array_y2_higher : temporary)), kkk : 4,
glob_h 5, 3
array_tmp4 : array_y2_higher , array_tmp5 :
3 4, 3 3
ats(3, array_m1, array_tmp4, 1), if not array_y1_set_initial
2, 4
then (if 3 <= glob_max_terms then (temporary :
1
array_tmp5 glob_h factorial_3(2, 3), array_y1 : temporary,
3 4
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y1_higher : temporary)), kkk : 4,
2, 3
array_tmp1 : array_y1 + array_const_0D0 ,
4 4 4
array_tmp2 : array_tmp1 - array_const_1D0 ,
4 4 4
if not array_y2_set_initial then (if 4 <= glob_max_terms
1, 8
4
then (temporary : array_tmp2 glob_h factorial_3(3, 7),
4
array_y2 : temporary, array_y2_higher : temporary,
8 1, 8
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 7
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 6
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 5
temporary 5.0
temporary : -------------, array_y2_higher : temporary)), kkk : 5,
glob_h 5, 4
array_tmp4 : array_y2_higher , array_tmp5 :
4 4, 4 4
ats(4, array_m1, array_tmp4, 1), if not array_y1_set_initial
2, 5
then (if 4 <= glob_max_terms then (temporary :
1
array_tmp5 glob_h factorial_3(3, 4), array_y1 : temporary,
4 5
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y1_higher : temporary)), kkk : 5,
2, 4
array_tmp1 : array_y1 + array_const_0D0 ,
5 5 5
array_tmp2 : array_tmp1 - array_const_1D0 ,
5 5 5
if not array_y2_set_initial then (if 5 <= glob_max_terms
1, 9
4
then (temporary : array_tmp2 glob_h factorial_3(4, 8),
5
array_y2 : temporary, array_y2_higher : temporary,
9 1, 9
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 8
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 7
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 6
temporary 5.0
temporary : -------------, array_y2_higher : temporary)), kkk : 6,
glob_h 5, 5
array_tmp4 : array_y2_higher , array_tmp5 :
5 4, 5 5
ats(5, array_m1, array_tmp4, 1), if not array_y1_set_initial
2, 6
then (if 5 <= glob_max_terms then (temporary :
1
array_tmp5 glob_h factorial_3(4, 5), array_y1 : temporary,
5 6
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y1_higher : temporary)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp1 :
kkk
array_y1 + array_const_0D0 , array_tmp2 :
kkk kkk kkk
array_tmp1 - array_const_1D0 , order_d : 4,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y2_set_initial
1, order_d + kkk
order_d
array_tmp2 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y2 : temporary, array_y2_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_y2_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), array_tmp4 : array_y2_higher ,
kkk 4, kkk
array_tmp5 : ats(kkk, array_m1, array_tmp4, 1), order_d : 1,
kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y1_set_initial
2, order_d + kkk
order_d
array_tmp5 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y1 : temporary, array_y1_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_y1_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk))
(%o8) atomall() := (array_tmp1 : array_y1 + array_const_0D0 ,
1 1 1
array_tmp2 : array_tmp1 - array_const_1D0 ,
1 1 1
if not array_y2_set_initial then (if 1 <= glob_max_terms
1, 5
4
then (temporary : array_tmp2 glob_h factorial_3(0, 4),
1
array_y2 : temporary, array_y2_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 4
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 3
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 2
temporary 5.0
temporary : -------------, array_y2_higher : temporary)), kkk : 2,
glob_h 5, 1
array_tmp4 : array_y2_higher , array_tmp5 : array_m1 array_tmp4 ,
1 4, 1 1 1 1
if not array_y1_set_initial then (if 1 <= glob_max_terms
2, 2
1
then (temporary : array_tmp5 glob_h factorial_3(0, 1),
1
array_y1 : temporary, array_y1_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_y1 + array_const_0D0 ,
2 2 2
array_tmp2 : array_tmp1 - array_const_1D0 ,
2 2 2
if not array_y2_set_initial then (if 2 <= glob_max_terms
1, 6
4
then (temporary : array_tmp2 glob_h factorial_3(1, 5),
2
array_y2 : temporary, array_y2_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 5
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 4
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 3
temporary 5.0
temporary : -------------, array_y2_higher : temporary)), kkk : 3,
glob_h 5, 2
array_tmp4 : array_y2_higher , array_tmp5 :
2 4, 2 2
ats(2, array_m1, array_tmp4, 1), if not array_y1_set_initial
2, 3
then (if 2 <= glob_max_terms then (temporary :
1
array_tmp5 glob_h factorial_3(1, 2), array_y1 : temporary,
2 3
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y1_higher : temporary)), kkk : 3,
2, 2
array_tmp1 : array_y1 + array_const_0D0 ,
3 3 3
array_tmp2 : array_tmp1 - array_const_1D0 ,
3 3 3
if not array_y2_set_initial then (if 3 <= glob_max_terms
1, 7
4
then (temporary : array_tmp2 glob_h factorial_3(2, 6),
3
array_y2 : temporary, array_y2_higher : temporary,
7 1, 7
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 6
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 5
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 4
temporary 5.0
temporary : -------------, array_y2_higher : temporary)), kkk : 4,
glob_h 5, 3
array_tmp4 : array_y2_higher , array_tmp5 :
3 4, 3 3
ats(3, array_m1, array_tmp4, 1), if not array_y1_set_initial
2, 4
then (if 3 <= glob_max_terms then (temporary :
1
array_tmp5 glob_h factorial_3(2, 3), array_y1 : temporary,
3 4
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y1_higher : temporary)), kkk : 4,
2, 3
array_tmp1 : array_y1 + array_const_0D0 ,
4 4 4
array_tmp2 : array_tmp1 - array_const_1D0 ,
4 4 4
if not array_y2_set_initial then (if 4 <= glob_max_terms
1, 8
4
then (temporary : array_tmp2 glob_h factorial_3(3, 7),
4
array_y2 : temporary, array_y2_higher : temporary,
8 1, 8
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 7
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 6
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 5
temporary 5.0
temporary : -------------, array_y2_higher : temporary)), kkk : 5,
glob_h 5, 4
array_tmp4 : array_y2_higher , array_tmp5 :
4 4, 4 4
ats(4, array_m1, array_tmp4, 1), if not array_y1_set_initial
2, 5
then (if 4 <= glob_max_terms then (temporary :
1
array_tmp5 glob_h factorial_3(3, 4), array_y1 : temporary,
4 5
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y1_higher : temporary)), kkk : 5,
2, 4
array_tmp1 : array_y1 + array_const_0D0 ,
5 5 5
array_tmp2 : array_tmp1 - array_const_1D0 ,
5 5 5
if not array_y2_set_initial then (if 5 <= glob_max_terms
1, 9
4
then (temporary : array_tmp2 glob_h factorial_3(4, 8),
5
array_y2 : temporary, array_y2_higher : temporary,
9 1, 9
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 8
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 7
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 6
temporary 5.0
temporary : -------------, array_y2_higher : temporary)), kkk : 6,
glob_h 5, 5
array_tmp4 : array_y2_higher , array_tmp5 :
5 4, 5 5
ats(5, array_m1, array_tmp4, 1), if not array_y1_set_initial
2, 6
then (if 5 <= glob_max_terms then (temporary :
1
array_tmp5 glob_h factorial_3(4, 5), array_y1 : temporary,
5 6
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y1_higher : temporary)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp1 :
kkk
array_y1 + array_const_0D0 , array_tmp2 :
kkk kkk kkk
array_tmp1 - array_const_1D0 , order_d : 4,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y2_set_initial
1, order_d + kkk
order_d
array_tmp2 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y2 : temporary, array_y2_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_y2_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), array_tmp4 : array_y2_higher ,
kkk 4, kkk
array_tmp5 : ats(kkk, array_m1, array_tmp4, 1), order_d : 1,
kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y1_set_initial
2, order_d + kkk
order_d
array_tmp5 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y1 : temporary, array_y1_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_y1_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), 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_y1(x) := sin(x) + 1.0
(%o49) exact_soln_y1(x) := sin(x) + 1.0
(%i50) exact_soln_y2(x) := sin(x) + 1.0
(%o50) exact_soln_y2(x) := sin(x) + 1.0
(%i51) exact_soln_y2p(x) := cos(x)
(%o51) exact_soln_y2p(x) := cos(x)
(%i52) exact_soln_y2pp(x) := - sin(x)
(%o52) exact_soln_y2pp(x) := - sin(x)
(%i53) exact_soln_y2ppp(x) := - cos(x)
(%o53) exact_soln_y2ppp(x) := - cos(x)
(%i54) mainprog() := (define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(years_in_century, 100.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(min_in_hour, 60.0, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_html_log, true,
boolean), define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_clock_sec, 0.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(hours_in_day, 24.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3,
DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2,
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/mtest8postode.ode#################"),
omniout_str(ALWAYS, "diff ( y2 , x , 4 ) = y1 - 1.0;"),
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"),
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 : 5.1,"),
omniout_str(ALWAYS, "array_y1_init[0 + 1] : exact_soln_y1(x_start),"),
omniout_str(ALWAYS, "array_y2_init[0 + 1] : exact_soln_y2(x_start),"),
omniout_str(ALWAYS, "array_y2_init[1 + 1] : exact_soln_y2p(x_start),"),
omniout_str(ALWAYS, "array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"),
omniout_str(ALWAYS, "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 20,"),
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 : 1000,"),
omniout_str(ALWAYS, "glob_max_minutes : 15,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y1 (x) := ("),
omniout_str(ALWAYS, "1.0 + sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2 (x) := ("),
omniout_str(ALWAYS, "1.0 + sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2p (x) := ("),
omniout_str(ALWAYS, "cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2pp (x) := ("),
omniout_str(ALWAYS, "-sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2ppp (x) := ("),
omniout_str(ALWAYS, "-cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_x, 1 + max_terms), array(array_last_rel_error, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_y1_init, 1 + max_terms), array(array_type_pole, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_y2_init, 1 + max_terms),
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_norms, 1 + max_terms), array(array_y2, 1 + max_terms),
array(array_y1, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y1_set_initial, 1 + 3, 1 + max_terms),
array(array_y1_higher_work, 1 + 2, 1 + max_terms),
array(array_y2_higher, 1 + 5, 1 + max_terms),
array(array_y2_set_initial, 1 + 3, 1 + max_terms),
array(array_real_pole, 1 + 2, 1 + 3), array(array_y1_higher_work2, 1 + 2,
1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms),
array(array_y2_higher_work2, 1 + 5, 1 + max_terms),
array(array_complex_pole, 1 + 2, 1 + 3), array(array_poles, 1 + 2, 1 + 3),
array(array_y2_higher_work, 1 + 5, 1 + max_terms), term : 1,
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_1st_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_y1_init : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_type_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y2_init : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp5 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 3 do (term : 1, while term <=
max_terms do (array_y1_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 5 do (term : 1, while term <=
max_terms do (array_y2_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_y2_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y1_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 5 do (term : 1,
while term <= max_terms do (array_y2_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 5 do (term : 1,
while term <= max_terms do (array_y2_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_y1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term),
term
array(array_y2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y2 : 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_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_const_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_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_4, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_4 : 0.0, term : 1 + term),
term
array_const_4 : 4, 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 : 5.1,
1
array_y1_init : exact_soln_y1(x_start),
1 + 0
array_y2_init : exact_soln_y2(x_start),
1 + 0
array_y2_init : exact_soln_y2p(x_start),
1 + 1
array_y2_init : exact_soln_y2pp(x_start),
1 + 2
array_y2_init : exact_soln_y2ppp(x_start), glob_h : 1.0E-5,
1 + 3
glob_look_poles : true, glob_max_iter : 20, glob_h : 1.0E-4,
glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_log10_abserr glob_log10_relerr
glob_abserr : 10.0 , glob_relerr : 10.0 ,
chk_data(), array_y2_set_initial : true, array_y2_set_initial : true,
1, 1 1, 2
array_y2_set_initial : true, array_y2_set_initial : true,
1, 3 1, 4
array_y2_set_initial : false, array_y2_set_initial : false,
1, 5 1, 6
array_y2_set_initial : false, array_y2_set_initial : false,
1, 7 1, 8
array_y2_set_initial : false, array_y2_set_initial : false,
1, 9 1, 10
array_y2_set_initial : false, array_y2_set_initial : false,
1, 11 1, 12
array_y2_set_initial : false, array_y2_set_initial : false,
1, 13 1, 14
array_y2_set_initial : false, array_y2_set_initial : false,
1, 15 1, 16
array_y2_set_initial : false, array_y2_set_initial : false,
1, 17 1, 18
array_y2_set_initial : false, array_y2_set_initial : false,
1, 19 1, 20
array_y2_set_initial : false, array_y2_set_initial : false,
1, 21 1, 22
array_y2_set_initial : false, array_y2_set_initial : false,
1, 23 1, 24
array_y2_set_initial : false, array_y2_set_initial : false,
1, 25 1, 26
array_y2_set_initial : false, array_y2_set_initial : false,
1, 27 1, 28
array_y2_set_initial : false, array_y2_set_initial : false,
1, 29 1, 30
array_y1_set_initial : true, array_y1_set_initial : false,
2, 1 2, 2
array_y1_set_initial : false, array_y1_set_initial : false,
2, 3 2, 4
array_y1_set_initial : false, array_y1_set_initial : false,
2, 5 2, 6
array_y1_set_initial : false, array_y1_set_initial : false,
2, 7 2, 8
array_y1_set_initial : false, array_y1_set_initial : false,
2, 9 2, 10
array_y1_set_initial : false, array_y1_set_initial : false,
2, 11 2, 12
array_y1_set_initial : false, array_y1_set_initial : false,
2, 13 2, 14
array_y1_set_initial : false, array_y1_set_initial : false,
2, 15 2, 16
array_y1_set_initial : false, array_y1_set_initial : false,
2, 17 2, 18
array_y1_set_initial : false, array_y1_set_initial : false,
2, 19 2, 20
array_y1_set_initial : false, array_y1_set_initial : false,
2, 21 2, 22
array_y1_set_initial : false, array_y1_set_initial : false,
2, 23 2, 24
array_y1_set_initial : false, array_y1_set_initial : false,
2, 25 2, 26
array_y1_set_initial : false, array_y1_set_initial : false,
2, 27 2, 28
array_y1_set_initial : false, array_y1_set_initial : false,
2, 29 2, 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 : 4, term_no : 1,
2
while term_no <= order_diff do (array_y2 :
term_no
term_no - 1
array_y2_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_y2_init glob_h
it
array_y2_higher : ---------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y1 :
term_no
term_no - 1
array_y1_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_y1_init glob_h
it
array_y1_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_y2(),
if !array_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), start_array_y1(),
if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_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,
if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2
then (subiter : 1, while subiter <= 5 do (atomall(), subiter : 1 + subiter))
else (subiter : 1, while subiter <= glob_max_terms + 5 do (atomall(),
subiter : 1 + subiter)), if glob_look_poles then check_for_pole(),
array_x : glob_h + array_x , array_x : glob_h, order_diff : 4, ord : 5,
1 1 2
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
5, iii
array_y2_higher
5, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 5, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_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 : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_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 : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_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 : 4, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 5, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_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 : 5, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y2 : array_y2_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y2_higher :
ord, term_no
array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
order_diff : 1, ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (array_y1_higher_work :
2, iii
array_y1_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_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_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_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_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_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y1 : array_y1_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y1_higher :
ord, term_no
array_y1_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 ( y2 , x , 4 ) = y1 - 1.0;"),
omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"),
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,
"2012-06-13T16:59:08-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mtest8"),
logitem_str(html_log_file, "diff ( y2 , x , 4 ) = y1 - 1.0;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_integer(html_log_file,
glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 090 | "), logitem_str(html_log_file, "mtest8 diffeq.max"), logitem_str(html_log_file, "\
mtest8 maxima results"),
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs"),
logend(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logitem_str(html_log_file,
"diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"), logditto(html_log_file),
logditto(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logditto(html_log_file),
logitem_float(html_log_file, array_1st_rel_error ),
2
logitem_float(html_log_file, array_last_rel_error ), logditto(html_log_file),
2
logitem_pole(html_log_file, array_type_pole ),
2
if (array_type_pole = 1) or (array_type_pole = 2)
2 2
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),
logditto(html_log_file), if glob_percent_done < 100.0
then (logditto(html_log_file), 0) else (logditto(html_log_file), 0),
logditto(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logend(html_log_file)),
if glob_html_log then close(html_log_file))
(%o54) mainprog() := (define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(years_in_century, 100.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(min_in_hour, 60.0, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_html_log, true,
boolean), define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_clock_sec, 0.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(hours_in_day, 24.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3,
DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2,
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/mtest8postode.ode#################"),
omniout_str(ALWAYS, "diff ( y2 , x , 4 ) = y1 - 1.0;"),
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"),
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 : 5.1,"),
omniout_str(ALWAYS, "array_y1_init[0 + 1] : exact_soln_y1(x_start),"),
omniout_str(ALWAYS, "array_y2_init[0 + 1] : exact_soln_y2(x_start),"),
omniout_str(ALWAYS, "array_y2_init[1 + 1] : exact_soln_y2p(x_start),"),
omniout_str(ALWAYS, "array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"),
omniout_str(ALWAYS, "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 20,"),
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 : 1000,"),
omniout_str(ALWAYS, "glob_max_minutes : 15,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y1 (x) := ("),
omniout_str(ALWAYS, "1.0 + sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2 (x) := ("),
omniout_str(ALWAYS, "1.0 + sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2p (x) := ("),
omniout_str(ALWAYS, "cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2pp (x) := ("),
omniout_str(ALWAYS, "-sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2ppp (x) := ("),
omniout_str(ALWAYS, "-cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_x, 1 + max_terms), array(array_last_rel_error, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_y1_init, 1 + max_terms), array(array_type_pole, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_y2_init, 1 + max_terms),
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_norms, 1 + max_terms), array(array_y2, 1 + max_terms),
array(array_y1, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y1_set_initial, 1 + 3, 1 + max_terms),
array(array_y1_higher_work, 1 + 2, 1 + max_terms),
array(array_y2_higher, 1 + 5, 1 + max_terms),
array(array_y2_set_initial, 1 + 3, 1 + max_terms),
array(array_real_pole, 1 + 2, 1 + 3), array(array_y1_higher_work2, 1 + 2,
1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms),
array(array_y2_higher_work2, 1 + 5, 1 + max_terms),
array(array_complex_pole, 1 + 2, 1 + 3), array(array_poles, 1 + 2, 1 + 3),
array(array_y2_higher_work, 1 + 5, 1 + max_terms), term : 1,
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_1st_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_y1_init : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_type_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y2_init : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp5 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 3 do (term : 1, while term <=
max_terms do (array_y1_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 5 do (term : 1, while term <=
max_terms do (array_y2_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_y2_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y1_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 5 do (term : 1,
while term <= max_terms do (array_y2_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 5 do (term : 1,
while term <= max_terms do (array_y2_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_y1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term),
term
array(array_y2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y2 : 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_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_const_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_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_4, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_4 : 0.0, term : 1 + term),
term
array_const_4 : 4, 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 : 5.1,
1
array_y1_init : exact_soln_y1(x_start),
1 + 0
array_y2_init : exact_soln_y2(x_start),
1 + 0
array_y2_init : exact_soln_y2p(x_start),
1 + 1
array_y2_init : exact_soln_y2pp(x_start),
1 + 2
array_y2_init : exact_soln_y2ppp(x_start), glob_h : 1.0E-5,
1 + 3
glob_look_poles : true, glob_max_iter : 20, glob_h : 1.0E-4,
glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_log10_abserr glob_log10_relerr
glob_abserr : 10.0 , glob_relerr : 10.0 ,
chk_data(), array_y2_set_initial : true, array_y2_set_initial : true,
1, 1 1, 2
array_y2_set_initial : true, array_y2_set_initial : true,
1, 3 1, 4
array_y2_set_initial : false, array_y2_set_initial : false,
1, 5 1, 6
array_y2_set_initial : false, array_y2_set_initial : false,
1, 7 1, 8
array_y2_set_initial : false, array_y2_set_initial : false,
1, 9 1, 10
array_y2_set_initial : false, array_y2_set_initial : false,
1, 11 1, 12
array_y2_set_initial : false, array_y2_set_initial : false,
1, 13 1, 14
array_y2_set_initial : false, array_y2_set_initial : false,
1, 15 1, 16
array_y2_set_initial : false, array_y2_set_initial : false,
1, 17 1, 18
array_y2_set_initial : false, array_y2_set_initial : false,
1, 19 1, 20
array_y2_set_initial : false, array_y2_set_initial : false,
1, 21 1, 22
array_y2_set_initial : false, array_y2_set_initial : false,
1, 23 1, 24
array_y2_set_initial : false, array_y2_set_initial : false,
1, 25 1, 26
array_y2_set_initial : false, array_y2_set_initial : false,
1, 27 1, 28
array_y2_set_initial : false, array_y2_set_initial : false,
1, 29 1, 30
array_y1_set_initial : true, array_y1_set_initial : false,
2, 1 2, 2
array_y1_set_initial : false, array_y1_set_initial : false,
2, 3 2, 4
array_y1_set_initial : false, array_y1_set_initial : false,
2, 5 2, 6
array_y1_set_initial : false, array_y1_set_initial : false,
2, 7 2, 8
array_y1_set_initial : false, array_y1_set_initial : false,
2, 9 2, 10
array_y1_set_initial : false, array_y1_set_initial : false,
2, 11 2, 12
array_y1_set_initial : false, array_y1_set_initial : false,
2, 13 2, 14
array_y1_set_initial : false, array_y1_set_initial : false,
2, 15 2, 16
array_y1_set_initial : false, array_y1_set_initial : false,
2, 17 2, 18
array_y1_set_initial : false, array_y1_set_initial : false,
2, 19 2, 20
array_y1_set_initial : false, array_y1_set_initial : false,
2, 21 2, 22
array_y1_set_initial : false, array_y1_set_initial : false,
2, 23 2, 24
array_y1_set_initial : false, array_y1_set_initial : false,
2, 25 2, 26
array_y1_set_initial : false, array_y1_set_initial : false,
2, 27 2, 28
array_y1_set_initial : false, array_y1_set_initial : false,
2, 29 2, 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 : 4, term_no : 1,
2
while term_no <= order_diff do (array_y2 :
term_no
term_no - 1
array_y2_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_y2_init glob_h
it
array_y2_higher : ---------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y1 :
term_no
term_no - 1
array_y1_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_y1_init glob_h
it
array_y1_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_y2(),
if !array_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), start_array_y1(),
if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_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,
if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2
then (subiter : 1, while subiter <= 5 do (atomall(), subiter : 1 + subiter))
else (subiter : 1, while subiter <= glob_max_terms + 5 do (atomall(),
subiter : 1 + subiter)), if glob_look_poles then check_for_pole(),
array_x : glob_h + array_x , array_x : glob_h, order_diff : 4, ord : 5,
1 1 2
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
5, iii
array_y2_higher
5, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 5, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_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 : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_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 : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_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 : 4, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 5, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_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 : 5, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_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_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y2 : array_y2_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y2_higher :
ord, term_no
array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
order_diff : 1, ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (array_y1_higher_work :
2, iii
array_y1_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_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_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_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_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_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y1 : array_y1_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y1_higher :
ord, term_no
array_y1_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 ( y2 , x , 4 ) = y1 - 1.0;"),
omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"),
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,
"2012-06-13T16:59:08-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mtest8"),
logitem_str(html_log_file, "diff ( y2 , x , 4 ) = y1 - 1.0;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_integer(html_log_file,
glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 090 | "), logitem_str(html_log_file, "mtest8 diffeq.max"), logitem_str(html_log_file, "\
mtest8 maxima results"),
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs"),
logend(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logitem_str(html_log_file,
"diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"), logditto(html_log_file),
logditto(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logditto(html_log_file),
logitem_float(html_log_file, array_1st_rel_error ),
2
logitem_float(html_log_file, array_last_rel_error ), logditto(html_log_file),
2
logitem_pole(html_log_file, array_type_pole ),
2
if (array_type_pole = 1) or (array_type_pole = 2)
2 2
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),
logditto(html_log_file), if glob_percent_done < 100.0
then (logditto(html_log_file), 0) else (logditto(html_log_file), 0),
logditto(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logend(html_log_file)),
if glob_html_log then close(html_log_file))
(%i55) mainprog()
"##############ECHO OF PROBLEM#################"
"##############temp/mtest8postode.ode#################"
"diff ( y2 , x , 4 ) = y1 - 1.0;"
"diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 32,"
"max_terms : 30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : 0.1,"
"x_end : 5.1,"
"array_y1_init[0 + 1] : exact_soln_y1(x_start),"
"array_y2_init[0 + 1] : exact_soln_y2(x_start),"
"array_y2_init[1 + 1] : exact_soln_y2p(x_start),"
"array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"
"array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"
"glob_h : 0.00001,"
"glob_look_poles : true,"
"glob_max_iter : 20,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_h : 0.0001 ,"
"glob_look_poles : true,"
"glob_max_iter : 1000,"
"glob_max_minutes : 15,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y1 (x) := ("
"1.0 + sin(x) "
");"
"exact_soln_y2 (x) := ("
"1.0 + sin(x) "
");"
"exact_soln_y2p (x) := ("
"cos(x) "
");"
"exact_soln_y2pp (x) := ("
"-sin(x) "
");"
"exact_soln_y2ppp (x) := ("
"-cos(x) "
");"
""
""
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = 0.1 " "
y2[1] (analytic) = 1.0998334166468282 " "
y2[1] (numeric) = 1.0998334166468282 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.0998334166468282 " "
y1[1] (numeric) = 1.0998334166468282 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
x[1] = 0.1 " "
y2[1] (analytic) = 1.0998334166468282 " "
y2[1] (numeric) = 1.0998334166468282 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.0998334166468282 " "
y1[1] (numeric) = 1.0998334166468282 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10010000000000001 " "
y2[1] (analytic) = 1.099932916564023 " "
y2[1] (numeric) = 1.099932916564023 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.099932916564023 " "
y1[1] (numeric) = 1.0999329165641225 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 9.043822719403443000000000000E-12 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10020000000000001 " "
y2[1] (analytic) = 1.1000324154818888 " "
y2[1] (numeric) = 1.1000324154818888 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1000324154818888 " "
y1[1] (numeric) = 1.1000324154823862 " "
absolute error = 4.9737991503207013000000000000E-13 " "
relative error = 4.521502348766549600000000000E-11 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10030000000000001 " "
y2[1] (analytic) = 1.1001319133994303 " "
y2[1] (numeric) = 1.1001319133994303 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1001319133994303 " "
y1[1] (numeric) = 1.1001319134006242 " "
absolute error = 1.1939338406818933000000000000E-12 " "
relative error = 1.0852642543498381000000000E-10 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10040000000000002 " "
y2[1] (analytic) = 1.1002314103156527 " "
y2[1] (numeric) = 1.1002314103156527 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1002314103156527 " "
y1[1] (numeric) = 1.1002314103178417 " "
absolute error = 2.1889157153509586000000000000E-12 " "
relative error = 1.98950483946187830000000000E-10 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10050000000000002 " "
y2[1] (analytic) = 1.1003309062295612 " "
y2[1] (numeric) = 1.100330906229561 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.017980260918948400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1003309062295612 " "
y1[1] (numeric) = 1.1003309062330435 " "
absolute error = 3.482325539039266000000000000E-12 " "
relative error = 3.16479844319918700000000000E-10 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10060000000000002 " "
y2[1] (analytic) = 1.1004304011401604 " "
y2[1] (numeric) = 1.1004304011401602 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.017797806158117800000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1004304011401604 " "
y1[1] (numeric) = 1.1004304011452348 " "
absolute error = 5.0743853563517400000000000000E-12 " "
relative error = 4.6112733264131460000000000E-10 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10070000000000003 " "
y2[1] (analytic) = 1.1005298950464557 " "
y2[1] (numeric) = 1.1005298950464555 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.017615386228634500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1005298950464557 " "
y1[1] (numeric) = 1.1005298950534206 " "
absolute error = 6.964873122683457000000000000E-12 " "
relative error = 6.3286541819833560000000000E-10 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10080000000000003 " "
y2[1] (analytic) = 1.100629387947452 " "
y2[1] (numeric) = 1.1006293879474518 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.01743300112237700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.100629387947452 " "
y1[1] (numeric) = 1.1006293879566058 " "
absolute error = 9.153788838034416000000000000E-12 " "
relative error = 8.3168675471269990000000000E-10 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10090000000000003 " "
y2[1] (analytic) = 1.1007288798421544 " "
y2[1] (numeric) = 1.1007288798421542 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.017250650831226600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1007288798421544 " "
y1[1] (numeric) = 1.1007288798537957 " "
absolute error = 1.164135454700954100000000000E-11 " "
relative error = 1.0576041712177955000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10100000000000003 " "
y2[1] (analytic) = 1.100828370729568 " "
y2[1] (numeric) = 1.1008283707295679 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.017068335347066100000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.100828370729568 " "
y1[1] (numeric) = 1.1008283707439952 " "
absolute error = 1.442712616039898400000000000E-11 " "
relative error = 1.3105699802084028000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10110000000000004 " "
y2[1] (analytic) = 1.100927860608698 " "
y2[1] (numeric) = 1.1009278606086979 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.016886054661781700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.100927860608698 " "
y1[1] (numeric) = 1.1009278606262094 " "
absolute error = 1.75113257228076700000000000E-11 " "
relative error = 1.5905970181484674000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10120000000000004 " "
y2[1] (analytic) = 1.1010273494785492 " "
y2[1] (numeric) = 1.1010273494785492 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1010273494785492 " "
y1[1] (numeric) = 1.1010273494994436 " "
absolute error = 2.089439732344544600000000000E-11 " "
relative error = 1.8977182840499934000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10130000000000004 " "
y2[1] (analytic) = 1.101126837338127 " "
y2[1] (numeric) = 1.101126837338127 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.101126837338127 " "
y1[1] (numeric) = 1.1011268373627028 " "
absolute error = 2.45756748284975400000000000E-11 " "
relative error = 2.2318659390690154000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10140000000000005 " "
y2[1] (analytic) = 1.1012263241864366 " "
y2[1] (numeric) = 1.1012263241864366 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1012263241864366 " "
y1[1] (numeric) = 1.101226324214992 " "
absolute error = 2.855538028256887600000000000E-11 " "
relative error = 2.593052822603474000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10150000000000005 " "
y2[1] (analytic) = 1.1013258100224828 " "
y2[1] (numeric) = 1.1013258100224828 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1013258100224828 " "
y1[1] (numeric) = 1.1013258100553165 " "
absolute error = 3.28337357302643800000000000E-11 " "
relative error = 2.981291769562188000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10160000000000005 " "
y2[1] (analytic) = 1.101425294845271 " "
y2[1] (numeric) = 1.101425294845271 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.101425294845271 " "
y1[1] (numeric) = 1.1014252948826813 " "
absolute error = 3.7410297082374200000000000E-11 " "
relative error = 3.3965351311120584000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10170000000000005 " "
y2[1] (analytic) = 1.101524778653806 " "
y2[1] (numeric) = 1.101524778653806 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.101524778653806 " "
y1[1] (numeric) = 1.1015247786960916 " "
absolute error = 4.22855084281081870000000000E-11 " "
relative error = 3.838815907508326000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10180000000000006 " "
y2[1] (analytic) = 1.1016242614470935 " "
y2[1] (numeric) = 1.1016242614470935 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1016242614470935 " "
y1[1] (numeric) = 1.1016242614945526 " "
absolute error = 4.745914772286141700000000000E-11 " "
relative error = 4.3081066189046247000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10190000000000006 " "
y2[1] (analytic) = 1.1017237432241382 " "
y2[1] (numeric) = 1.1017237432241382 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1017237432241382 " "
y1[1] (numeric) = 1.1017237432770695 " "
absolute error = 5.29312149666338900000000000E-11 " "
relative error = 4.804399949821667000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10200000000000006 " "
y2[1] (analytic) = 1.1018232239839456 " "
y2[1] (numeric) = 1.1018232239839456 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1018232239839456 " "
y1[1] (numeric) = 1.1018232240426473 " "
absolute error = 5.8701710159425600000000000E-11 " "
relative error = 5.327688587573366000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10210000000000007 " "
y2[1] (analytic) = 1.1019227037255206 " "
y2[1] (numeric) = 1.1019227037255208 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.015065159963713000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1019227037255206 " "
y1[1] (numeric) = 1.1019227037902912 " "
absolute error = 6.47706333012365600000000000E-11 " "
relative error = 5.87796522226575000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10220000000000007 " "
y2[1] (analytic) = 1.1020221824478686 " "
y2[1] (numeric) = 1.1020221824478689 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.014883261531218400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1020221824478686 " "
y1[1] (numeric) = 1.1020221825190066 " "
absolute error = 7.11379843920667600000000000E-11 " "
relative error = 6.455222546795871000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10230000000000007 " "
y2[1] (analytic) = 1.102121660149995 " "
y2[1] (numeric) = 1.102121660149995 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.102121660149995 " "
y1[1] (numeric) = 1.1021216602277986 " "
absolute error = 7.78035413873112700000000000E-11 " "
relative error = 7.059433109836756000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10240000000000007 " "
y2[1] (analytic) = 1.1022211368309045 " "
y2[1] (numeric) = 1.1022211368309047 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.01451956876323200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1022211368309045 " "
y1[1] (numeric) = 1.1022211369156725 " "
absolute error = 8.47679704207848800000000000E-11 " "
relative error = 7.690650050906203000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10250000000000008 " "
y2[1] (analytic) = 1.1023206124896028 " "
y2[1] (numeric) = 1.102320612489603 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.014337774411577300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1023206124896028 " "
y1[1] (numeric) = 1.1023206125816334 " "
absolute error = 9.2030605358672800000000000E-11 " "
relative error = 8.348805630225920000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10260000000000008 " "
y2[1] (analytic) = 1.102420087125095 " "
y2[1] (numeric) = 1.102420087125095 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.102420087125095 " "
y1[1] (numeric) = 1.1024200872246865 " "
absolute error = 9.95914462009750400000000000E-11 " "
relative error = 9.033892557300082000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10270000000000008 " "
y2[1] (analytic) = 1.1025195607363862 " "
y2[1] (numeric) = 1.1025195607363865 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.01397428973255580000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1025195607363862 " "
y1[1] (numeric) = 1.1025195608438374 " "
absolute error = 1.07451159081506380000000000E-10 " "
relative error = 9.745963963645093000000000E-9 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10280000000000009 " "
y2[1] (analytic) = 1.102619033322482 " "
y2[1] (numeric) = 1.1026190333224821 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.013792599389041500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.102619033322482 " "
y1[1] (numeric) = 1.102619033438091 " "
absolute error = 1.15609077866452030000000000E-10 " "
relative error = 1.048495213420100200000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10290000000000009 " "
y2[1] (analytic) = 1.1027185048823873 " "
y2[1] (numeric) = 1.1027185048823875 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.01361094369876310000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1027185048823873 " "
y1[1] (numeric) = 1.1027185050064525 " "
absolute error = 1.240652025558120000000000E-10 " "
relative error = 1.12508497868224700000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10300000000000009 " "
y2[1] (analytic) = 1.1028179754151077 " "
y2[1] (numeric) = 1.1028179754151077 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1028179754151077 " "
y1[1] (numeric) = 1.1028179755479275 " "
absolute error = 1.3281975519419120000000000E-10 " "
relative error = 1.204366977643767500000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1031000000000001 " "
y2[1] (analytic) = 1.1029174449196482 " "
y2[1] (numeric) = 1.1029174449196482 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1029174449196482 " "
y1[1] (numeric) = 1.1029174450615211 " "
absolute error = 1.41872957826194580000000000E-10 " "
relative error = 1.286342495349056500000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1032000000000001 " "
y2[1] (analytic) = 1.1030169133950143 " "
y2[1] (numeric) = 1.1030169133950143 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1030169133950143 " "
y1[1] (numeric) = 1.1030169135462387 " "
absolute error = 1.51224366362612270000000000E-10 " "
relative error = 1.371006777195768500000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1033000000000001 " "
y2[1] (analytic) = 1.1031163808402111 " "
y2[1] (numeric) = 1.1031163808402111 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1031163808402111 " "
y1[1] (numeric) = 1.1031163810010856 " "
absolute error = 1.60874424892654130000000000E-10 " "
relative error = 1.458363121850487200000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1034000000000001 " "
y2[1] (analytic) = 1.1032158472542444 " "
y2[1] (numeric) = 1.1032158472542444 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1032158472542444 " "
y1[1] (numeric) = 1.103215847425067 " "
absolute error = 1.7082268932711030000000000E-10 " "
relative error = 1.54840677599279390000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1035000000000001 " "
y2[1] (analytic) = 1.103315312636119 " "
y2[1] (numeric) = 1.103315312636119 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.103315312636119 " "
y1[1] (numeric) = 1.1033153128171884 " "
absolute error = 1.81069381710585730000000000E-10 " "
relative error = 1.641139025596970700000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10360000000000011 " "
y2[1] (analytic) = 1.1034147769848406 " "
y2[1] (numeric) = 1.1034147769848406 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1034147769848406 " "
y1[1] (numeric) = 1.103414777176455 " "
absolute error = 1.9161450204308040000000000E-10 " "
relative error = 1.736559143848704400000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10370000000000011 " "
y2[1] (analytic) = 1.1035142402994143 " "
y2[1] (numeric) = 1.1035142402994145 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.01215894472539320000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1035142402994143 " "
y1[1] (numeric) = 1.1035142405018723 " "
absolute error = 2.0245805032459430000000000E-10 " "
relative error = 1.83466640421116600000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10380000000000011 " "
y2[1] (analytic) = 1.1036137025788457 " "
y2[1] (numeric) = 1.103613702578846 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.01197760055147300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1036137025788457 " "
y1[1] (numeric) = 1.1036137027924455 " "
absolute error = 2.13599804510522520000000000E-10 " "
relative error = 1.935458068447299400000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10390000000000012 " "
y2[1] (analytic) = 1.10371316382214 " "
y2[1] (numeric) = 1.1037131638221402 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.011796290950219300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.10371316382214 " "
y1[1] (numeric) = 1.1037131640471802 " "
absolute error = 2.2504020869007490000000000E-10 " "
relative error = 2.03893743471142900000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10400000000000012 " "
y2[1] (analytic) = 1.1038126240283028 " "
y2[1] (numeric) = 1.103812624028303 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.011615015913587600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1038126240283028 " "
y1[1] (numeric) = 1.1038126242650816 " "
absolute error = 2.3677881877404160000000000E-10 " "
relative error = 2.145099753524565300000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10410000000000012 " "
y2[1] (analytic) = 1.1039120831963394 " "
y2[1] (numeric) = 1.1039120831963396 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.011433775433536500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1039120831963394 " "
y1[1] (numeric) = 1.1039120834451552 " "
absolute error = 2.48815856807027560000000000E-10 " "
relative error = 2.253946311436231500000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10420000000000013 " "
y2[1] (analytic) = 1.104011541325255 " "
y2[1] (numeric) = 1.1040115413252551 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.011252569502027500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.104011541325255 " "
y1[1] (numeric) = 1.1040115415864062 " "
absolute error = 2.61151322789032750000000000E-10 " "
relative error = 2.365476383295294400000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10430000000000013 " "
y2[1] (analytic) = 1.1041109984140551 " "
y2[1] (numeric) = 1.1041109984140554 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.011071398111024500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1041109984140551 " "
y1[1] (numeric) = 1.1041109986878404 " "
absolute error = 2.7378521672005720000000000E-10 " "
relative error = 2.479689244227457300000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10440000000000013 " "
y2[1] (analytic) = 1.1042104544617455 " "
y2[1] (numeric) = 1.1042104544617457 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.01089026125249300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1042104544617455 " "
y1[1] (numeric) = 1.1042104547484628 " "
absolute error = 2.86717316555495900000000000E-10 " "
relative error = 2.59658215874489400000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10450000000000013 " "
y2[1] (analytic) = 1.1043099094673312 " "
y2[1] (numeric) = 1.1043099094673314 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.01070915891840100000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1043099094673312 " "
y1[1] (numeric) = 1.104309909767279 " "
absolute error = 2.9994784433995390000000000E-10 " "
relative error = 2.716156413779128000000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10460000000000014 " "
y2[1] (analytic) = 1.1044093634298178 " "
y2[1] (numeric) = 1.104409363429818 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.010528091100720300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1044093634298178 " "
y1[1] (numeric) = 1.1044093637432946 " "
absolute error = 3.13476800073431150000000000E-10 " "
relative error = 2.838411285285628000000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10470000000000014 " "
y2[1] (analytic) = 1.1045088163482106 " "
y2[1] (numeric) = 1.104508816348211 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.020694115582847400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1045088163482106 " "
y1[1] (numeric) = 1.1045088166755148 " "
absolute error = 3.2730418375592760000000000E-10 " "
relative error = 2.963346049496274300000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10480000000000014 " "
y2[1] (analytic) = 1.1046082682215155 " "
y2[1] (numeric) = 1.104608268221516 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.02033211796497260000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1046082682215155 " "
y1[1] (numeric) = 1.1046082685629453 " "
absolute error = 3.4142977334283840000000000E-10 " "
relative error = 3.09095797275318700000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10490000000000015 " "
y2[1] (analytic) = 1.1047077190487378 " "
y2[1] (numeric) = 1.104707719048738 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00998509466588680000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1047077190487378 " "
y1[1] (numeric) = 1.1047077194045913 " "
absolute error = 3.5585356883416350000000000E-10 " "
relative error = 3.22124633238363270000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10500000000000015 " "
y2[1] (analytic) = 1.1048071688288825 " "
y2[1] (numeric) = 1.104807168828883 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01960832966721200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1048071688288825 " "
y1[1] (numeric) = 1.1048071691994585 " "
absolute error = 3.7057601431911280000000000E-10 " "
relative error = 3.35421442559909100000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10510000000000015 " "
y2[1] (analytic) = 1.1049066175609559 " "
y2[1] (numeric) = 1.1049066175609563 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01924653895525230000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1049066175609559 " "
y1[1] (numeric) = 1.1049066179465525 " "
absolute error = 3.8559666570847640000000000E-10 " "
relative error = 3.489857509946569500000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10520000000000015 " "
y2[1] (analytic) = 1.105006065243963 " "
y2[1] (numeric) = 1.1050060652439635 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01888481717986470000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.105006065243963 " "
y1[1] (numeric) = 1.1050060656448786 " "
absolute error = 4.0091552300225430000000000E-10 " "
relative error = 3.62817486358086360000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10530000000000016 " "
y2[1] (analytic) = 1.1051055118769093 " "
y2[1] (numeric) = 1.10510551187691 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.0277847464875400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1051055118769093 " "
y1[1] (numeric) = 1.1051055122934423 " "
absolute error = 4.1653303028965640000000000E-10 " "
relative error = 3.769169783455494400000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10540000000000016 " "
y2[1] (analytic) = 1.1052049574588008 " "
y2[1] (numeric) = 1.1052049574588012 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.018161580374716000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1052049574588008 " "
y1[1] (numeric) = 1.1052049578912493 " "
absolute error = 4.32448521436867850000000000E-10 " "
relative error = 3.91283551994914440000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10550000000000016 " "
y2[1] (analytic) = 1.1053044019886424 " "
y2[1] (numeric) = 1.1053044019886429 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01780006531292100000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1053044019886424 " "
y1[1] (numeric) = 1.105304402437305 " "
absolute error = 4.4866266257770350000000000E-10 " "
relative error = 4.05917737928554570000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10560000000000017 " "
y2[1] (analytic) = 1.1054038454654402 " "
y2[1] (numeric) = 1.1054038454654407 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01743861912362800000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1054038454654402 " "
y1[1] (numeric) = 1.1054038459306152 " "
absolute error = 4.65175009622953440000000000E-10 " "
relative error = 4.208190622198236000000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10570000000000017 " "
y2[1] (analytic) = 1.1055032878881994 " "
y2[1] (numeric) = 1.1055032878881998 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.017077241790833500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1055032878881994 " "
y1[1] (numeric) = 1.1055032883701852 " "
absolute error = 4.8198578461722263000000000E-10 " "
relative error = 4.35987653675767600000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10580000000000017 " "
y2[1] (analytic) = 1.1056027292559258 " "
y2[1] (numeric) = 1.1056027292559263 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01671593329853700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1056027292559258 " "
y1[1] (numeric) = 1.1056027297550206 " "
absolute error = 4.9909476551590615000000000E-10 " "
relative error = 4.51423239387079400000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10590000000000017 " "
y2[1] (analytic) = 1.105702169567625 " "
y2[1] (numeric) = 1.1057021695676255 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01635469363074260000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.105702169567625 " "
y1[1] (numeric) = 1.105702170084127 " "
absolute error = 5.165019523190040000000000E-10 " "
relative error = 4.67125747361947800000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10600000000000018 " "
y2[1] (analytic) = 1.1058016088223024 " "
y2[1] (numeric) = 1.1058016088223028 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.0159935227714600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1058016088223024 " "
y1[1] (numeric) = 1.10580160935651 " "
absolute error = 5.342075670711210000000000E-10 " "
relative error = 4.830953064357188500000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10610000000000018 " "
y2[1] (analytic) = 1.1059010470189636 " "
y2[1] (numeric) = 1.105901047018964 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01563242070470300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1059010470189636 " "
y1[1] (numeric) = 1.1059010475711752 " "
absolute error = 5.5221160977225740000000000E-10 " "
relative error = 4.993318446173676000000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10620000000000018 " "
y2[1] (analytic) = 1.1060004841566144 " "
y2[1] (numeric) = 1.106000484156615 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01527138741448900000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1060004841566144 " "
y1[1] (numeric) = 1.1060004847271283 " "
absolute error = 5.705138583778080000000000E-10 " "
relative error = 5.15835089179780800000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10630000000000019 " "
y2[1] (analytic) = 1.1060999202342605 " "
y2[1] (numeric) = 1.106099920234261 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01491042288484300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1060999202342605 " "
y1[1] (numeric) = 1.1060999208233748 " "
absolute error = 5.8911431288777290000000000E-10 " "
relative error = 5.32604968241028900000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10640000000000019 " "
y2[1] (analytic) = 1.1061993552509073 " "
y2[1] (numeric) = 1.1061993552509077 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01454952709979330000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1061993552509073 " "
y1[1] (numeric) = 1.1061993558589205 " "
absolute error = 6.0801319534675710000000000E-10 " "
relative error = 5.49641610674097800000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10650000000000019 " "
y2[1] (analytic) = 1.1062987892055607 " "
y2[1] (numeric) = 1.106298789205561 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00709435002168620000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1062987892055607 " "
y1[1] (numeric) = 1.106298789832771 " "
absolute error = 6.2721028371015560000000000E-10 " "
relative error = 5.669447438883657000000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1066000000000002 " "
y2[1] (analytic) = 1.106398222097226 " "
y2[1] (numeric) = 1.1063982220972262 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.006913970849809600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.106398222097226 " "
y1[1] (numeric) = 1.1063982227439317 " "
absolute error = 6.4670580002257340000000000E-10 " "
relative error = 5.845144967755953000000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1067000000000002 " "
y2[1] (analytic) = 1.1064976539249092 " "
y2[1] (numeric) = 1.1064976539249094 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.006733626026287500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1064976539249092 " "
y1[1] (numeric) = 1.1064976545914087 " "
absolute error = 6.6649952223940550000000000E-10 " "
relative error = 6.02350596836092800000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1068000000000002 " "
y2[1] (analytic) = 1.1065970846876156 " "
y2[1] (numeric) = 1.106597084687616 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01310663108628900000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1065970846876156 " "
y1[1] (numeric) = 1.1065970853742073 " "
absolute error = 6.8659167240525680000000000E-10 " "
relative error = 6.20453172980368600000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1069000000000002 " "
y2[1] (analytic) = 1.1066965143843515 " "
y2[1] (numeric) = 1.106696514384352 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.012746078784812400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1066965143843515 " "
y1[1] (numeric) = 1.1066965150913333 " "
absolute error = 7.0698180643091750000000000E-10 " "
relative error = 6.38821752162296400000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1070000000000002 " "
y2[1] (analytic) = 1.106795943014122 " "
y2[1] (numeric) = 1.1067959430141225 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01238559513220300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.106795943014122 " "
y1[1] (numeric) = 1.1067959437417925 " "
absolute error = 7.2767036840559740000000000E-10 " "
relative error = 6.57456663984458300000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10710000000000021 " "
y2[1] (analytic) = 1.1068953705759332 " "
y2[1] (numeric) = 1.1068953705759337 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01202518011252300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1068953705759332 " "
y1[1] (numeric) = 1.1068953713245906 " "
absolute error = 7.4865735832929660000000000E-10 " "
relative error = 6.76357836730096300000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10720000000000021 " "
y2[1] (analytic) = 1.1069947970687908 " "
y2[1] (numeric) = 1.1069947970687912 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01166483370983760000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1069947970687908 " "
y1[1] (numeric) = 1.1069947978387331 " "
absolute error = 7.6994233211280520000000000E-10 " "
relative error = 6.95524797543343400000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10730000000000021 " "
y2[1] (analytic) = 1.1070942224917002 " "
y2[1] (numeric) = 1.1070942224917006 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01130455590822050000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1070942224917002 " "
y1[1] (numeric) = 1.107094223283226 " "
absolute error = 7.915257338453330000000000E-10 " "
relative error = 7.14957876000718700000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10740000000000022 " "
y2[1] (analytic) = 1.1071936468436676 " "
y2[1] (numeric) = 1.1071936468436678 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00547217334587300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1071936468436676 " "
y1[1] (numeric) = 1.107193647657075 " "
absolute error = 8.1340734148227510000000000E-10 " "
relative error = 7.34656799920317600000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10750000000000022 " "
y2[1] (analytic) = 1.1072930701236983 " "
y2[1] (numeric) = 1.1072930701236987 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.010584206044497400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1072930701236983 " "
y1[1] (numeric) = 1.1072930709592856 " "
absolute error = 8.3558737706823650000000000E-10 " "
relative error = 7.54621698278027800000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10760000000000022 " "
y2[1] (analytic) = 1.1073924923307985 " "
y2[1] (numeric) = 1.1073924923307987 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00511206697527900000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1073924923307985 " "
y1[1] (numeric) = 1.107392493188864 " "
absolute error = 8.5806539651400730000000000E-10 " "
relative error = 7.74852098471412900000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10770000000000023 " "
y2[1] (analytic) = 1.1074919134639738 " "
y2[1] (numeric) = 1.107491913463974 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.0049320651970098000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1074919134639738 " "
y1[1] (numeric) = 1.1074919143448156 " "
absolute error = 8.8084184390879730000000000E-10 " "
relative error = 7.95348330042186500000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10780000000000023 " "
y2[1] (analytic) = 1.1075913335222298 " "
y2[1] (numeric) = 1.10759133352223 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00475209767948910000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1075913335222298 " "
y1[1] (numeric) = 1.1075913344261463 " "
absolute error = 9.0391649720800160000000000E-10 " "
relative error = 8.16110120989728500000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10790000000000023 " "
y2[1] (analytic) = 1.1076907525045725 " "
y2[1] (numeric) = 1.1076907525045727 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00457216441476700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1076907525045725 " "
y1[1] (numeric) = 1.107690753431862 " "
absolute error = 9.2728957845622520000000000E-10 " "
relative error = 8.3713760032712500000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10800000000000023 " "
y2[1] (analytic) = 1.1077901704100077 " "
y2[1] (numeric) = 1.107790170410008 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00439226539489600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1077901704100077 " "
y1[1] (numeric) = 1.1077901713609686 " "
absolute error = 9.509608656088631000000000E-10 " "
relative error = 8.58430496144319400000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10810000000000024 " "
y2[1] (analytic) = 1.1078895872375412 " "
y2[1] (numeric) = 1.1078895872375414 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.004212400611930200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1078895872375412 " "
y1[1] (numeric) = 1.1078895882124715 " "
absolute error = 9.7493035866591530000000000E-10 " "
relative error = 8.79988737051720100000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10820000000000024 " "
y2[1] (analytic) = 1.1079890029861788 " "
y2[1] (numeric) = 1.107989002986179 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00403257005792800000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1079890029861788 " "
y1[1] (numeric) = 1.1079890039853768 " "
absolute error = 9.9919805762738180000000000E-10 " "
relative error = 9.01812251686983500000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10830000000000024 " "
y2[1] (analytic) = 1.1080884176549264 " "
y2[1] (numeric) = 1.1080884176549266 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00385277372494800000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1080884176549264 " "
y1[1] (numeric) = 1.1080884186786903 " "
absolute error = 1.0237639624932626000000000E-9 " "
relative error = 9.23900968715004200000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10840000000000025 " "
y2[1] (analytic) = 1.1081878312427897 " "
y2[1] (numeric) = 1.10818783124279 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.003673011605053300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1081878312427897 " "
y1[1] (numeric) = 1.1081878322914178 " "
absolute error = 1.0486280732635578000000000E-9 " "
relative error = 9.46254816827903600000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10850000000000025 " "
y2[1] (analytic) = 1.108287243748775 " "
y2[1] (numeric) = 1.1082872437487752 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.003493283690307400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.108287243748775 " "
y1[1] (numeric) = 1.1082872448225654 " "
absolute error = 1.0737903899382673000000000E-9 " "
relative error = 9.68873724745019800000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10860000000000025 " "
y2[1] (analytic) = 1.1083866551718877 " "
y2[1] (numeric) = 1.108386655171888 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00331358997277720000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1083866551718877 " "
y1[1] (numeric) = 1.1083866562711386 " "
absolute error = 1.099250912517391000000000E-9 " "
relative error = 9.91757621212897100000000E-8 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10870000000000025 " "
y2[1] (analytic) = 1.1084860655111337 " "
y2[1] (numeric) = 1.1084860655111342 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.00626786088906560000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1084860655111337 " "
y1[1] (numeric) = 1.1084860666361436 " "
absolute error = 1.125009863045534100000000E-9 " "
relative error = 1.01490663531866860000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10880000000000026 " "
y2[1] (analytic) = 1.1085854747655193 " "
y2[1] (numeric) = 1.1085854747655197 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.00590861019528900000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1085854747655193 " "
y1[1] (numeric) = 1.108585475916586 " "
absolute error = 1.1510667974334865000000000E-9 " "
relative error = 1.03832029521851040000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10890000000000026 " "
y2[1] (analytic) = 1.1086848829340499 " "
y2[1] (numeric) = 1.1086848829340505 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.00832414177256300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1086848829340499 " "
y1[1] (numeric) = 1.108684884111472 " "
absolute error = 1.1774221597704582000000000E-9 " "
relative error = 1.06199893034935250000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10900000000000026 " "
y2[1] (analytic) = 1.1087842900157319 " "
y2[1] (numeric) = 1.1087842900157325 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.00778547074871100000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1087842900157319 " "
y1[1] (numeric) = 1.1087842912198074 " "
absolute error = 1.2040755059672392000000000E-9 " "
relative error = 1.08594206899355990000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10910000000000027 " "
y2[1] (analytic) = 1.108883696009571 " "
y2[1] (numeric) = 1.1088836960095716 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.00724690219761700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.108883696009571 " "
y1[1] (numeric) = 1.108883697240598 " "
absolute error = 1.2310270580684346000000000E-9 " "
relative error = 1.11014984032898010000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10920000000000027 " "
y2[1] (analytic) = 1.108983100914573 " "
y2[1] (numeric) = 1.1089831009145736 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.00670843609552500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.108983100914573 " "
y1[1] (numeric) = 1.10898310217285 " "
absolute error = 1.2582770381186492000000000E-9 " "
relative error = 1.13462237348878820000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10930000000000027 " "
y2[1] (analytic) = 1.109082504729744 " "
y2[1] (numeric) = 1.1090825047297446 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.00617007241868200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.109082504729744 " "
y1[1] (numeric) = 1.1090825060155691 " "
absolute error = 1.2858252240732782000000000E-9 " "
relative error = 1.15935939715017140000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10940000000000027 " "
y2[1] (analytic) = 1.1091819074540898 " "
y2[1] (numeric) = 1.1091819074540905 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.00563181114334800000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1091819074540898 " "
y1[1] (numeric) = 1.1091819087677615 " "
absolute error = 1.3136716159323214000000000E-9 " "
relative error = 1.18436084027695480000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10950000000000028 " "
y2[1] (analytic) = 1.109281309086617 " "
y2[1] (numeric) = 1.1092813090866174 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.00339576816385700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.109281309086617 " "
y1[1] (numeric) = 1.109281310428433 " "
absolute error = 1.341815991651174000000000E-9 " "
relative error = 1.20962643169028620000000E-7 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10960000000000028 " "
y2[1] (analytic) = 1.1093807096263306 " "
y2[1] (numeric) = 1.1093807096263313 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.0045555957022700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.1093807096263306 " "
y1[1] (numeric) = 1.1093807109965894 " "
absolute error = 1.370258795319046000000000E-9 " "
relative error = 1.23515650076571660000000E-7 "%"
h = 1.0000E-4 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y2 , x , 4 ) = y1 - 1.0;"
"diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"
Iterations = 96
"Total Elapsed Time "= 15 Minutes 19 Seconds
"Elapsed Time(since restart) "= 15 Minutes 19 Seconds
"Expected Time Remaining "= 5 Days 11 Hours 22 Minutes 34 Seconds
"Optimized Time Remaining "= 5 Days 11 Hours 19 Minutes 56 Seconds
"Time to Timeout " Unknown
Percent Done = 0.19400000000000556 "%"
(%o55) true
(%o55) diffeq.max