(%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) factorial_1(nnn) := (if nnn <= glob_max_terms then ret : array_fact_1
nnn
else ret : nnn!, ret)
(%o39) factorial_1(nnn) := (if nnn <= glob_max_terms then ret : array_fact_1
nnn
else ret : nnn!, ret)
(%i40) factorial_3(mmm, nnn) := (if (nnn <= glob_max_terms)
mmm!
and (mmm <= glob_max_terms) then ret : array_fact_2 else ret : ----,
mmm, nnn nnn!
ret)
(%o40) factorial_3(mmm, nnn) := (if (nnn <= glob_max_terms)
mmm!
and (mmm <= glob_max_terms) then ret : array_fact_2 else ret : ----,
mmm, nnn nnn!
ret)
(%i41) convfp(mmm) := mmm
(%o41) convfp(mmm) := mmm
(%i42) convfloat(mmm) := mmm
(%o42) convfloat(mmm) := mmm
(%i43) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%o43) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%i44) arcsin(x) := asin(x)
(%o44) arcsin(x) := asin(x)
(%i45) arccos(x) := acos(x)
(%o45) arccos(x) := acos(x)
(%i46) arctan(x) := atan(x)
(%o46) arctan(x) := atan(x)
(%i47) exact_soln_y1(x) := sin(x) + 1.0
(%o47) exact_soln_y1(x) := sin(x) + 1.0
(%i48) exact_soln_y2(x) := sin(x) + 1.0
(%o48) exact_soln_y2(x) := sin(x) + 1.0
(%i49) exact_soln_y2p(x) := cos(x)
(%o49) exact_soln_y2p(x) := cos(x)
(%i50) exact_soln_y2pp(x) := - sin(x)
(%o50) exact_soln_y2pp(x) := - sin(x)
(%i51) exact_soln_y2ppp(x) := - cos(x)
(%o51) exact_soln_y2ppp(x) := - cos(x)
(%i52) mainprog() := (define_variable(glob_iolevel, 5, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(MAX_UNCHANGED, 10,
fixnum), define_variable(glob_warned, false, boolean),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_dump, false, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_h, 0.1, float), define_variable(centuries_in_millinium,
10.0, float), define_variable(hours_in_day, 24.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_log10abserr, 0.0, 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(glob_start, 0, fixnum),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_almost_1, 0.999, float),
define_variable(sec_in_min, 60.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(years_in_century, 100.0, float),
define_variable(days_in_year, 365.0, 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 : 0.001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 1000,"),
omniout_str(ALWAYS, "glob_max_minutes : 15,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_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_norms, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y2, 1 + max_terms),
array(array_y1, 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_type_pole, 1 + max_terms),
array(array_y2_init, 1 + max_terms), array(array_last_rel_error,
1 + max_terms), array(array_1st_rel_error, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_y1_init, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3),
array(array_y2_higher_work, 1 + 5, 1 + max_terms),
array(array_y2_higher_work2, 1 + 5, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_y1_set_initial, 1 + 3,
1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms),
array(array_y2_higher, 1 + 5, 1 + max_terms),
array(array_complex_pole, 1 + 2, 1 + 3),
array(array_y1_higher_work2, 1 + 2, 1 + max_terms),
array(array_y1_higher_work, 1 + 2, 1 + max_terms),
array(array_y2_set_initial, 1 + 3, 1 + max_terms),
array(array_fact_2, 1 + max_terms, 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_norms : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_type_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_y2_init : 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_pole : 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_fact_1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_real_pole : 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), ord : 1,
while ord <= 5 do (term : 1, while term <=
max_terms do (array_y2_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), 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 <= 3 do (term : 1,
while term <= max_terms do (array_y1_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_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 : 0.0, term : 1 + term),
ord, 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, term
ord : 1 + ord), 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_work : 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 <= max_terms do (term : 1, while term <=
max_terms do (array_fact_2 : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_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_const_1D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_const_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_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (temp1 : iiif!, temp2 : jjjf!,
temp1
array_fact_1 : temp1, array_fact_2 : -----, jjjf : 1 + jjjf),
iiif iiif, jjjf temp2
iiif : 1 + iiif), x_start : 0.1, x_end : 5.1,
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 : 0.001,
glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_log10_abserr glob_log10_relerr
glob_abserr : 10.0 , glob_relerr : 10.0 ,
chk_data(), array_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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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,
"2012-06-17T00:57:48-05:00"), 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, " 091 | "), 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 for speeding factorials"),
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))
(%o52) mainprog() := (define_variable(glob_iolevel, 5, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(MAX_UNCHANGED, 10,
fixnum), define_variable(glob_warned, false, boolean),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_dump, false, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_h, 0.1, float), define_variable(centuries_in_millinium,
10.0, float), define_variable(hours_in_day, 24.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_log10abserr, 0.0, 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(glob_start, 0, fixnum),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_almost_1, 0.999, float),
define_variable(sec_in_min, 60.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_warned2, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(years_in_century, 100.0, float),
define_variable(days_in_year, 365.0, 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 : 0.001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 1000,"),
omniout_str(ALWAYS, "glob_max_minutes : 15,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_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_norms, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y2, 1 + max_terms),
array(array_y1, 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_type_pole, 1 + max_terms),
array(array_y2_init, 1 + max_terms), array(array_last_rel_error,
1 + max_terms), array(array_1st_rel_error, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_y1_init, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3),
array(array_y2_higher_work, 1 + 5, 1 + max_terms),
array(array_y2_higher_work2, 1 + 5, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_y1_set_initial, 1 + 3,
1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms),
array(array_y2_higher, 1 + 5, 1 + max_terms),
array(array_complex_pole, 1 + 2, 1 + 3),
array(array_y1_higher_work2, 1 + 2, 1 + max_terms),
array(array_y1_higher_work, 1 + 2, 1 + max_terms),
array(array_y2_set_initial, 1 + 3, 1 + max_terms),
array(array_fact_2, 1 + max_terms, 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_norms : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_type_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_y2_init : 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_pole : 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_fact_1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_real_pole : 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), ord : 1,
while ord <= 5 do (term : 1, while term <=
max_terms do (array_y2_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), 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 <= 3 do (term : 1,
while term <= max_terms do (array_y1_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_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 : 0.0, term : 1 + term),
ord, 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, term
ord : 1 + ord), 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_work : 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 <= max_terms do (term : 1, while term <=
max_terms do (array_fact_2 : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_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_const_1D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_const_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_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (temp1 : iiif!, temp2 : jjjf!,
temp1
array_fact_1 : temp1, array_fact_2 : -----, jjjf : 1 + jjjf),
iiif iiif, jjjf temp2
iiif : 1 + iiif), x_start : 0.1, x_end : 5.1,
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 : 0.001,
glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_log10_abserr glob_log10_relerr
glob_abserr : 10.0 , glob_relerr : 10.0 ,
chk_data(), array_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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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 factorial_1(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,
"2012-06-17T00:57:48-05:00"), 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, " 091 | "), 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 for speeding factorials"),
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))
(%i53) 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 : 0.001 ,"
"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 = 1.000E-3 " "
y1[1] (analytic) = 1.0998334166468282 " "
y1[1] (numeric) = 1.0998334166468282 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
x[1] = 0.1 " "
y2[1] (analytic) = 1.0998334166468282 " "
y2[1] (numeric) = 1.0998334166468282 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.0998334166468282 " "
y1[1] (numeric) = 1.0998334166468282 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.101 " "
y2[1] (analytic) = 1.100828370729568 " "
y2[1] (numeric) = 1.1008283707295623 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 5.2443776719023730000000000000E-13 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.100828370729568 " "
y1[1] (numeric) = 1.1008318740131053 " "
absolute error = 3.503283537265034000000E-6 " "
relative error = 3.182406658853870000E-4 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10200000000000001 " "
y2[1] (analytic) = 1.1018232239839456 " "
y2[1] (numeric) = 1.10182322414602 " "
absolute error = 1.620743539376690000000000E-10 " "
relative error = 1.470965127705735600000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1018232239839456 " "
y1[1] (numeric) = 1.1018303708975024 " "
absolute error = 7.146913556743684000000E-6 " "
relative error = 6.486443016604830000E-4 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10300000000000001 " "
y2[1] (analytic) = 1.1028179754151075 " "
y2[1] (numeric) = 1.1028179767200674 " "
absolute error = 1.3049599179026927000000000E-9 " "
relative error = 1.18329583575340040000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1028179754151075 " "
y1[1] (numeric) = 1.1028289062958572 " "
absolute error = 1.093088074965997700000E-5 " "
relative error = 9.9117723807009270000E-4 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10400000000000001 " "
y2[1] (analytic) = 1.1038126240283028 " "
y2[1] (numeric) = 1.1038126284453693 " "
absolute error = 4.417066490347565400000000E-9 " "
relative error = 4.001645201544920000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1038126240283028 " "
y1[1] (numeric) = 1.103827479203826 " "
absolute error = 1.485517552324289200000E-5 " "
relative error = 1.3458059094332292000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10500000000000001 " "
y2[1] (analytic) = 1.1048071688288825 " "
y2[1] (numeric) = 1.1048071793170064 " "
absolute error = 1.04881239249010600000000E-8 " "
relative error = 9.4931714970845820000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1048071688288825 " "
y1[1] (numeric) = 1.1048260886168855 " "
absolute error = 1.891978800294680200000E-5 " "
relative error = 1.7124968534556262000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10600000000000001 " "
y2[1] (analytic) = 1.1058016088223022 " "
y2[1] (numeric) = 1.1058016293300716 " "
absolute error = 2.050776948259169800000000E-8 " "
relative error = 1.8545613714952744000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1058016088223022 " "
y1[1] (numeric) = 1.1058247335303322 " "
absolute error = 2.31247080300089900000E-5 " "
relative error = 2.0912167106211035000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10700000000000001 " "
y2[1] (analytic) = 1.1067959430141219 " "
y2[1] (numeric) = 1.1067959784796584 " "
absolute error = 3.54655365075728900000000E-8 " "
relative error = 3.2043428358609716000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1067959430141219 " "
y1[1] (numeric) = 1.106823412939285 " "
absolute error = 2.746992516322599400000E-5 " "
relative error = 2.481932223966916000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10800000000000001 " "
y2[1] (analytic) = 1.1077901704100075 " "
y2[1] (numeric) = 1.107790226760861 " "
absolute error = 5.635085353894453000000000E-8 " "
relative error = 5.0867804250409940000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1077901704100075 " "
y1[1] (numeric) = 1.1078221258386856 " "
absolute error = 3.195542867806544500000E-5 " "
relative error = 2.8846102386193160000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10900000000000001 " "
y2[1] (analytic) = 1.1087842900157316 " "
y2[1] (numeric) = 1.1087843741687744 " "
absolute error = 8.41530427564407500000000E-8 " "
relative error = 7.589667667030778000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1087842900157316 " "
y1[1] (numeric) = 1.1088208712232985 " "
absolute error = 3.658120756688809600000E-5 " "
relative error = 3.2992177014312740000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11000000000000001 " "
y2[1] (analytic) = 1.1097783008371749 " "
y2[1] (numeric) = 1.1097784206984942 " "
absolute error = 1.1986131931429611000000E-7 " "
relative error = 1.080047422299366100000E-5 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1097783008371749 " "
y1[1] (numeric) = 1.109819648087714 " "
absolute error = 4.13472505391698800000E-5 " "
relative error = 3.725721660621682000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11100000000000002 " "
y2[1] (analytic) = 1.1107722018803263 " "
y2[1] (numeric) = 1.1107723663451166 " "
absolute error = 1.64464790231022560000000E-7 " "
relative error = 1.480634732779726700000E-5 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1107722018803263 " "
y1[1] (numeric) = 1.1108184554263476 " "
absolute error = 4.625354602127984500000E-5 " "
relative error = 4.164089265376049000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11200000000000002 " "
y2[1] (analytic) = 1.1117659921512852 " "
y2[1] (numeric) = 1.1117662111037383 " "
absolute error = 2.18952453057141840000000E-7 " "
relative error = 1.969411320393649500000E-5 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1117659921512852 " "
y1[1] (numeric) = 1.1118172922334413 " "
absolute error = 5.1300082156036100000E-5 " "
relative error = 4.61428776542891050E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11300000000000002 " "
y2[1] (analytic) = 1.1127596706562612 " "
y2[1] (numeric) = 1.112759954969457 " "
absolute error = 2.84313195653140840000000E-7 " "
relative error = 2.555027856872852400000E-5 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1127596706562612 " "
y1[1] (numeric) = 1.112816157503065 " "
absolute error = 5.64868468038159900000E-5 " "
relative error = 5.076284510787699000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11400000000000002 " "
y2[1] (analytic) = 1.113753236401576 " "
y2[1] (numeric) = 1.1137535979373705 " "
absolute error = 3.6153579441311480000000E-7 " "
relative error = 3.24610319949507230000E-5 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.113753236401576 " "
y1[1] (numeric) = 1.1138150502291175 " "
absolute error = 6.18138275414459300000E-5 " "
relative error = 5.550046951258265000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11500000000000002 " "
y2[1] (analytic) = 1.1147466883936639 " "
y2[1] (numeric) = 1.114747140002578 " "
absolute error = 4.51608914042722630000000E-7 " "
relative error = 4.051224540469238000000E-5 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1147466883936639 " "
y1[1] (numeric) = 1.114813969405327 " "
absolute error = 6.72810116630895300000E-5 " "
relative error = 6.035542636151773000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11600000000000002 " "
y2[1] (analytic) = 1.1157400256390728 " "
y2[1] (numeric) = 1.1157405811601786 " "
absolute error = 5.5552110578283020000000E-7 " "
relative error = 4.97894754169672500000E-5 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1157400256390728 " "
y1[1] (numeric) = 1.1158129140252522 " "
absolute error = 7.28883861793594400000E-5 " "
relative error = 6.5327392138334800000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11700000000000002 " "
y2[1] (analytic) = 1.1167332471444658 " "
y2[1] (numeric) = 1.1167339214052727 " "
absolute error = 6.742608069654210000000E-7 " "
relative error = 6.03779648084745800000E-5 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1167332471444658 " "
y1[1] (numeric) = 1.1168118830822835 " "
absolute error = 7.86359378177614600000E-5 " "
relative error = 7.041604431392804000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11800000000000002 " "
y2[1] (analytic) = 1.1177263519166214 " "
y2[1] (numeric) = 1.117727160732961 " "
absolute error = 8.0881633968132860000000E-7 " "
relative error = 7.23626438881404900000E-5 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1177263519166214 " "
y1[1] (numeric) = 1.1178108755696443 " "
absolute error = 8.45236530229165300000E-5 " "
relative error = 7.56210613429482000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11900000000000002 " "
y2[1] (analytic) = 1.118719338962435 " "
y2[1] (numeric) = 1.1187202991383451 " "
absolute error = 9.6017591011410270000000E-7 " "
relative error = 8.5828131924904890000E-5 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.118719338962435 " "
y1[1] (numeric) = 1.1188098904803914 " "
absolute error = 9.05515179563387600000E-5 " "
relative error = 8.094212265993495000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12000000000000002 " "
y2[1] (analytic) = 1.1197122072889194 " "
y2[1] (numeric) = 1.1197133366165273 " "
absolute error = 1.1293276078738756000000E-6 " "
relative error = 1.00858738568925440000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1197122072889194 " "
y1[1] (numeric) = 1.119808926807416 " "
absolute error = 9.67195184966573900000E-5 " "
relative error = 8.637890867586197000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12100000000000002 " "
y2[1] (analytic) = 1.1207049559032065 " "
y2[1] (numeric) = 1.1207062731626103 " "
absolute error = 1.3172594037769159000000E-6 " "
relative error = 1.17538465127541150000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1207049559032065 " "
y1[1] (numeric) = 1.1208079835434455 " "
absolute error = 1.03027640238950720000E-4 " "
relative error = 9.193110077390346000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12200000000000003 " "
y2[1] (analytic) = 1.1216975838125478 " "
y2[1] (numeric) = 1.1216991087716979 " "
absolute error = 1.524959150067673000000E-6 " "
relative error = 1.35951006053206950000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1216975838125478 " "
y1[1] (numeric) = 1.1218070596810434 " "
absolute error = 1.09475868495634290000E-4 " "
relative error = 9.759838130660475000E-3 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12300000000000003 " "
y2[1] (analytic) = 1.1226900900243153 " "
y2[1] (numeric) = 1.1226918434388942 " "
absolute error = 1.753414578864465000000E-6 " "
relative error = 1.56179750266299180000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1226900900243153 " "
y1[1] (numeric) = 1.122806154212611 " "
absolute error = 1.16064188295794680000E-4 " "
relative error = 1.033804335916788400E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12400000000000003 " "
y2[1] (analytic) = 1.1236824735460031 " "
y2[1] (numeric) = 1.1236844771593042 " "
absolute error = 2.0036133010492563000000E-6 " "
relative error = 1.7830778251141150000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1236824735460031 " "
y1[1] (numeric) = 1.1238052661303883 " "
absolute error = 1.22792584385189580000E-4 " "
relative error = 1.092769419084140300E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12500000000000003 " "
y2[1] (analytic) = 1.1246747333852278 " "
y2[1] (numeric) = 1.1246770099280339 " "
absolute error = 2.2765428060456117000000E-6 " "
relative error = 2.0241788478641332000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1246747333852278 " "
y1[1] (numeric) = 1.1248043944264547 " "
absolute error = 1.2966104122691390000E-4 " "
relative error = 1.152875914946885500E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12600000000000003 " "
y2[1] (analytic) = 1.1256668685497293 " "
y2[1] (numeric) = 1.1256694417401893 " "
absolute error = 2.5731904600423405000000E-6 " "
relative error = 2.2859253762683368000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1256668685497293 " "
y1[1] (numeric) = 1.1258035380927305 " "
absolute error = 1.36669543001177730000E-4 " "
relative error = 1.214120685432077100E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12700000000000003 " "
y2[1] (analytic) = 1.1266588780473727 " "
y2[1] (numeric) = 1.126661772590878 " "
absolute error = 2.8945435053273627000000E-6 " "
relative error = 2.56913921482954440000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1266588780473727 " "
y1[1] (numeric) = 1.1268026961209774 " "
absolute error = 1.43818073604640160000E-4 " "
relative error = 1.276500601973626000E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12800000000000003 " "
y2[1] (analytic) = 1.1276507608861488 " "
y2[1] (numeric) = 1.1276540024752078 " "
absolute error = 3.241589058955441000000E-6 " "
relative error = 2.8746391803150850000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1276507608861488 " "
y1[1] (numeric) = 1.1278018675027999 " "
absolute error = 1.5110661665107550000E-4 " "
relative error = 1.340012545482880000E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12900000000000003 " "
y2[1] (analytic) = 1.1286425160741744 " "
y2[1] (numeric) = 1.1286461313882872 " "
absolute error = 3.6153141127481800000000E-6 " "
relative error = 3.20324111599441240000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1286425160741744 " "
y1[1] (numeric) = 1.1288010512296456 " "
absolute error = 1.58535155471151160000E-4 " "
relative error = 1.404653406311447400E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13000000000000003 " "
y2[1] (analytic) = 1.129634142619695 " "
y2[1] (numeric) = 1.1296381593252256 " "
absolute error = 4.016705530629494000000E-6 " "
relative error = 3.5557579034522570000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.129634142619695 " "
y1[1] (numeric) = 1.1298002462928074 " "
absolute error = 1.66103673112427690000E-4 " "
relative error = 1.470420084216138000E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13100000000000003 " "
y2[1] (analytic) = 1.1306256395310834 " "
y2[1] (numeric) = 1.1306300862811332 " "
absolute error = 4.446750049735826000000E-6 " "
relative error = 3.93299947768748160000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1306256395310834 " "
y1[1] (numeric) = 1.1307994516834232 " "
absolute error = 1.73812152339802850000E-4 " "
relative error = 1.537309488327983000E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13200000000000003 " "
y2[1] (analytic) = 1.1316170058168433 " "
y2[1] (numeric) = 1.1316219122511209 " "
absolute error = 4.90643427752957000000E-6 " "
relative error = 4.33577283860975800000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1316170058168433 " "
y1[1] (numeric) = 1.131798666392478 " "
absolute error = 1.81660575634623460000E-4 " "
relative error = 1.605318537109594600E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13300000000000003 " "
y2[1] (analytic) = 1.1326082404856084 " "
y2[1] (numeric) = 1.1326136372303002 " "
absolute error = 5.396744691799071000000E-6 " "
relative error = 4.76488206503354160000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1326082404856084 " "
y1[1] (numeric) = 1.1327978894108037 " "
absolute error = 1.89648925195351480000E-4 " "
relative error = 1.6744441583264402E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13400000000000004 " "
y2[1] (analytic) = 1.1335993425461441 " "
y2[1] (numeric) = 1.1336052612137835 " "
absolute error = 5.918667639326358000000E-6 " "
relative error = 5.2211283274323470000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1335993425461441 " "
y1[1] (numeric) = 1.1337971197290817 " "
absolute error = 1.97777182937564080000E-4 " "
relative error = 1.744683289012346800E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13500000000000004 " "
y2[1] (analytic) = 1.1345903110073483 " "
y2[1] (numeric) = 1.134596784196684 " "
absolute error = 6.473189335665097000000E-6 " "
relative error = 5.7053099016136170000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1345903110073483 " "
y1[1] (numeric) = 1.1347963563378423 " "
absolute error = 2.06045330493953570000E-4 " "
relative error = 1.816032875435149900E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13600000000000004 " "
y2[1] (analytic) = 1.1355811448782527 " "
y2[1] (numeric) = 1.1355882061741156 " "
absolute error = 7.061295862920147000000E-6 " "
relative error = 6.2182221805709880000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1355811448782527 " "
y1[1] (numeric) = 1.1357955982274666 " "
absolute error = 2.14453349213883370000E-4 " "
relative error = 1.888489873058567200E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13700000000000004 " "
y2[1] (analytic) = 1.1365718431680236 " "
y2[1] (numeric) = 1.136579527141193 " "
absolute error = 7.68397316930347100000E-6 " "
relative error = 6.7606576878462410000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1365718431680236 " "
y1[1] (numeric) = 1.1367948443881872 " "
absolute error = 2.23001220163610010000E-4 " "
relative error = 1.962051246510097800E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13800000000000004 " "
y2[1] (analytic) = 1.1375624048859627 " "
y2[1] (numeric) = 1.1375707470930316 " "
absolute error = 8.342207068912089000000E-6 " "
relative error = 7.3334060910252840000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1375624048859627 " "
y1[1] (numeric) = 1.1377940938100897 " "
absolute error = 2.3168892412694930000E-4 " "
relative error = 2.036713969552953200E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13900000000000004 " "
y2[1] (analytic) = 1.1385528290415083 " "
y2[1] (numeric) = 1.1385618660247478 " "
absolute error = 9.036983239507634000000E-6 " "
relative error = 7.9372542134170680000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1385528290415083 " "
y1[1] (numeric) = 1.1387933454831127 " "
absolute error = 2.40516441604388120000E-4 " "
relative error = 2.112475025044442700E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14000000000000004 " "
y2[1] (analytic) = 1.1395431146442365 " "
y2[1] (numeric) = 1.1395528839314586 " "
absolute error = 9.769287222072265000000E-6 " "
relative error = 8.5729860472389590000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1395431146442365 " "
y1[1] (numeric) = 1.1397925983970498 " "
absolute error = 2.4948375281330648000E-4 " "
relative error = 2.189331404904279500E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14100000000000004 " "
y2[1] (analytic) = 1.1405332607038616 " "
y2[1] (numeric) = 1.1405438008082818 " "
absolute error = 1.054010442014252600000E-5 " "
relative error = 9.2413827665471780000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1405332607038616 " "
y1[1] (numeric) = 1.14079185154155 " "
absolute error = 2.5859083768842160000E-4 " "
relative error = 2.267280110084965400E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14200000000000004 " "
y2[1] (analytic) = 1.1415232662302377 " "
y2[1] (numeric) = 1.141534616650336 " "
absolute error = 1.135042009825504300000E-5 " "
relative error = 9.9432227393302530000E-4 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1415232662302377 " "
y1[1] (numeric) = 1.141791103906119 " "
absolute error = 2.6783767588134390000E-4 " "
relative error = 2.34631815053450500E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14300000000000004 " "
y2[1] (analytic) = 1.1425131302333595 " "
y2[1] (numeric) = 1.1425253314527408 " "
absolute error = 1.220121938128038200000E-5 " "
relative error = 1.067928154032529000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1425131302333595 " "
y1[1] (numeric) = 1.1427903544801201 " "
absolute error = 2.7722424676057680000E-4 " "
relative error = 2.42644254516316520E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14400000000000004 " "
y2[1] (analytic) = 1.1435028517233627 " "
y2[1] (numeric) = 1.1435159452106165 " "
absolute error = 1.309348725375692000000E-5 " "
relative error = 1.1450331963775903000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1435028517233627 " "
y1[1] (numeric) = 1.1437896022527752 " "
absolute error = 2.8675052941240510000E-4 " "
relative error = 2.507650321818139500E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14500000000000005 " "
y2[1] (analytic) = 1.1444924297105263 " "
y2[1] (numeric) = 1.144506457919084 " "
absolute error = 1.402820855767039600000E-5 " "
relative error = 1.2257144034774013000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1444924297105263 " "
y1[1] (numeric) = 1.1447888462131655 " "
absolute error = 2.96416502639118560000E-4 " "
relative error = 2.589938517235020000E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14600000000000005 " "
y2[1] (analytic) = 1.1454818632052723 " "
y2[1] (numeric) = 1.1454968695732652 " "
absolute error = 1.500636799289800600000E-5 " "
relative error = 1.3100485022877080000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1454818632052723 " "
y1[1] (numeric) = 1.1457880853502331 " "
absolute error = 3.06222144960788260000E-4 " "
relative error = 2.673304177020503000E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14700000000000005 " "
y2[1] (analytic) = 1.1464711512181671 " "
y2[1] (numeric) = 1.146487180168283 " "
absolute error = 1.602895011587612800000E-5 " "
relative error = 1.3981119454113425000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1464711512181671 " "
y1[1] (numeric) = 1.146787318652782 " "
absolute error = 3.16167434614822440000E-4 " "
relative error = 2.757744355615779000E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14800000000000005 " "
y2[1] (analytic) = 1.1474602927599231 " "
y2[1] (numeric) = 1.1474773896992607 " "
absolute error = 1.709693933760192400000E-5 " "
relative error = 1.4899809122352808000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1474602927599231 " "
y1[1] (numeric) = 1.147786545109478 " "
absolute error = 3.2625234955485640000E-4 " "
relative error = 2.843256116254267400E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14900000000000005 " "
y2[1] (analytic) = 1.1484492868413985 " "
y2[1] (numeric) = 1.1484674981613228 " "
absolute error = 1.821131992429947400000E-5 " "
relative error = 1.5857313102946327000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1484492868413985 " "
y1[1] (numeric) = 1.1487857637088512 " "
absolute error = 3.36476867452750740000E-4 " "
relative error = 2.929836530946607000E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15000000000000005 " "
y2[1] (analytic) = 1.1494381324735992 " "
y2[1] (numeric) = 1.1494575055495946 " "
absolute error = 1.937307599542137400000E-5 " "
relative error = 1.68543877639855000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1494381324735992 " "
y1[1] (numeric) = 1.149784973439296 " "
absolute error = 3.4684096569681520000E-4 " "
relative error = 3.017482680432838600E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15100000000000005 " "
y2[1] (analytic) = 1.1504268286676802 " "
y2[1] (numeric) = 1.150447411859202 " "
absolute error = 2.05831915218723800000E-5 " "
relative error = 1.789178677770403000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1504268286676802 " "
y1[1] (numeric) = 1.1507841732890727 " "
absolute error = 3.5734462139247470000E-4 " "
relative error = 3.106191654156038600E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15200000000000005 " "
y2[1] (analytic) = 1.151415374434945 " "
y2[1] (numeric) = 1.1514372170852722 " "
absolute error = 2.184265032734167300000E-5 " "
relative error = 1.8970261134528377000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.151415374434945 " "
y1[1] (numeric) = 1.1517833622463078 " "
absolute error = 3.67987811362935350000E-4 " "
relative error = 3.195960550236049400E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15300000000000005 " "
y2[1] (analytic) = 1.1524037687868478 " "
y2[1] (numeric) = 1.1524269212229328 " "
absolute error = 2.315243608497219400000E-5 " "
relative error = 2.0090559153017265000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1524037687868478 " "
y1[1] (numeric) = 1.1527825392989959 " "
absolute error = 3.78770512148074450000E-4 " "
relative error = 3.286786475427893600E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15400000000000005 " "
y2[1] (analytic) = 1.1533920107349946 " "
y2[1] (numeric) = 1.1534165242673124 " "
absolute error = 2.45135323178047320000E-5 " "
relative error = 2.1253426493030395000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1533920107349946 " "
y1[1] (numeric) = 1.1537817034349998 " "
absolute error = 3.8969270000510650000E-4 " "
relative error = 3.378666545095767600E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15500000000000005 " "
y2[1] (analytic) = 1.1543800992911435 " "
y2[1] (numeric) = 1.1544060262135407 " "
absolute error = 2.592692239722360600000E-5 " "
relative error = 2.2459606167105828000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1543800992911435 " "
y1[1] (numeric) = 1.154780853642052 " "
absolute error = 4.00754350908583130000E-4 " "
relative error = 3.47159788318136800E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15600000000000006 " "
y2[1] (analytic) = 1.1553680334672058 " "
y2[1] (numeric) = 1.155395427056748 " "
absolute error = 2.739358954206849700000E-5 " "
relative error = 2.3709838552362925000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1553680334672058 " "
y1[1] (numeric) = 1.155779988907756 " "
absolute error = 4.1195544055017130000E-4 " "
relative error = 3.56557762217041900E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15700000000000006 " "
y2[1] (analytic) = 1.1563558122752478 " "
y2[1] (numeric) = 1.1563847267920653 " "
absolute error = 2.891451681752421600000E-5 " "
relative error = 2.5004861402159567000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1563558122752478 " "
y1[1] (numeric) = 1.1567791082195866 " "
absolute error = 4.2329594433887510000E-4 " "
relative error = 3.66060290306317700E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15800000000000006 " "
y2[1] (analytic) = 1.1573434347274905 " "
y2[1] (numeric) = 1.1573739254146251 " "
absolute error = 3.04906871346766200000E-5 " "
relative error = 2.634540985827253000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1573434347274905 " "
y1[1] (numeric) = 1.1577782105648915 " "
absolute error = 4.34775837401035760000E-4 " "
relative error = 3.7566708753431400E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15900000000000006 " "
y2[1] (analytic) = 1.1583308998363115 " "
y2[1] (numeric) = 1.1583630229195603 " "
absolute error = 3.21230832487362500000E-5 " "
relative error = 2.7732216461872594000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1583308998363115 " "
y1[1] (numeric) = 1.1587772949308917 " "
absolute error = 4.46395094580109840000E-4 " "
relative error = 3.85377869694395400E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16000000000000006 " "
y2[1] (analytic) = 1.159318206614246 " "
y2[1] (numeric) = 1.1593520193020048 " "
absolute error = 3.381268775881629600000E-5 " "
relative error = 2.9166011165791345000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.159318206614246 " "
y1[1] (numeric) = 1.1597763603046831 " "
absolute error = 4.58153690437113070000E-4 " "
relative error = 3.951923534222215000E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16100000000000006 " "
y2[1] (analytic) = 1.1603053540739872 " "
y2[1] (numeric) = 1.1603409145570935 " "
absolute error = 3.55604831063782700000E-5 " "
relative error = 3.06475213455843000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1603053540739872 " "
y1[1] (numeric) = 1.1607754056732376 " "
absolute error = 4.7005159925039840000E-4 " "
relative error = 4.05110256192462100E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16200000000000006 " "
y2[1] (analytic) = 1.1612923412283875 " "
y2[1] (numeric) = 1.1613297086799619 " "
absolute error = 3.736745157434384600000E-5 " "
relative error = 3.2177471811118160000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1612923412283875 " "
y1[1] (numeric) = 1.161774430023403 " "
absolute error = 4.820887950154340000E-4 " "
relative error = 4.151312963155271400E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16300000000000006 " "
y2[1] (analytic) = 1.16227916709046 " "
y2[1] (numeric) = 1.1623184016657468 " "
absolute error = 3.9234575286872797000E-5 " "
relative error = 3.375658481867909000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.16227916709046 " "
y1[1] (numeric) = 1.1627734323419054 " "
absolute error = 4.9426525144546930000E-4 " "
relative error = 4.25255192935072800E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16400000000000006 " "
y2[1] (analytic) = 1.163265830673379 " "
y2[1] (numeric) = 1.1633069935095857 " "
absolute error = 4.11628362066984700000E-5 " "
relative error = 3.5385580080926615000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.163265830673379 " "
y1[1] (numeric) = 1.1637724116153496 " "
absolute error = 5.0658094197064680000E-4 " "
relative error = 4.354816660241818000E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16500000000000006 " "
y2[1] (analytic) = 1.164252330990481 " "
y2[1] (numeric) = 1.1642954842066169 " "
absolute error = 4.315321613579392600000E-5 " "
relative error = 3.706517477966445000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.164252330990481 " "
y1[1] (numeric) = 1.1647713668302198 " "
absolute error = 5.1903583973866850000E-4 " "
relative error = 4.45810436382894500E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16600000000000006 " "
y2[1] (analytic) = 1.1652386670552657 " "
y2[1] (numeric) = 1.16528387375198 " "
absolute error = 4.520669671426169600000E-5 " "
relative error = 3.879608357702878000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1652386670552657 " "
y1[1] (numeric) = 1.165770296972881 " "
absolute error = 5.3162991761523950000E-4 " "
relative error = 4.5624122563555900E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16700000000000007 " "
y2[1] (analytic) = 1.166224837881397 " "
y2[1] (numeric) = 1.1662721621408152 " "
absolute error = 4.73242594181133570000E-5 " "
relative error = 4.057901862567443000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.166224837881397 " "
y1[1] (numeric) = 1.1667692010295798 " "
absolute error = 5.443631481827360000E-4 " "
relative error = 4.667737562266674500E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16800000000000007 " "
y2[1] (analytic) = 1.1672108424827043 " "
y2[1] (numeric) = 1.1672603493682636 " "
absolute error = 4.95068855592695200000E-5 " "
relative error = 4.241468958081848000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1672108424827043 " "
y1[1] (numeric) = 1.1677680779864459 " "
absolute error = 5.5723550374153770000E-4 " "
relative error = 4.77407751418994200E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16900000000000007 " "
y2[1] (analytic) = 1.168196679873183 " "
y2[1] (numeric) = 1.1682484354294675 " "
absolute error = 5.17555562844496100000E-5 " "
relative error = 4.430380361127895000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.168196679873183 " "
y1[1] (numeric) = 1.1687669268294922 " "
absolute error = 5.7024695630913950000E-4 " "
relative error = 4.88142935289838600E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17000000000000007 " "
y2[1] (analytic) = 1.1691823490669961 " "
y2[1] (numeric) = 1.1692364203195702 " "
absolute error = 5.407125257406165000000E-5 " "
relative error = 4.624706541046427000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1691823490669961 " "
y1[1] (numeric) = 1.169765746544617 " "
absolute error = 5.8339747762081730000E-4 " "
relative error = 4.989790327286130000E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17100000000000007 " "
y2[1] (analytic) = 1.170167849078474 " "
y2[1] (numeric) = 1.1702243040337155 " "
absolute error = 5.6454955241536100000E-5 " "
relative error = 4.824517720769314600E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.170167849078474 " "
y1[1] (numeric) = 1.1707645361176038 " "
absolute error = 5.9668703912985070000E-4 " "
relative error = 5.09915769434061500E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17200000000000007 " "
y2[1] (analytic) = 1.171153178922117 " "
y2[1] (numeric) = 1.1712120865670483 " "
absolute error = 5.890764493132750000000E-5 " "
relative error = 5.029883877832595000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.171153178922117 " "
y1[1] (numeric) = 1.171763294534123 " "
absolute error = 6.1011561200596810000E-4 " "
relative error = 5.20952871909970300E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17300000000000007 " "
y2[1] (analytic) = 1.1721383376125956 " "
y2[1] (numeric) = 1.1721997679147147 " "
absolute error = 6.14303021191364700000E-5 " "
relative error = 5.240874745574601000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1721383376125956 " "
y1[1] (numeric) = 1.172762020779733 " "
absolute error = 6.2368316713734550000E-4 " "
relative error = 5.32090067463930700E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17400000000000007 " "
y2[1] (analytic) = 1.1731233241647505 " "
y2[1] (numeric) = 1.1731873480718615 " "
absolute error = 6.40239071110215700000E-5 " "
relative error = 5.457559814234008000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1731233241647505 " "
y1[1] (numeric) = 1.1737607138398807 " "
absolute error = 6.3738967513016220000E-4 " "
relative error = 5.43327084204020800E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17500000000000007 " "
y2[1] (analytic) = 1.174108137593596 " "
y2[1] (numeric) = 1.174174827033637 " "
absolute error = 6.66894400409567800000E-5 " "
relative error = 5.680008331910614000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.174108137593596 " "
y1[1] (numeric) = 1.1747593726999028 " "
absolute error = 6.5123510630682450000E-4 " "
relative error = 5.546636510343667000E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17600000000000007 " "
y2[1] (analytic) = 1.1750927769143182 " "
y2[1] (numeric) = 1.1751622047951895 " "
absolute error = 6.9427880871275600000E-5 " "
relative error = 5.908289305767551000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1750927769143182 " "
y1[1] (numeric) = 1.1757579963450273 " "
absolute error = 6.6521943070907420000E-4 " "
relative error = 5.660994976548805000E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17700000000000007 " "
y2[1] (analytic) = 1.1760772411422784 " "
y2[1] (numeric) = 1.1761494813516693 " "
absolute error = 7.2240209390894700000E-5 " "
relative error = 6.142471503039254000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1760772411422784 " "
y1[1] (numeric) = 1.1767565837603733 " "
absolute error = 6.7934261809488030000E-4 " "
relative error = 5.77634354555710100E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17800000000000007 " "
y2[1] (analytic) = 1.1770615292930118 " "
y2[1] (numeric) = 1.1771366566982269 " "
absolute error = 7.51274052150918700000E-5 " "
relative error = 6.382623452167048000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1770615292930118 " "
y1[1] (numeric) = 1.177755133930953 " "
absolute error = 6.9360463794132520000E-4 " "
relative error = 5.89267953016806800E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17900000000000008 " "
y2[1] (analytic) = 1.1780456403822308 " "
y2[1] (numeric) = 1.1781237308300143 " "
absolute error = 7.8090447783507600000E-5 " "
relative error = 6.628813443778819000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1780456403822308 " "
y1[1] (numeric) = 1.1787536458416727 " "
absolute error = 7.0800545944194050000E-4 " "
relative error = 6.01000025102779400E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18000000000000008 " "
y2[1] (analytic) = 1.1790295734258243 " "
y2[1] (numeric) = 1.1791107037421842 " "
absolute error = 8.11303163599230700000E-5 " "
relative error = 6.88110953181508000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1790295734258243 " "
y1[1] (numeric) = 1.1797521184773332 " "
absolute error = 7.2254505150892710000E-4 " "
relative error = 6.12830303661915900E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18100000000000008 " "
y2[1] (analytic) = 1.1800133274398592 " "
y2[1] (numeric) = 1.1800975754298904 " "
absolute error = 8.42479900311499100000E-5 " "
relative error = 7.1395795345746820000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1800133274398592 " "
y1[1] (numeric) = 1.1807505508226313 " "
absolute error = 7.3722338277204540000E-4 " "
relative error = 6.24758522322383500E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18200000000000008 " "
y2[1] (analytic) = 1.1809969014405817 " "
y2[1] (numeric) = 1.1810843458882878 " "
absolute error = 8.74444477061420100000E-5 " "
relative error = 7.404291035774705000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1809969014405817 " "
y1[1] (numeric) = 1.1817489418621605 " "
absolute error = 7.5204042157883680000E-4 " "
relative error = 6.36784415489572300E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18300000000000008 " "
y2[1] (analytic) = 1.1819802944444178 " "
y2[1] (numeric) = 1.1820710151125322 " "
absolute error = 9.07206681144412400000E-5 " "
relative error = 7.6753113855492750000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1819802944444178 " "
y1[1] (numeric) = 1.1827472905804124 " "
absolute error = 7.6699613599462420000E-4 " "
relative error = 6.4890771834326210E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18400000000000008 " "
y2[1] (analytic) = 1.1829635054679746 " "
y2[1] (numeric) = 1.1830575830977803 " "
absolute error = 9.40776298057333100000E-5 " "
relative error = 7.952707701537813000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1829635054679746 " "
y1[1] (numeric) = 1.1837455959617775 " "
absolute error = 7.820904938029560000E-4 " "
relative error = 6.61128166835176300E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18500000000000008 " "
y2[1] (analytic) = 1.1839465335280412 " "
y2[1] (numeric) = 1.18404404983919 " "
absolute error = 9.7516311148737600000E-5 " "
relative error = 8.236546869912176000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1839465335280412 " "
y1[1] (numeric) = 1.1847438569905462 " "
absolute error = 7.9732346250493970000E-4 " "
relative error = 6.7344549768560590E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18600000000000008 " "
y2[1] (analytic) = 1.1849293776415897 " "
y2[1] (numeric) = 1.1850304153319202 " "
absolute error = 1.010376903305410000E-4 " "
relative error = 8.526895546436715000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1849293776415897 " "
y1[1] (numeric) = 1.1857420726509096 " "
absolute error = 8.1269500931990810000E-4 " "
relative error = 6.85859448381173600E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18700000000000008 " "
y2[1] (analytic) = 1.1859120368257758 " "
y2[1] (numeric) = 1.1860166795711307 " "
absolute error = 1.04642745354821540000E-4 " "
relative error = 8.823820157430005000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1859120368257758 " "
y1[1] (numeric) = 1.1867402419269608 " "
absolute error = 8.2820510118497560000E-4 " "
relative error = 6.98369757171668300E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18800000000000008 " "
y2[1] (analytic) = 1.186894510097941 " "
y2[1] (numeric) = 1.1870028425519825 " "
absolute error = 1.08332454041626390000E-4 " "
relative error = 9.1273869008532990E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.186894510097941 " "
y1[1] (numeric) = 1.1877383638026962 " "
absolute error = 8.4385370475525970000E-4 " "
relative error = 7.10976163067454000E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18900000000000008 " "
y2[1] (analytic) = 1.1878767964756112 " "
y2[1] (numeric) = 1.1879889042696374 " "
absolute error = 1.12107794026261590000E-4 " "
relative error = 9.437661747319375000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1878767964756112 " "
y1[1] (numeric) = 1.1887364372620157 " "
absolute error = 8.5964078640454740000E-4 " "
relative error = 7.23678405837264800E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.19000000000000009 " "
y2[1] (analytic) = 1.1888588949765007 " "
y2[1] (numeric) = 1.1889748647192586 " "
absolute error = 1.15969742757959790000E-4 " "
relative error = 9.754710441078214000E-3 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1888588949765007 " "
y1[1] (numeric) = 1.1897344612887246 " "
absolute error = 8.7556631222396320000E-4 " "
relative error = 7.36476226004323200E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1910000000000001 " "
y2[1] (analytic) = 1.189840804618511 " "
y2[1] (numeric) = 1.1899607238960102 " "
absolute error = 1.19919277499214160000E-4 " "
relative error = 1.007859850105434200E-2 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.189840804618511 " "
y1[1] (numeric) = 1.1907324348665338 " "
absolute error = 8.9163024802285660000E-4 " "
relative error = 7.49369364844343900E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1920000000000001 " "
y2[1] (analytic) = 1.1908225244197324 " "
y2[1] (numeric) = 1.190946481795057 " "
absolute error = 1.2395737532466810000E-4 " "
relative error = 1.040939122184226800E-2 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1908225244197324 " "
y1[1] (numeric) = 1.1917303569790614 " "
absolute error = 9.0783255932902480000E-4 " "
relative error = 7.6235756438298500E-2 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1930000000000001 " "
y2[1] (analytic) = 1.1918040533984455 " "
y2[1] (numeric) = 1.1919321384115653 " "
absolute error = 1.28085013119783040000E-4 " "
relative error = 1.074715367467889300E-2 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.1918040533984455 " "
y1[1] (numeric) = 1.1927282266098334 " "
absolute error = 9.2417321138782430000E-4 " "
relative error = 7.7544056739237600E-2 "%"
h = 1.000E-3 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y2 , x , 4 ) = y1 - 1.0;"
"diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"
Iterations = 93
"Total Elapsed Time "= 15 Minutes 31 Seconds
"Elapsed Time(since restart) "= 15 Minutes 30 Seconds
"Expected Time Remaining "= 13 Hours 30 Minutes 21 Seconds
"Optimized Time Remaining "= 13 Hours 29 Minutes 46 Seconds
"Time to Timeout " Unknown
Percent Done = 1.880000000000002 "%"
(%o53) true
(%o53) diffeq.max