(%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_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
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_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
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_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
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_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
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_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), 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 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_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), 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 glob_look_poles
and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float)
! 1! 1
array_pole
1
then (sz2 : -----------, if sz2 < hnew
10.0
then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2)
1
(%i5) prog_report(x_start, x_end) := (clock_sec1 : elapsed_time_seconds(),
total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), percent_done :
comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o5) prog_report(x_start, x_end) := (clock_sec1 : elapsed_time_seconds(),
total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), percent_done :
comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((!array_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)
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_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)
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 - 1 + glob_max_terms,
2, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y1_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_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,
1, 1
array_complex_pole : glob_large_float)
1, 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 :
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_y2_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_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,
2, 1
array_complex_pole : glob_large_float)
2, 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 :
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 - 1 + n,
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)
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_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)
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 - 1 + glob_max_terms,
2, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y1_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_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,
1, 1
array_complex_pole : glob_large_float)
1, 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 :
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_y2_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_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,
2, 1
array_complex_pole : glob_large_float)
2, 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 :
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_y1 ! > array_norms
! iii! iii
then array_norms : !array_y1 !, iii : 1 + iii), iii : 1,
iii ! iii!
while iii <= glob_max_terms do (if !array_y2 ! > array_norms
! iii! iii
then array_norms : !array_y2 !, 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_y1 ! > array_norms
! iii! iii
then array_norms : !array_y1 !, iii : 1 + iii), iii : 1,
iii ! iii!
while iii <= glob_max_terms do (if !array_y2 ! > array_norms
! iii! iii
then array_norms : !array_y2 !, iii : 1 + iii))
iii ! iii!
(%i8) atomall() := (array_tmp1 : array_m1 array_y2 ,
1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
array_tmp3 : array_const_1D0 + array_tmp2 ,
1 1 1
if not array_y1_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp3 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_tmp5 : array_y1 - array_const_1D0 ,
1 1 1
if not array_y2_set_initial then (if 1 <= glob_max_terms
2, 2
1
then (temporary : array_tmp5 glob_h factorial_3(0, 1),
1
array_y2 : temporary, array_y2_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : ats(2, array_m1, array_y2, 1),
2
array_tmp2 : array_tmp1 + array_const_0D0 ,
2 2 2
array_tmp3 : array_const_1D0 + array_tmp2 ,
2 2 2
if not array_y1_set_initial then (if 2 <= glob_max_terms
1, 3
1
then (temporary : array_tmp3 glob_h factorial_3(1, 2),
2
array_y1 : temporary, array_y1_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp5 : array_y1 - array_const_1D0 ,
2 2 2
if not array_y2_set_initial then (if 2 <= glob_max_terms
2, 3
1
then (temporary : array_tmp5 glob_h factorial_3(1, 2),
2
array_y2 : temporary, array_y2_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1 : ats(3, array_m1, array_y2, 1),
3
array_tmp2 : array_tmp1 + array_const_0D0 ,
3 3 3
array_tmp3 : array_const_1D0 + array_tmp2 ,
3 3 3
if not array_y1_set_initial then (if 3 <= glob_max_terms
1, 4
1
then (temporary : array_tmp3 glob_h factorial_3(2, 3),
3
array_y1 : temporary, array_y1_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp5 : array_y1 - array_const_1D0 ,
3 3 3
if not array_y2_set_initial then (if 3 <= glob_max_terms
2, 4
1
then (temporary : array_tmp5 glob_h factorial_3(2, 3),
3
array_y2 : temporary, array_y2_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp1 : ats(4, array_m1, array_y2, 1),
4
array_tmp2 : array_tmp1 + array_const_0D0 ,
4 4 4
array_tmp3 : array_const_1D0 + array_tmp2 ,
4 4 4
if not array_y1_set_initial then (if 4 <= glob_max_terms
1, 5
1
then (temporary : array_tmp3 glob_h factorial_3(3, 4),
4
array_y1 : temporary, array_y1_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp5 : array_y1 - array_const_1D0 ,
4 4 4
if not array_y2_set_initial then (if 4 <= glob_max_terms
2, 5
1
then (temporary : array_tmp5 glob_h factorial_3(3, 4),
4
array_y2 : temporary, array_y2_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp1 : ats(5, array_m1, array_y2, 1),
5
array_tmp2 : array_tmp1 + array_const_0D0 ,
5 5 5
array_tmp3 : array_const_1D0 + array_tmp2 ,
5 5 5
if not array_y1_set_initial then (if 5 <= glob_max_terms
1, 6
1
then (temporary : array_tmp3 glob_h factorial_3(4, 5),
5
array_y1 : temporary, array_y1_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 6,
glob_h 2, 5
array_tmp5 : array_y1 - array_const_1D0 ,
5 5 5
if not array_y2_set_initial then (if 5 <= glob_max_terms
2, 6
1
then (temporary : array_tmp5 glob_h factorial_3(4, 5),
5
array_y2 : temporary, array_y2_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 :
kkk
ats(kkk, array_m1, array_y2, 1), array_tmp2 :
kkk
array_tmp1 + array_const_0D0 , array_tmp3 :
kkk kkk kkk
array_const_1D0 + array_tmp2 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y1_set_initial
1, order_d + kkk
order_d
array_tmp3 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))), array_tmp5 :
kkk
array_y1 - array_const_1D0 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y2_set_initial
2, order_d + kkk
order_d
array_tmp5 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))), kkk : 1 + kkk))
(%o8) atomall() := (array_tmp1 : array_m1 array_y2 ,
1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
array_tmp3 : array_const_1D0 + array_tmp2 ,
1 1 1
if not array_y1_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp3 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_tmp5 : array_y1 - array_const_1D0 ,
1 1 1
if not array_y2_set_initial then (if 1 <= glob_max_terms
2, 2
1
then (temporary : array_tmp5 glob_h factorial_3(0, 1),
1
array_y2 : temporary, array_y2_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : ats(2, array_m1, array_y2, 1),
2
array_tmp2 : array_tmp1 + array_const_0D0 ,
2 2 2
array_tmp3 : array_const_1D0 + array_tmp2 ,
2 2 2
if not array_y1_set_initial then (if 2 <= glob_max_terms
1, 3
1
then (temporary : array_tmp3 glob_h factorial_3(1, 2),
2
array_y1 : temporary, array_y1_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp5 : array_y1 - array_const_1D0 ,
2 2 2
if not array_y2_set_initial then (if 2 <= glob_max_terms
2, 3
1
then (temporary : array_tmp5 glob_h factorial_3(1, 2),
2
array_y2 : temporary, array_y2_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp1 : ats(3, array_m1, array_y2, 1),
3
array_tmp2 : array_tmp1 + array_const_0D0 ,
3 3 3
array_tmp3 : array_const_1D0 + array_tmp2 ,
3 3 3
if not array_y1_set_initial then (if 3 <= glob_max_terms
1, 4
1
then (temporary : array_tmp3 glob_h factorial_3(2, 3),
3
array_y1 : temporary, array_y1_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp5 : array_y1 - array_const_1D0 ,
3 3 3
if not array_y2_set_initial then (if 3 <= glob_max_terms
2, 4
1
then (temporary : array_tmp5 glob_h factorial_3(2, 3),
3
array_y2 : temporary, array_y2_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp1 : ats(4, array_m1, array_y2, 1),
4
array_tmp2 : array_tmp1 + array_const_0D0 ,
4 4 4
array_tmp3 : array_const_1D0 + array_tmp2 ,
4 4 4
if not array_y1_set_initial then (if 4 <= glob_max_terms
1, 5
1
then (temporary : array_tmp3 glob_h factorial_3(3, 4),
4
array_y1 : temporary, array_y1_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp5 : array_y1 - array_const_1D0 ,
4 4 4
if not array_y2_set_initial then (if 4 <= glob_max_terms
2, 5
1
then (temporary : array_tmp5 glob_h factorial_3(3, 4),
4
array_y2 : temporary, array_y2_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp1 : ats(5, array_m1, array_y2, 1),
5
array_tmp2 : array_tmp1 + array_const_0D0 ,
5 5 5
array_tmp3 : array_const_1D0 + array_tmp2 ,
5 5 5
if not array_y1_set_initial then (if 5 <= glob_max_terms
1, 6
1
then (temporary : array_tmp3 glob_h factorial_3(4, 5),
5
array_y1 : temporary, array_y1_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 6,
glob_h 2, 5
array_tmp5 : array_y1 - array_const_1D0 ,
5 5 5
if not array_y2_set_initial then (if 5 <= glob_max_terms
2, 6
1
then (temporary : array_tmp5 glob_h factorial_3(4, 5),
5
array_y2 : temporary, array_y2_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 :
kkk
ats(kkk, array_m1, array_y2, 1), array_tmp2 :
kkk
array_tmp1 + array_const_0D0 , array_tmp3 :
kkk kkk kkk
array_const_1D0 + array_tmp2 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y1_set_initial
1, order_d + kkk
order_d
array_tmp3 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))), array_tmp5 :
kkk
array_y1 - array_const_1D0 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y2_set_initial
2, order_d + kkk
order_d
array_tmp5 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))), 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 (if array_fact_1 = 0 then (ret : nnn!, array_fact_1 : ret)
nnn nnn
else ret : array_fact_1 ) else ret : nnn!, ret)
nnn
(%o39) factorial_1(nnn) := (if nnn <= glob_max_terms
then (if array_fact_1 = 0 then (ret : nnn!, array_fact_1 : ret)
nnn nnn
else ret : array_fact_1 ) else ret : nnn!, ret)
nnn
(%i40) factorial_3(mmm, nnn) := (if (nnn <= glob_max_terms)
and (mmm <= glob_max_terms) then (if array_fact_2 = 0
mmm, nnn
factorial_1(mmm)
then (ret : ----------------, array_fact_2 : ret)
factorial_1(nnn) mmm, nnn
mmm!
else ret : array_fact_2 ) else ret : ----, ret)
mmm, nnn nnn!
(%o40) factorial_3(mmm, nnn) := (if (nnn <= glob_max_terms)
and (mmm <= glob_max_terms) then (if array_fact_2 = 0
mmm, nnn
factorial_1(mmm)
then (ret : ----------------, array_fact_2 : ret)
factorial_1(nnn) mmm, nnn
mmm!
else ret : array_fact_2 ) else ret : ----, ret)
mmm, nnn nnn!
(%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) := cos(x) + 1.0
(%o47) exact_soln_y1(x) := cos(x) + 1.0
(%i48) exact_soln_y2(x) := sin(x) + 1.0
(%o48) exact_soln_y2(x) := sin(x) + 1.0
(%i49) mainprog() := (define_variable(INFO, 2, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(glob_max_rel_trunc_err,
1.0E-11, float), define_variable(glob_initial_pass, true, boolean),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(hours_in_day, 24.0, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_clock_sec, 0.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_percent_done, 0.0, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(years_in_century, 100.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_iter, 0, fixnum), define_variable(glob_start, 0, fixnum),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_dump, false, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_h, 0.1, float), define_variable(glob_optimal_done, false,
boolean), define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_disp_incr, 0.1, 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/mtest2postode.ode#################"),
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"),
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 - 1.0;"),
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 : 10.0,"),
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, "/* # testing comment */"),
omniout_str(ALWAYS, "glob_h : 0.00001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 10,"),
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 + cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2 (x) := ("),
omniout_str(ALWAYS, "1.0 + sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_type_pole, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms), array(array_x, 1 + max_terms),
array(array_norms, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms),
array(array_m1, 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_y2_init, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_y1, 1 + max_terms),
array(array_y2, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_y1_init, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3),
array(array_y2_higher_work, 1 + 2, 1 + max_terms),
array(array_y1_set_initial, 1 + 3, 1 + max_terms),
array(array_y2_higher_work2, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_y2_higher, 1 + 2,
1 + max_terms), array(array_fact_2, 1 + max_terms, 1 + max_terms),
array(array_y2_set_initial, 1 + 3, 1 + max_terms),
array(array_y1_higher_work, 1 + 2, 1 + max_terms),
array(array_real_pole, 1 + 2, 1 + 3), array(array_y1_higher_work2, 1 + 2,
1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms), term : 1,
while term <= max_terms do (array_type_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 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_y2_init : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1_init : 0.0, term : 1 + term),
term
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_y2_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 3 do (term : 1, while term <=
max_terms do (array_y1_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y2_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y2_higher : 0.0, term : 1 + term),
ord, 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, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_y2_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y1_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, 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 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_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_y2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y2 : 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_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_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 (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 10.0, array_y1_init : exact_soln_y1(x_start),
1 + 0
array_y2_init : exact_soln_y2(x_start), glob_h : 1.0E-5,
1 + 0
glob_look_poles : true, glob_max_iter : 10, 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_y1_set_initial : true, array_y1_set_initial : false,
1, 1 1, 2
array_y1_set_initial : false, array_y1_set_initial : false,
1, 3 1, 4
array_y1_set_initial : false, array_y1_set_initial : false,
1, 5 1, 6
array_y1_set_initial : false, array_y1_set_initial : false,
1, 7 1, 8
array_y1_set_initial : false, array_y1_set_initial : false,
1, 9 1, 10
array_y1_set_initial : false, array_y1_set_initial : false,
1, 11 1, 12
array_y1_set_initial : false, array_y1_set_initial : false,
1, 13 1, 14
array_y1_set_initial : false, array_y1_set_initial : false,
1, 15 1, 16
array_y1_set_initial : false, array_y1_set_initial : false,
1, 17 1, 18
array_y1_set_initial : false, array_y1_set_initial : false,
1, 19 1, 20
array_y1_set_initial : false, array_y1_set_initial : false,
1, 21 1, 22
array_y1_set_initial : false, array_y1_set_initial : false,
1, 23 1, 24
array_y1_set_initial : false, array_y1_set_initial : false,
1, 25 1, 26
array_y1_set_initial : false, array_y1_set_initial : false,
1, 27 1, 28
array_y1_set_initial : false, array_y1_set_initial : false,
1, 29 1, 30
array_y2_set_initial : true, array_y2_set_initial : false,
2, 1 2, 2
array_y2_set_initial : false, array_y2_set_initial : false,
2, 3 2, 4
array_y2_set_initial : false, array_y2_set_initial : false,
2, 5 2, 6
array_y2_set_initial : false, array_y2_set_initial : false,
2, 7 2, 8
array_y2_set_initial : false, array_y2_set_initial : false,
2, 9 2, 10
array_y2_set_initial : false, array_y2_set_initial : false,
2, 11 2, 12
array_y2_set_initial : false, array_y2_set_initial : false,
2, 13 2, 14
array_y2_set_initial : false, array_y2_set_initial : false,
2, 15 2, 16
array_y2_set_initial : false, array_y2_set_initial : false,
2, 17 2, 18
array_y2_set_initial : false, array_y2_set_initial : false,
2, 19 2, 20
array_y2_set_initial : false, array_y2_set_initial : false,
2, 21 2, 22
array_y2_set_initial : false, array_y2_set_initial : false,
2, 23 2, 24
array_y2_set_initial : false, array_y2_set_initial : false,
2, 25 2, 26
array_y2_set_initial : false, array_y2_set_initial : false,
2, 27 2, 28
array_y2_set_initial : false, array_y2_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 : 1, term_no : 1,
2
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), order_diff : 1, term_no : 1,
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), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(), 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), 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), 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 <= 2 do (atomall(), subiter : 1 + subiter))
else (subiter : 1, while subiter <= glob_max_terms + 2 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 : 1, ord : 2,
1 1 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
order_diff : 1, ord : 2, 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 : 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
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 ( y1 , x , 1 ) = m1 * y2 + 1.0;"),
omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 - 1.0;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-06-17T21:24:21-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mtest2"),
logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 + 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, " 092 | "), logitem_str(html_log_file, "mtest2 diffeq.max"), logitem_str(html_log_file, "\
mtest2 maxima results"),
logitem_str(html_log_file, "Mostly affecting speed of factorials"),
logend(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logitem_str(html_log_file,
"diff ( y2 , x , 1 ) = y1 - 1.0;"), 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))
(%o49) mainprog() := (define_variable(INFO, 2, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(glob_max_rel_trunc_err,
1.0E-11, float), define_variable(glob_initial_pass, true, boolean),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(hours_in_day, 24.0, float),
define_variable(djd_debug, true, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_clock_sec, 0.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_hmax, 1.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_percent_done, 0.0, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(years_in_century, 100.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_iter, 0, fixnum), define_variable(glob_start, 0, fixnum),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_dump, false, boolean),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_h, 0.1, float), define_variable(glob_optimal_done, false,
boolean), define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_disp_incr, 0.1, 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/mtest2postode.ode#################"),
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"),
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 - 1.0;"),
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 : 10.0,"),
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, "/* # testing comment */"),
omniout_str(ALWAYS, "glob_h : 0.00001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 10,"),
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 + cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2 (x) := ("),
omniout_str(ALWAYS, "1.0 + sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_type_pole, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms), array(array_x, 1 + max_terms),
array(array_norms, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms),
array(array_m1, 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_y2_init, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_y1, 1 + max_terms),
array(array_y2, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_y1_init, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3),
array(array_y2_higher_work, 1 + 2, 1 + max_terms),
array(array_y1_set_initial, 1 + 3, 1 + max_terms),
array(array_y2_higher_work2, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_y2_higher, 1 + 2,
1 + max_terms), array(array_fact_2, 1 + max_terms, 1 + max_terms),
array(array_y2_set_initial, 1 + 3, 1 + max_terms),
array(array_y1_higher_work, 1 + 2, 1 + max_terms),
array(array_real_pole, 1 + 2, 1 + 3), array(array_y1_higher_work2, 1 + 2,
1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms), term : 1,
while term <= max_terms do (array_type_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 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_y2_init : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1_init : 0.0, term : 1 + term),
term
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_y2_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 3 do (term : 1, while term <=
max_terms do (array_y1_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y2_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y2_higher : 0.0, term : 1 + term),
ord, 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, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_y2_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y1_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, 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 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_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_y2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y2 : 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_const_0D0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, array(array_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 (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 10.0, array_y1_init : exact_soln_y1(x_start),
1 + 0
array_y2_init : exact_soln_y2(x_start), glob_h : 1.0E-5,
1 + 0
glob_look_poles : true, glob_max_iter : 10, 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_y1_set_initial : true, array_y1_set_initial : false,
1, 1 1, 2
array_y1_set_initial : false, array_y1_set_initial : false,
1, 3 1, 4
array_y1_set_initial : false, array_y1_set_initial : false,
1, 5 1, 6
array_y1_set_initial : false, array_y1_set_initial : false,
1, 7 1, 8
array_y1_set_initial : false, array_y1_set_initial : false,
1, 9 1, 10
array_y1_set_initial : false, array_y1_set_initial : false,
1, 11 1, 12
array_y1_set_initial : false, array_y1_set_initial : false,
1, 13 1, 14
array_y1_set_initial : false, array_y1_set_initial : false,
1, 15 1, 16
array_y1_set_initial : false, array_y1_set_initial : false,
1, 17 1, 18
array_y1_set_initial : false, array_y1_set_initial : false,
1, 19 1, 20
array_y1_set_initial : false, array_y1_set_initial : false,
1, 21 1, 22
array_y1_set_initial : false, array_y1_set_initial : false,
1, 23 1, 24
array_y1_set_initial : false, array_y1_set_initial : false,
1, 25 1, 26
array_y1_set_initial : false, array_y1_set_initial : false,
1, 27 1, 28
array_y1_set_initial : false, array_y1_set_initial : false,
1, 29 1, 30
array_y2_set_initial : true, array_y2_set_initial : false,
2, 1 2, 2
array_y2_set_initial : false, array_y2_set_initial : false,
2, 3 2, 4
array_y2_set_initial : false, array_y2_set_initial : false,
2, 5 2, 6
array_y2_set_initial : false, array_y2_set_initial : false,
2, 7 2, 8
array_y2_set_initial : false, array_y2_set_initial : false,
2, 9 2, 10
array_y2_set_initial : false, array_y2_set_initial : false,
2, 11 2, 12
array_y2_set_initial : false, array_y2_set_initial : false,
2, 13 2, 14
array_y2_set_initial : false, array_y2_set_initial : false,
2, 15 2, 16
array_y2_set_initial : false, array_y2_set_initial : false,
2, 17 2, 18
array_y2_set_initial : false, array_y2_set_initial : false,
2, 19 2, 20
array_y2_set_initial : false, array_y2_set_initial : false,
2, 21 2, 22
array_y2_set_initial : false, array_y2_set_initial : false,
2, 23 2, 24
array_y2_set_initial : false, array_y2_set_initial : false,
2, 25 2, 26
array_y2_set_initial : false, array_y2_set_initial : false,
2, 27 2, 28
array_y2_set_initial : false, array_y2_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 : 1, term_no : 1,
2
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), order_diff : 1, term_no : 1,
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), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(), 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), 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), 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 <= 2 do (atomall(), subiter : 1 + subiter))
else (subiter : 1, while subiter <= glob_max_terms + 2 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 : 1, ord : 2,
1 1 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
order_diff : 1, ord : 2, 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 : 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
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 ( y1 , x , 1 ) = m1 * y2 + 1.0;"),
omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 - 1.0;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2012-06-17T21:24:21-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mtest2"),
logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 + 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, " 092 | "), logitem_str(html_log_file, "mtest2 diffeq.max"), logitem_str(html_log_file, "\
mtest2 maxima results"),
logitem_str(html_log_file, "Mostly affecting speed of factorials"),
logend(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logitem_str(html_log_file,
"diff ( y2 , x , 1 ) = y1 - 1.0;"), 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))
(%i50) mainprog()
"##############ECHO OF PROBLEM#################"
"##############temp/mtest2postode.ode#################"
"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"
"diff ( y2 , x , 1 ) = y1 - 1.0;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : 0.1,"
"x_end : 10.0,"
"array_y1_init[0 + 1] : exact_soln_y1(x_start),"
"array_y2_init[0 + 1] : exact_soln_y2(x_start),"
"/* # testing comment */"
"glob_h : 0.00001 ,"
"glob_look_poles : true,"
"glob_max_iter : 10,"
"/* 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 + cos(x) "
");"
"exact_soln_y2 (x) := ("
"1.0 + sin(x) "
");"
""
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = 0.1 " "
y1[1] (analytic) = 1.9950041652780257 " "
y1[1] (numeric) = 1.9950041652780257 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.0998334166468282 " "
y2[1] (numeric) = 1.0998334166468282 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
x[1] = 0.1 " "
y1[1] (analytic) = 1.9950041652780257 " "
y1[1] (numeric) = 1.9950041652780257 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.0998334166468282 " "
y2[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 " "
y1[1] (analytic) = 1.9949038343759766 " "
y1[1] (numeric) = 1.9949038343759766 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.100828370729568 " "
y2[1] (numeric) = 1.100828370729568 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10200000000000001 " "
y1[1] (analytic) = 1.9948025085701762 " "
y1[1] (numeric) = 1.9948025085701762 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1018232239839456 " "
y2[1] (numeric) = 1.1018232239839456 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10300000000000001 " "
y1[1] (analytic) = 1.99470018796195 " "
y1[1] (numeric) = 1.99470018796195 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1028179754151075 " "
y2[1] (numeric) = 1.1028179754151077 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.013429322653653200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10400000000000001 " "
y1[1] (analytic) = 1.9945968726536185 " "
y1[1] (numeric) = 1.9945968726536185 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1038126240283028 " "
y2[1] (numeric) = 1.1038126240283028 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10500000000000001 " "
y1[1] (analytic) = 1.9944925627484973 " "
y1[1] (numeric) = 1.9944925627484975 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113288708477529900000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1048071688288825 " "
y2[1] (numeric) = 1.1048071688288825 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10600000000000001 " "
y1[1] (analytic) = 1.9943872583508964 " "
y1[1] (numeric) = 1.9943872583508966 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113347490540196500000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1058016088223022 " "
y2[1] (numeric) = 1.1058016088223022 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10700000000000001 " "
y1[1] (analytic) = 1.9942809595661202 " "
y1[1] (numeric) = 1.9942809595661202 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1067959430141219 " "
y2[1] (numeric) = 1.1067959430141219 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10800000000000001 " "
y1[1] (analytic) = 1.9941736665004668 " "
y1[1] (numeric) = 1.994173666500467 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113466738905908300000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1077901704100075 " "
y2[1] (numeric) = 1.1077901704100075 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10900000000000001 " "
y1[1] (analytic) = 1.99406537926123 " "
y1[1] (numeric) = 1.9940653792612302 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11352720544847600000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1087842900157316 " "
y2[1] (numeric) = 1.1087842900157316 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11000000000000001 " "
y1[1] (analytic) = 1.9939560979566968 " "
y1[1] (numeric) = 1.993956097956697 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113588233725763300000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1097783008371749 " "
y2[1] (numeric) = 1.1097783008371749 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11100000000000002 " "
y1[1] (analytic) = 1.9938458226961484 " "
y1[1] (numeric) = 1.9938458226961486 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113649823860376500000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1107722018803263 " "
y2[1] (numeric) = 1.1107722018803263 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11200000000000002 " "
y1[1] (analytic) = 1.9937345535898603 " "
y1[1] (numeric) = 1.9937345535898603 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1117659921512852 " "
y2[1] (numeric) = 1.1117659921512852 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11300000000000002 " "
y1[1] (analytic) = 1.9936222907491012 " "
y1[1] (numeric) = 1.9936222907491012 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1127596706562612 " "
y2[1] (numeric) = 1.1127596706562612 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11400000000000002 " "
y1[1] (analytic) = 1.9935090342861344 " "
y1[1] (numeric) = 1.9935090342861344 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.113753236401576 " "
y2[1] (numeric) = 1.113753236401576 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11500000000000002 " "
y1[1] (analytic) = 1.9933947843142157 " "
y1[1] (numeric) = 1.993394784314216 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11390180546409400000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1147466883936639 " "
y2[1] (numeric) = 1.1147466883936639 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11600000000000002 " "
y1[1] (analytic) = 1.9932795409475959 " "
y1[1] (numeric) = 1.9932795409475959 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1157400256390728 " "
y2[1] (numeric) = 1.1157400256390728 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11700000000000002 " "
y1[1] (analytic) = 1.9931633043015178 " "
y1[1] (numeric) = 1.9931633043015178 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1167332471444658 " "
y2[1] (numeric) = 1.1167332471444658 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11800000000000002 " "
y1[1] (analytic) = 1.993046074492218 " "
y1[1] (numeric) = 1.993046074492218 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1177263519166214 " "
y2[1] (numeric) = 1.1177263519166214 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11900000000000002 " "
y1[1] (analytic) = 1.9929278516369267 " "
y1[1] (numeric) = 1.9929278516369267 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.118719338962435 " "
y2[1] (numeric) = 1.1187193389624348 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.984810641880637400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12000000000000002 " "
y1[1] (analytic) = 1.9928086358538661 " "
y1[1] (numeric) = 1.9928086358538664 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.114229439445855500000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1197122072889194 " "
y2[1] (numeric) = 1.1197122072889192 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.98305067569685900000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12100000000000002 " "
y1[1] (analytic) = 1.992688427262253 " "
y1[1] (numeric) = 1.992688427262253 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1207049559032065 " "
y2[1] (numeric) = 1.1207049559032063 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.981294039572436300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12200000000000003 " "
y1[1] (analytic) = 1.9925672259822949 " "
y1[1] (numeric) = 1.9925672259822949 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1216975838125478 " "
y2[1] (numeric) = 1.1216975838125476 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.979540725855198400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12300000000000003 " "
y1[1] (analytic) = 1.9924450321351936 " "
y1[1] (numeric) = 1.9924450321351936 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1226900900243153 " "
y2[1] (numeric) = 1.122690090024315 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.97779072691576200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12400000000000003 " "
y1[1] (analytic) = 1.9923218458431429 " "
y1[1] (numeric) = 1.9923218458431429 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1236824735460031 " "
y2[1] (numeric) = 1.123682473546003 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.97604403514745120000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12500000000000003 " "
y1[1] (analytic) = 1.9921976672293291 " "
y1[1] (numeric) = 1.9921976672293291 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1246747333852278 " "
y2[1] (numeric) = 1.1246747333852274 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.948601285932432600000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12600000000000003 " "
y1[1] (analytic) = 1.9920724964179306 " "
y1[1] (numeric) = 1.9920724964179308 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11464118562102300000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1256668685497293 " "
y2[1] (numeric) = 1.1256668685497289 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.945121085621112000000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12700000000000003 " "
y1[1] (analytic) = 1.9919463335341185 " "
y1[1] (numeric) = 1.9919463335341188 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.114711783078407300000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1266588780473727 " "
y2[1] (numeric) = 1.1266588780473723 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.941647454282874400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12800000000000003 " "
y1[1] (analytic) = 1.9918191787040556 " "
y1[1] (numeric) = 1.9918191787040558 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.114782944652139400000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1276507608861488 " "
y2[1] (numeric) = 1.1276507608861484 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.93818037688442870000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.12900000000000003 " "
y1[1] (analytic) = 1.9916910320548964 " "
y1[1] (numeric) = 1.9916910320548968 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.229709340970825500000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1286425160741744 " "
y2[1] (numeric) = 1.128642516074174 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.93471983843710740000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13000000000000003 " "
y1[1] (analytic) = 1.991561893714788 " "
y1[1] (numeric) = 1.9915618937147883 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.114926960722569200000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.129634142619695 " "
y2[1] (numeric) = 1.1296341426196943 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.89689873599505600000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13100000000000003 " "
y1[1] (analytic) = 1.9914317638128685 " "
y1[1] (numeric) = 1.9914317638128687 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.114999815509101500000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1306256395310834 " "
y2[1] (numeric) = 1.130625639531083 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.92781831866332500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13200000000000003 " "
y1[1] (analytic) = 1.9913006424792679 " "
y1[1] (numeric) = 1.9913006424792679 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1316170058168433 " "
y2[1] (numeric) = 1.1316170058168429 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.92437730758122100000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13300000000000003 " "
y1[1] (analytic) = 1.9911685298451072 " "
y1[1] (numeric) = 1.9911685298451072 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1326082404856084 " "
y2[1] (numeric) = 1.132608240485608 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.920942775938645600000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13400000000000004 " "
y1[1] (analytic) = 1.9910354260424992 " "
y1[1] (numeric) = 1.9910354260424994 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.115221768637137800000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1335993425461441 " "
y2[1] (numeric) = 1.1335993425461435 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.87627206345154000000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13500000000000004 " "
y1[1] (analytic) = 1.9909013312045478 " "
y1[1] (numeric) = 1.990901331204548 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11529688309911600000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1345903110073483 " "
y2[1] (numeric) = 1.1345903110073476 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.87113963791622400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13600000000000004 " "
y1[1] (analytic) = 1.9907662454653479 " "
y1[1] (numeric) = 1.990766245465348 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.115372562855201900000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1355811448782527 " "
y2[1] (numeric) = 1.135581144878252 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.86601686528100200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13700000000000004 " "
y1[1] (analytic) = 1.990630168959985 " "
y1[1] (numeric) = 1.9906301689599852 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.115448808057800400000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1365718431680236 " "
y2[1] (numeric) = 1.136571843168023 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.86090372358992900000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13800000000000004 " "
y1[1] (analytic) = 1.9904931018245358 " "
y1[1] (numeric) = 1.990493101824536 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.115525618860470600000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1375624048859627 " "
y2[1] (numeric) = 1.137562404885962 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.85580019095191400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.13900000000000004 " "
y1[1] (analytic) = 1.9903550441960673 " "
y1[1] (numeric) = 1.9903550441960673 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1385528290415083 " "
y2[1] (numeric) = 1.1385528290415077 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.85070624554048300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14000000000000004 " "
y1[1] (analytic) = 1.9902159962126371 " "
y1[1] (numeric) = 1.9902159962126371 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1395431146442365 " "
y2[1] (numeric) = 1.1395431146442359 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.8456218655935610000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14100000000000004 " "
y1[1] (analytic) = 1.9900759580132932 " "
y1[1] (numeric) = 1.9900759580132932 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1405332607038616 " "
y2[1] (numeric) = 1.140533260703861 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.84054702941324300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14200000000000004 " "
y1[1] (analytic) = 1.989934929738074 " "
y1[1] (numeric) = 1.9899349297380737 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.115838521183494200000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1415232662302377 " "
y2[1] (numeric) = 1.141523266230237 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.83548171536557400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14300000000000004 " "
y1[1] (analytic) = 1.9897929115280073 " "
y1[1] (numeric) = 1.989792911528007 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.115918162330361300000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1425131302333595 " "
y2[1] (numeric) = 1.1425131302333587 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.77390120250708900000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14400000000000004 " "
y1[1] (analytic) = 1.9896499035251116 " "
y1[1] (numeric) = 1.9896499035251114 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.115998370022934400000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1435028517233627 " "
y2[1] (numeric) = 1.143502851723362 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.82537956745074700000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14500000000000005 " "
y1[1] (analytic) = 1.9895059058723947 " "
y1[1] (numeric) = 1.9895059058723947 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1444924297105263 " "
y2[1] (numeric) = 1.1444924297105257 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.82034269063341400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14600000000000005 " "
y1[1] (analytic) = 1.9893609187138546 " "
y1[1] (numeric) = 1.9893609187138546 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1454818632052723 " "
y2[1] (numeric) = 1.1454818632052717 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.81531525004793200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14700000000000005 " "
y1[1] (analytic) = 1.989214942194478 " "
y1[1] (numeric) = 1.989214942194478 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1464711512181671 " "
y2[1] (numeric) = 1.1464711512181665 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.81029722437675500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14800000000000005 " "
y1[1] (analytic) = 1.989067976460242 " "
y1[1] (numeric) = 1.989067976460242 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1474602927599231 " "
y2[1] (numeric) = 1.1474602927599222 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.74038478981994700000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.14900000000000005 " "
y1[1] (analytic) = 1.9889200216581118 " "
y1[1] (numeric) = 1.9889200216581118 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1484492868413985 " "
y2[1] (numeric) = 1.1484492868413976 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.73371911042671200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15000000000000005 " "
y1[1] (analytic) = 1.9887710779360424 " "
y1[1] (numeric) = 1.9887710779360424 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1494381324735992 " "
y2[1] (numeric) = 1.1494381324735985 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.7952994246116500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15100000000000005 " "
y1[1] (analytic) = 1.9886211454429774 " "
y1[1] (numeric) = 1.9886211454429774 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1504268286676802 " "
y2[1] (numeric) = 1.1504268286676793 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.72042512889527100000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15200000000000005 " "
y1[1] (analytic) = 1.9884702243288492 " "
y1[1] (numeric) = 1.9884702243288492 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.151415374434945 " "
y2[1] (numeric) = 1.151415374434944 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.71379677065713300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15300000000000005 " "
y1[1] (analytic) = 1.9883183147445793 " "
y1[1] (numeric) = 1.988318314744579 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.116745760869558200000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1524037687868478 " "
y2[1] (numeric) = 1.152403768786847 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.70718079684105400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15400000000000005 " "
y1[1] (analytic) = 1.9881654168420768 " "
y1[1] (numeric) = 1.9881654168420766 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.116831643102001900000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1533920107349946 " "
y2[1] (numeric) = 1.1533920107349938 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.70057717960207600000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15500000000000005 " "
y1[1] (analytic) = 1.9880115307742399 " "
y1[1] (numeric) = 1.9880115307742396 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.116918093722298700000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1543800992911435 " "
y2[1] (numeric) = 1.1543800992911426 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.69398589117673100000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15600000000000006 " "
y1[1] (analytic) = 1.9878566566949545 " "
y1[1] (numeric) = 1.9878566566949543 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.117005112904904300000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1553680334672058 " "
y2[1] (numeric) = 1.155368033467205 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.68740690388276500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15700000000000006 " "
y1[1] (analytic) = 1.9877007947590948 " "
y1[1] (numeric) = 1.9877007947590946 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.117092700825441200000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1563558122752478 " "
y2[1] (numeric) = 1.1563558122752469 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.68084019011885000000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15800000000000006 " "
y1[1] (analytic) = 1.9875439451225225 " "
y1[1] (numeric) = 1.9875439451225223 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11718085766070100000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1573434347274905 " "
y2[1] (numeric) = 1.1573434347274896 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.67428572236431100000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.15900000000000006 " "
y1[1] (analytic) = 1.9873861079420876 " "
y1[1] (numeric) = 1.9873861079420874 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.117269583588644500000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1583308998363115 " "
y2[1] (numeric) = 1.1583308998363107 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.66774347317884100000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16000000000000006 " "
y1[1] (analytic) = 1.9872272833756268 " "
y1[1] (numeric) = 1.9872272833756266 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.117358878788402300000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.159318206614246 " "
y2[1] (numeric) = 1.1593182066142451 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.6612134152022300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16100000000000006 " "
y1[1] (analytic) = 1.9870674715819652 " "
y1[1] (numeric) = 1.9870674715819647 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.234897486880551600000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1603053540739872 " "
y2[1] (numeric) = 1.1603053540739863 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.65469552115408300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16200000000000006 " "
y1[1] (analytic) = 1.986906672720914 " "
y1[1] (numeric) = 1.9869066727209137 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.117539177725738300000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1612923412283875 " "
y2[1] (numeric) = 1.1612923412283866 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.6481897638335500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16300000000000006 " "
y1[1] (analytic) = 1.9867448869532724 " "
y1[1] (numeric) = 1.9867448869532722 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.117630181827435200000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.16227916709046 " "
y2[1] (numeric) = 1.1622791670904593 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.73127208708928700000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16400000000000006 " "
y1[1] (analytic) = 1.9865821144408262 " "
y1[1] (numeric) = 1.986582114440826 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.117721755929184800000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.163265830673379 " "
y2[1] (numeric) = 1.1632658306733783 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.72641091322599500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16500000000000006 " "
y1[1] (analytic) = 1.9864183553463477 " "
y1[1] (numeric) = 1.9864183553463475 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.117813900215979800000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.164252330990481 " "
y2[1] (numeric) = 1.1642523309904802 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.62874504141651500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16600000000000006 " "
y1[1] (analytic) = 1.9862536098335961 " "
y1[1] (numeric) = 1.986253609833596 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.117906614873987500000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1652386670552657 " "
y2[1] (numeric) = 1.1652386670552648 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.62228756057921100000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16700000000000007 " "
y1[1] (analytic) = 1.9860878780673166 " "
y1[1] (numeric) = 1.9860878780673166 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.166224837881397 " "
y2[1] (numeric) = 1.1662248378813962 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.6158420816488500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16800000000000007 " "
y1[1] (analytic) = 1.9859211602132416 " "
y1[1] (numeric) = 1.9859211602132414 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.118093756054187500000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1672108424827043 " "
y2[1] (numeric) = 1.1672108424827035 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.60940857789612400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.16900000000000007 " "
y1[1] (analytic) = 1.985753456438088 " "
y1[1] (numeric) = 1.985753456438088 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.168196679873183 " "
y2[1] (numeric) = 1.1681966798731822 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.60298702266936700000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17000000000000007 " "
y1[1] (analytic) = 1.9855847669095605 " "
y1[1] (numeric) = 1.9855847669095605 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1691823490669961 " "
y2[1] (numeric) = 1.169182349066995 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.4957217367428700000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17100000000000007 " "
y1[1] (analytic) = 1.9854150917963485 " "
y1[1] (numeric) = 1.9854150917963482 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.118378750330398200000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.170167849078474 " "
y2[1] (numeric) = 1.170167849078473 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.59017965157374700000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17200000000000007 " "
y1[1] (analytic) = 1.9852444312681263 " "
y1[1] (numeric) = 1.9852444312681263 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.171153178922117 " "
y2[1] (numeric) = 1.1711531789221161 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.58379378278740200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17300000000000007 " "
y1[1] (analytic) = 1.9850727854955552 " "
y1[1] (numeric) = 1.9850727854955552 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1721383376125956 " "
y2[1] (numeric) = 1.1721383376125944 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.47177469586441700000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17400000000000007 " "
y1[1] (analytic) = 1.9849001546502807 " "
y1[1] (numeric) = 1.9849001546502807 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1731233241647505 " "
y2[1] (numeric) = 1.1731233241647496 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.57105754701874600000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17500000000000007 " "
y1[1] (analytic) = 1.9847265389049333 " "
y1[1] (numeric) = 1.9847265389049336 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.118766744800740700000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.174108137593596 " "
y2[1] (numeric) = 1.1741081375935951 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.56470712757769800000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17600000000000007 " "
y1[1] (analytic) = 1.9845519384331296 " "
y1[1] (numeric) = 1.9845519384331296 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1750927769143182 " "
y2[1] (numeric) = 1.1750927769143173 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.55836847225286500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17700000000000007 " "
y1[1] (analytic) = 1.984376353409469 " "
y1[1] (numeric) = 1.9843763534094692 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.118964175034256600000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1760772411422784 " "
y2[1] (numeric) = 1.1760772411422773 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.44005194375532400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17800000000000007 " "
y1[1] (analytic) = 1.9841997840095373 " "
y1[1] (numeric) = 1.9841997840095373 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1770615292930118 " "
y2[1] (numeric) = 1.1770615292930109 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.54572634986719100000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.17900000000000008 " "
y1[1] (analytic) = 1.9840222304099036 " "
y1[1] (numeric) = 1.9840222304099036 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1780456403822308 " "
y2[1] (numeric) = 1.17804564038223 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.53942283095199300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18000000000000008 " "
y1[1] (analytic) = 1.9838436927881213 " "
y1[1] (numeric) = 1.9838436927881213 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1790295734258243 " "
y2[1] (numeric) = 1.1790295734258234 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.53313097244377800000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18100000000000008 " "
y1[1] (analytic) = 1.9836641713227285 " "
y1[1] (numeric) = 1.9836641713227283 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11936590948743900000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1800133274398592 " "
y2[1] (numeric) = 1.1800133274398583 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.52685074860217900000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18200000000000008 " "
y1[1] (analytic) = 1.983483666193246 " "
y1[1] (numeric) = 1.983483666193246 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1809969014405817 " "
y2[1] (numeric) = 1.1809969014405808 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.52058213376109700000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18300000000000008 " "
y1[1] (analytic) = 1.9833021775801796 " "
y1[1] (numeric) = 1.9833021775801793 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11957021695981400000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1819802944444178 " "
y2[1] (numeric) = 1.1819802944444169 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.51432510232844300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18400000000000008 " "
y1[1] (analytic) = 1.9831197056650174 " "
y1[1] (numeric) = 1.9831197056650172 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.119673231478334200000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1829635054679746 " "
y2[1] (numeric) = 1.1829635054679737 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.50807962878589500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18500000000000008 " "
y1[1] (analytic) = 1.9829362506302315 " "
y1[1] (numeric) = 1.9829362506302313 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.1197768201295400000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1839465335280412 " "
y2[1] (numeric) = 1.1839465335280404 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.50184568768864200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18600000000000008 " "
y1[1] (analytic) = 1.9827518126592767 " "
y1[1] (numeric) = 1.9827518126592767 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1849293776415897 " "
y2[1] (numeric) = 1.1849293776415888 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.49562325366513200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18700000000000008 " "
y1[1] (analytic) = 1.9825663919365915 " "
y1[1] (numeric) = 1.9825663919365912 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.119985720670548800000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1859120368257758 " "
y2[1] (numeric) = 1.185912036825775 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.48941230141682900000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18800000000000008 " "
y1[1] (analytic) = 1.982379988647596 " "
y1[1] (numeric) = 1.9823799886475957 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.120091032983605200000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.186894510097941 " "
y2[1] (numeric) = 1.1868945100979398 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.35401600714744700000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.18900000000000008 " "
y1[1] (analytic) = 1.9821926029786936 " "
y1[1] (numeric) = 1.9821926029786934 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.12019692027585500000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1878767964756112 " "
y2[1] (numeric) = 1.18787679647561 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.34628092676908400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.19000000000000009 " "
y1[1] (analytic) = 1.9820042351172704 " "
y1[1] (numeric) = 1.98200423511727 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.24060676552382320000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1888588949765007 " "
y2[1] (numeric) = 1.1888588949764995 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.33856010428471900000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1910000000000001 " "
y1[1] (analytic) = 1.9818148852516937 " "
y1[1] (numeric) = 1.9818148852516932 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.240820841315169200000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.189840804618511 " "
y2[1] (numeric) = 1.1898408046185098 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.33085350843315900000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1920000000000001 " "
y1[1] (analytic) = 1.9816245535713135 " "
y1[1] (numeric) = 1.981624553571313 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.241036068359762700000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1908225244197324 " "
y2[1] (numeric) = 1.1908225244197312 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.32316110804294200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1930000000000001 " "
y1[1] (analytic) = 1.9814332402664618 " "
y1[1] (numeric) = 1.9814332402664612 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.36187867064101900000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1918040533984455 " "
y2[1] (numeric) = 1.1918040533984442 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.11785794464384340000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1940000000000001 " "
y1[1] (analytic) = 1.9812409455284512 " "
y1[1] (numeric) = 1.9812409455284508 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.24146997795672900000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.192785390573121 " "
y2[1] (numeric) = 1.1927853905731198 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.30781876940751200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1950000000000001 " "
y1[1] (analytic) = 1.9810476695495773 " "
y1[1] (numeric) = 1.9810476695495767 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.362532992083678300000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.193766534962422 " "
y2[1] (numeric) = 1.193766534962421 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.30016876926529600000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1960000000000001 " "
y1[1] (analytic) = 1.9808534125231154 " "
y1[1] (numeric) = 1.9808534125231148 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.36286274675219300000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1947474855852043 " "
y2[1] (numeric) = 1.1947474855852032 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.29253284078981300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1970000000000001 " "
y1[1] (analytic) = 1.9806581746433225 " "
y1[1] (numeric) = 1.980658174643322 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.24212948773977300000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.195728241460517 " "
y2[1] (numeric) = 1.195728241460516 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.28491095325372200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1980000000000001 " "
y1[1] (analytic) = 1.980461956105437 " "
y1[1] (numeric) = 1.9804619561054364 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.36352744732870750000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1967088016076048 " "
y2[1] (numeric) = 1.1967088016076037 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.27730307601759800000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1990000000000001 " "
y1[1] (analytic) = 1.980264757105677 " "
y1[1] (numeric) = 1.9802647571056764 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.36386239458558200000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1976891650459074 " "
y2[1] (numeric) = 1.1976891650459063 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.26970917852965400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2000000000000001 " "
y1[1] (analytic) = 1.9800665778412416 " "
y1[1] (numeric) = 1.980066577841241 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.36419907406014240000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.1986693307950613 " "
y2[1] (numeric) = 1.1986693307950602 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.26212923032543400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2010000000000001 " "
y1[1] (analytic) = 1.97986741851031 " "
y1[1] (numeric) = 1.9798674185103093 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.36453748643586300000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.199649297874901 " "
y2[1] (numeric) = 1.1996492978748998 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.25456320102752500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2020000000000001 " "
y1[1] (analytic) = 1.9796672793120416 " "
y1[1] (numeric) = 1.979667279312041 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.36487763239984200000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2006290653054594 " "
y2[1] (numeric) = 1.2006290653054583 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.24701106034525200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2030000000000001 " "
y1[1] (analytic) = 1.9794661604465755 " "
y1[1] (numeric) = 1.9794661604465749 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.365219512642800300000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2016086321069694 " "
y2[1] (numeric) = 1.201608632106968 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.10873673336892840000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2040000000000001 " "
y1[1] (analytic) = 1.9792640621150306 " "
y1[1] (numeric) = 1.97926406211503 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.365563127859085000000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2025879972998639 " "
y2[1] (numeric) = 1.2025879972998628 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.23194832409693200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2050000000000001 " "
y1[1] (analytic) = 1.979060984519505 " "
y1[1] (numeric) = 1.9790609845195044 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.36590847874667200000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2035671599047781 " "
y2[1] (numeric) = 1.203567159904777 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.22443766838066100000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2060000000000001 " "
y1[1] (analytic) = 1.9788569278630765 " "
y1[1] (numeric) = 1.978856927863076 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.244170377338116400000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2045461189425493 " "
y2[1] (numeric) = 1.2045461189425481 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.21694078097900200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2070000000000001 " "
y1[1] (analytic) = 1.978651892349802 " "
y1[1] (numeric) = 1.9786518923498013 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.36660439034583600000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2055248734342185 " "
y2[1] (numeric) = 1.2055248734342174 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.20945763203066400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2080000000000001 " "
y1[1] (analytic) = 1.9784458781847165 " "
y1[1] (numeric) = 1.9784458781847158 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.366954952471541400000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2065034224010316 " "
y2[1] (numeric) = 1.2065034224010305 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.20198819175937400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2090000000000001 " "
y1[1] (analytic) = 1.9782388855738344 " "
y1[1] (numeric) = 1.9782388855738338 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.36730725309681840000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2074817648644394 " "
y2[1] (numeric) = 1.2074817648644383 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.19453243047358300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2100000000000001 " "
y1[1] (analytic) = 1.9780309147241484 " "
y1[1] (numeric) = 1.9780309147241475 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.4902150572504500000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2084598998460996 " "
y2[1] (numeric) = 1.2084598998460985 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.18709031856618700000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2110000000000001 " "
y1[1] (analytic) = 1.9778219658436287 " "
y1[1] (numeric) = 1.977821965843628 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.368017072714420400000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2094378263678776 " "
y2[1] (numeric) = 1.2094378263678762 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.10155941918170910000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2120000000000001 " "
y1[1] (analytic) = 1.977612039141225 " "
y1[1] (numeric) = 1.9776120391412242 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.491166124200049500000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2104155434518462 " "
y2[1] (numeric) = 1.210415543451845 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.1722469248786910000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2130000000000001 " "
y1[1] (analytic) = 1.9774011348268636 " "
y1[1] (numeric) = 1.9774011348268627 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.49164513996241800000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2113930501202892 " "
y2[1] (numeric) = 1.211393050120288 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.16484558430406500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2140000000000001 " "
y1[1] (analytic) = 1.9771892531114488 " "
y1[1] (numeric) = 1.9771892531114479 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.492126478547377500000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2123703453956995 " "
y2[1] (numeric) = 1.2123703453956984 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.15745777551822600000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2150000000000001 " "
y1[1] (analytic) = 1.9769763942068623 " "
y1[1] (numeric) = 1.9769763942068614 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.492610140934187000000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2133474283007823 " "
y2[1] (numeric) = 1.2133474283007812 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.15008346933206800000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2160000000000001 " "
y1[1] (analytic) = 1.9767625583259631 " "
y1[1] (numeric) = 1.9767625583259623 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.4930961281069900000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2143242978584545 " "
y2[1] (numeric) = 1.2143242978584534 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.14272263663925900000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2170000000000001 " "
y1[1] (analytic) = 1.9765477456825868 " "
y1[1] (numeric) = 1.976547745682586 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.493584441054820400000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2153009530918468 " "
y2[1] (numeric) = 1.2153009530918457 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.13537524841594600000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2180000000000001 " "
y1[1] (analytic) = 1.9763319564915465 " "
y1[1] (numeric) = 1.9763319564915454 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.61759385096450700000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2162773930243038 " "
y2[1] (numeric) = 1.2162773930243027 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.12804127572049500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2190000000000001 " "
y1[1] (analytic) = 1.9761151909686308 " "
y1[1] (numeric) = 1.9761151909686296 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.61821006032021600000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.217253616679386 " "
y2[1] (numeric) = 1.2172536166793848 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.12072068969321100000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2200000000000001 " "
y1[1] (analytic) = 1.9758974493306054 " "
y1[1] (numeric) = 1.9758974493306043 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.618829180640310000000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2182296230808694 " "
y2[1] (numeric) = 1.2182296230808682 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.11341346155606500000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.2210000000000001 " "
y1[1] (analytic) = 1.9756787317952123 " "
y1[1] (numeric) = 1.975678731795211 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.74334145582270300000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.219205411252748 " "
y2[1] (numeric) = 1.2192054112527468 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.10611956261241700000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.22200000000000011 " "
y1[1] (analytic) = 1.9754590385811683 " "
y1[1] (numeric) = 1.9754590385811672 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.62007615922297600000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2201809802192336 " "
y2[1] (numeric) = 1.2201809802192325 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.09883896424675700000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.22300000000000011 " "
y1[1] (analytic) = 1.9752383699081673 " "
y1[1] (numeric) = 1.9752383699081661 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.620704020025558000000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2211563290047573 " "
y2[1] (numeric) = 1.2211563290047562 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.0915716379244290000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.22400000000000012 " "
y1[1] (analytic) = 1.9750167259968778 " "
y1[1] (numeric) = 1.9750167259968765 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.7456017562470700000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2221314566339705 " "
y2[1] (numeric) = 1.2221314566339694 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.08431755519135900000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.22500000000000012 " "
y1[1] (analytic) = 1.9747941070689432 " "
y1[1] (numeric) = 1.974794107068942 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.62196849104936500000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2231063621317455 " "
y2[1] (numeric) = 1.2231063621317444 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.07707668767379200000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.22600000000000012 " "
y1[1] (analytic) = 1.974570513346983 " "
y1[1] (numeric) = 1.9745705133469817 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.74712612461702300000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2240810445231771 " "
y2[1] (numeric) = 1.2240810445231758 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.08838188084936250000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.22700000000000012 " "
y1[1] (analytic) = 1.9743459450545906 " "
y1[1] (numeric) = 1.9743459450545893 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.74789356387768500000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2250555028335828 " "
y2[1] (numeric) = 1.2250555028335814 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.0875161382228160000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.22800000000000012 " "
y1[1] (analytic) = 1.9741204024163344 " "
y1[1] (numeric) = 1.974120402416333 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.74866450860588400000000000000E-14 "%"
h = 1.000E-3 " "
y2[1] (analytic) = 1.2260297360885042 " "
y2[1] (numeric) = 1.226029736088503 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.05543309387572800000000000000E-14 "%"
h = 1.000E-3 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"
"diff ( y2 , x , 1 ) = y1 - 1.0;"
Iterations = 128
"Total Elapsed Time "= 15 Minutes 19 Seconds
"Elapsed Time(since restart) "= 15 Minutes 19 Seconds
"Expected Time Remaining "= 19 Hours 21 Minutes 3 Seconds
"Optimized Time Remaining "= 19 Hours 20 Minutes 25 Seconds
"Time to Timeout " Unknown
Percent Done = 1.303030303030304 "%"
(%o50) true
(%o50) diffeq.max