(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/local/share/maxima/5.26.0/share/contrib/stringproc/stringproc.mac
(%i3) display_alot(iter) := if iter >= 0
then (ind_var : array_x , omniout_float(ALWAYS,
1
"x[1] ", 33, ind_var, 20, " "),
analytic_val_y : exact_soln_y2(ind_var),
omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y2 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val,
abserr 100.0
20, " "), if abs(analytic_val_y) # 0.0 then relerr : -------------------
abs(analytic_val_y)
else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_float(ALWAYS, "h ", 4, glob_h,
20, " "), analytic_val_y : exact_soln_y1(ind_var),
omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y1 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val,
abserr 100.0
20, " "), if abs(analytic_val_y) # 0.0 then relerr : -------------------
abs(analytic_val_y)
else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr
2
else array_last_rel_error : relerr, omniout_float(ALWAYS,
2
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_float(ALWAYS, "h ", 4, glob_h,
20, " "))
(%o3) display_alot(iter) := if iter >= 0
then (ind_var : array_x , omniout_float(ALWAYS,
1
"x[1] ", 33, ind_var, 20, " "),
analytic_val_y : exact_soln_y2(ind_var),
omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y2 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val,
abserr 100.0
20, " "), if abs(analytic_val_y) # 0.0 then relerr : -------------------
abs(analytic_val_y)
else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_float(ALWAYS, "h ", 4, glob_h,
20, " "), analytic_val_y : exact_soln_y1(ind_var),
omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y1 ,
term_no
abserr : abs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val,
abserr 100.0
20, " "), if abs(analytic_val_y) # 0.0 then relerr : -------------------
abs(analytic_val_y)
else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr
2
else array_last_rel_error : relerr, omniout_float(ALWAYS,
2
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_float(ALWAYS, "h ", 4, glob_h,
20, " "))
(%i4) adjust_for_pole(h_param) := block(hnew : h_param,
glob_normmax : glob_small_float, if !array_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if glob_look_poles
and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float)
! 1! 1
array_pole
1
then (sz2 : -----------, if sz2 < hnew
10.0
then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2)
1
(%o4) adjust_for_pole(h_param) := block(hnew : h_param,
glob_normmax : glob_small_float, if !array_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if glob_look_poles
and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float)
! 1! 1
array_pole
1
then (sz2 : -----------, if sz2 < hnew
10.0
then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2)
1
(%i5) prog_report(x_start, x_end) := (clock_sec1 : elapsed_time_seconds(),
total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), percent_done :
comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o5) prog_report(x_start, x_end) := (clock_sec1 : elapsed_time_seconds(),
total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), percent_done :
comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i6) check_for_pole() := (n : glob_max_terms, m : - 1 - 5 + n,
while (m >= 10) and ((!array_y2_higher ! < glob_small_float)
! 1, m!
or (!array_y2_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y2_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y2_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y2_higher
1, m - 1
array_y2_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y2_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : glob_max_terms, m : - 1 - 1 + n,
1, 2
while (m >= 10) and ((!array_y1_higher ! < glob_small_float)
! 1, m!
or (!array_y1_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y1_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y1_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y1_higher
1, m - 1
array_y1_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y1_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
2, 1 2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float))
2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float), n : - 1 - 5 + glob_max_terms,
2, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y2_higher ! >
! 1, n!
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
elseif (!array_y2_higher ! >= glob_large_float)
! 1, m!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 5!
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
array_y2_higher array_y2_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y2_higher array_y2_higher
1, m - 1 1, m - 2
array_y2_higher array_y2_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y2_higher array_y2_higher
1, m - 3 1, m - 4
array_y2_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y2_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (abs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h
else rad_c : glob_large_float) else (rad_c : glob_large_float,
ord_no : glob_large_float)) else (rad_c : glob_large_float,
ord_no : glob_large_float)), array_complex_pole : rad_c,
1, 1
array_complex_pole : ord_no), n : - 1 - 1 + glob_max_terms, cnt : 0,
1, 2
while (cnt < 5) and (n >= 10) do (if !array_y1_higher ! > glob_small_float
! 1, n!
then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
elseif (!array_y1_higher ! >= glob_large_float)
! 1, m!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 5!
then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
array_y1_higher array_y1_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y1_higher array_y1_higher
1, m - 1 1, m - 2
array_y1_higher array_y1_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y1_higher array_y1_higher
1, m - 3 1, m - 4
array_y1_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y1_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (abs(dr1) <= glob_small_float) then (array_complex_pole :
2, 1
glob_large_float, array_complex_pole : glob_large_float)
2, 2
else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h
else rad_c : glob_large_float) else (rad_c : glob_large_float,
ord_no : glob_large_float)) else (rad_c : glob_large_float,
ord_no : glob_large_float)), array_complex_pole : rad_c,
2, 1
array_complex_pole : ord_no), found : false,
2, 2
if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
1, 1 1, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
1, 1 1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")), found : false,
if (not found) and ((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
2, 1 2, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
2, 1 2, 2
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
2, 1 2, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
2, 1 2, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
2, 1 2, 2 2, 1 2, 2
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
2, 1 2, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
2, 1 2, 2
found : true, array_type_pole : 3, if glob_display_flag
2
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
2, 1 2, 1
and (array_real_pole > 0.0) and (array_real_pole >
2, 1 2, 2
0.0))
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
2, 1
and (array_complex_pole # glob_large_float)
2, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
2, 1 2, 2
0.0))
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
2, 1 2, 2
array_type_pole : 3, if glob_display_flag
2
then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float,
1
array_pole : glob_large_float, if array_pole > array_poles
2 1 1, 1
then (array_pole : array_poles , array_pole : array_poles ),
1 1, 1 2 1, 2
if array_pole > array_poles then (array_pole : array_poles ,
1 2, 1 1 2, 1
array_pole : array_poles ), display_pole())
2 2, 2
(%o6) check_for_pole() := (n : glob_max_terms, m : - 1 - 5 + n,
while (m >= 10) and ((!array_y2_higher ! < glob_small_float)
! 1, m!
or (!array_y2_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y2_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y2_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y2_higher
1, m - 1
array_y2_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y2_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : glob_max_terms, m : - 1 - 1 + n,
1, 2
while (m >= 10) and ((!array_y1_higher ! < glob_small_float)
! 1, m!
or (!array_y1_higher ! < glob_small_float)
! 1, m - 1!
or (!array_y1_higher ! < glob_small_float)) do m :
! 1, m - 2!
array_y1_higher
1, m
m - 1, if m > 10 then (rm0 : -----------------------,
array_y1_higher
1, m - 1
array_y1_higher
1, m - 1
rm1 : -----------------------, hdrc : convfloat(m - 1) rm0
array_y1_higher
1, m - 2
- convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
2, 1 2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float))
2, 2
else (array_real_pole : glob_large_float,
2, 1
array_real_pole : glob_large_float), n : - 1 - 5 + glob_max_terms,
2, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y2_higher ! >
! 1, n!
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
elseif (!array_y2_higher ! >= glob_large_float)
! 1, m!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y2_higher ! >= glob_large_float)
! 1, m - 5!
then (array_complex_pole : glob_large_float,
1, 1
array_complex_pole : glob_large_float)
1, 2
array_y2_higher array_y2_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y2_higher array_y2_higher
1, m - 1 1, m - 2
array_y2_higher array_y2_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y2_higher array_y2_higher
1, m - 3 1, m - 4
array_y2_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y2_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (abs(dr1) <= glob_small_float) then (array_complex_pole :
1, 1
glob_large_float, array_complex_pole : glob_large_float)
1, 2
else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h
else rad_c : glob_large_float) else (rad_c : glob_large_float,
ord_no : glob_large_float)) else (rad_c : glob_large_float,
ord_no : glob_large_float)), array_complex_pole : rad_c,
1, 1
array_complex_pole : ord_no), n : - 1 - 1 + glob_max_terms, cnt : 0,
1, 2
while (cnt < 5) and (n >= 10) do (if !array_y1_higher ! > glob_small_float
! 1, n!
then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
elseif (!array_y1_higher ! >= glob_large_float)
! 1, m!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 1!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 2!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 3!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 4!
or (!array_y1_higher ! >= glob_large_float)
! 1, m - 5!
then (array_complex_pole : glob_large_float,
2, 1
array_complex_pole : glob_large_float)
2, 2
array_y1_higher array_y1_higher
1, m 1, m - 1
else (rm0 : -----------------------, rm1 : -----------------------,
array_y1_higher array_y1_higher
1, m - 1 1, m - 2
array_y1_higher array_y1_higher
1, m - 2 1, m - 3
rm2 : -----------------------, rm3 : -----------------------,
array_y1_higher array_y1_higher
1, m - 3 1, m - 4
array_y1_higher
1, m - 4
rm4 : -----------------------, nr1 : convfloat(m - 3) rm2
array_y1_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (abs(dr1) <= glob_small_float) then (array_complex_pole :
2, 1
glob_large_float, array_complex_pole : glob_large_float)
2, 2
else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h
else rad_c : glob_large_float) else (rad_c : glob_large_float,
ord_no : glob_large_float)) else (rad_c : glob_large_float,
ord_no : glob_large_float)), array_complex_pole : rad_c,
2, 1
array_complex_pole : ord_no), found : false,
2, 2
if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
1, 1 1, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
1, 1 1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
array_type_pole : 3, if glob_display_flag
1
then omniout_str(ALWAYS, "NO POLE")), found : false,
if (not found) and ((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
2, 1 2, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
2, 1 2, 2
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if (not found)
and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float)
2, 1 2, 2
and (array_real_pole > 0.0) and (array_real_pole > 0.0)
2, 1 2, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
2, 1 2, 2 2, 1 2, 2
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and (((array_real_pole = glob_large_float)
2, 1
or (array_real_pole = glob_large_float))
2, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
2, 1 2, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
2, 1 2, 2
found : true, array_type_pole : 3, if glob_display_flag
2
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
2, 1 2, 1
and (array_real_pole > 0.0) and (array_real_pole >
2, 1 2, 2
0.0))
then (array_poles : array_real_pole ,
2, 1 2, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")),
if (not found) and ((array_complex_pole # glob_large_float)
2, 1
and (array_complex_pole # glob_large_float)
2, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
2, 1 2, 2
0.0))
then (array_poles : array_complex_pole ,
2, 1 2, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
2, 2 2, 2 2
if glob_display_flag then omniout_str(ALWAYS,
"Complex estimate of poles used")), if not found
then (array_poles : glob_large_float, array_poles : glob_large_float,
2, 1 2, 2
array_type_pole : 3, if glob_display_flag
2
then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float,
1
array_pole : glob_large_float, if array_pole > array_poles
2 1 1, 1
then (array_pole : array_poles , array_pole : array_poles ),
1 1, 1 2 1, 2
if array_pole > array_poles then (array_pole : array_poles ,
1 2, 1 1 2, 1
array_pole : array_poles ), display_pole())
2 2, 2
(%i7) get_norms() := if not glob_initial_pass
then (set_z(array_norms, 1 + glob_max_terms), iii : 1,
while iii <= glob_max_terms do (if !array_y2 ! > array_norms
! iii! iii
then array_norms : !array_y2 !, iii : 1 + iii), iii : 1,
iii ! iii!
while iii <= glob_max_terms do (if !array_y1 ! > array_norms
! iii! iii
then array_norms : !array_y1 !, iii : 1 + iii))
iii ! iii!
(%o7) get_norms() := if not glob_initial_pass
then (set_z(array_norms, 1 + glob_max_terms), iii : 1,
while iii <= glob_max_terms do (if !array_y2 ! > array_norms
! iii! iii
then array_norms : !array_y2 !, iii : 1 + iii), iii : 1,
iii ! iii!
while iii <= glob_max_terms do (if !array_y1 ! > array_norms
! iii! iii
then array_norms : !array_y1 !, iii : 1 + iii))
iii ! iii!
(%i8) atomall() := (array_tmp1 : array_y1 + array_const_0D0 ,
1 1 1
if not array_y2_set_initial then (if 1 <= glob_max_terms
1, 6
5
then (temporary : array_tmp1 glob_h factorial_3(0, 5),
1
array_y2 : temporary, array_y2_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 5
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 4
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 3
temporary 5.0
temporary : -------------, array_y2_higher : temporary,
glob_h 5, 2
temporary 6.0
temporary : -------------, array_y2_higher : temporary)), kkk : 2,
glob_h 6, 1
array_tmp3 : array_m1 array_y2 , array_tmp4 :
1 1 1 1
array_const_1D0 + array_tmp3 , if not array_y1_set_initial
1 1 2, 2
then (if 1 <= glob_max_terms then (temporary :
1
array_tmp4 glob_h factorial_3(0, 1), array_y1 : temporary,
1 2
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 2 glob_h
array_y1_higher : temporary)), kkk : 2,
2, 1
array_tmp1 : array_y1 + array_const_0D0 ,
2 2 2
if not array_y2_set_initial then (if 2 <= glob_max_terms
1, 7
5
then (temporary : array_tmp1 glob_h factorial_3(1, 6),
2
array_y2 : temporary, array_y2_higher : temporary,
7 1, 7
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 6
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 5
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 4
temporary 5.0
temporary : -------------, array_y2_higher : temporary,
glob_h 5, 3
temporary 6.0
temporary : -------------, array_y2_higher : temporary)), kkk : 3,
glob_h 6, 2
array_tmp3 : ats(2, array_m1, array_y2, 1),
2
array_tmp4 : array_const_1D0 + array_tmp3 ,
2 2 2
if not array_y1_set_initial then (if 2 <= glob_max_terms
2, 3
1
then (temporary : array_tmp4 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_tmp1 : array_y1 + array_const_0D0 ,
3 3 3
if not array_y2_set_initial then (if 3 <= glob_max_terms
1, 8
5
then (temporary : array_tmp1 glob_h factorial_3(2, 7),
3
array_y2 : temporary, array_y2_higher : temporary,
8 1, 8
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 7
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 6
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 5
temporary 5.0
temporary : -------------, array_y2_higher : temporary,
glob_h 5, 4
temporary 6.0
temporary : -------------, array_y2_higher : temporary)), kkk : 4,
glob_h 6, 3
array_tmp3 : ats(3, array_m1, array_y2, 1),
3
array_tmp4 : array_const_1D0 + array_tmp3 ,
3 3 3
if not array_y1_set_initial then (if 3 <= glob_max_terms
2, 4
1
then (temporary : array_tmp4 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_tmp1 : array_y1 + array_const_0D0 ,
4 4 4
if not array_y2_set_initial then (if 4 <= glob_max_terms
1, 9
5
then (temporary : array_tmp1 glob_h factorial_3(3, 8),
4
array_y2 : temporary, array_y2_higher : temporary,
9 1, 9
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 8
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 7
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 6
temporary 5.0
temporary : -------------, array_y2_higher : temporary,
glob_h 5, 5
temporary 6.0
temporary : -------------, array_y2_higher : temporary)), kkk : 5,
glob_h 6, 4
array_tmp3 : ats(4, array_m1, array_y2, 1),
4
array_tmp4 : array_const_1D0 + array_tmp3 ,
4 4 4
if not array_y1_set_initial then (if 4 <= glob_max_terms
2, 5
1
then (temporary : array_tmp4 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_tmp1 : array_y1 + array_const_0D0 ,
5 5 5
if not array_y2_set_initial then (if 5 <= glob_max_terms
1, 10
5
then (temporary : array_tmp1 glob_h factorial_3(4, 9),
5
array_y2 : temporary, array_y2_higher : temporary,
10 1, 10
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 9
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 8
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 7
temporary 5.0
temporary : -------------, array_y2_higher : temporary,
glob_h 5, 6
temporary 6.0
temporary : -------------, array_y2_higher : temporary)), kkk : 6,
glob_h 6, 5
array_tmp3 : ats(5, array_m1, array_y2, 1),
5
array_tmp4 : array_const_1D0 + array_tmp3 ,
5 5 5
if not array_y1_set_initial then (if 5 <= glob_max_terms
2, 6
1
then (temporary : array_tmp4 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
while kkk <= glob_max_terms do (array_tmp1 :
kkk
array_y1 + array_const_0D0 , order_d : 5,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y2_set_initial
1, order_d + kkk
order_d
array_tmp1 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y2 : temporary, array_y2_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_y2_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), array_tmp3 :
kkk
ats(kkk, array_m1, array_y2, 1), array_tmp4 :
kkk
array_const_1D0 + array_tmp3 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y1_set_initial
2, order_d + kkk
order_d
array_tmp4 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y1 : temporary, array_y1_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_y1_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk))
(%o8) atomall() := (array_tmp1 : array_y1 + array_const_0D0 ,
1 1 1
if not array_y2_set_initial then (if 1 <= glob_max_terms
1, 6
5
then (temporary : array_tmp1 glob_h factorial_3(0, 5),
1
array_y2 : temporary, array_y2_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 5
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 4
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 3
temporary 5.0
temporary : -------------, array_y2_higher : temporary,
glob_h 5, 2
temporary 6.0
temporary : -------------, array_y2_higher : temporary)), kkk : 2,
glob_h 6, 1
array_tmp3 : array_m1 array_y2 , array_tmp4 :
1 1 1 1
array_const_1D0 + array_tmp3 , if not array_y1_set_initial
1 1 2, 2
then (if 1 <= glob_max_terms then (temporary :
1
array_tmp4 glob_h factorial_3(0, 1), array_y1 : temporary,
1 2
temporary 2.0
array_y1_higher : temporary, temporary : -------------,
1, 2 glob_h
array_y1_higher : temporary)), kkk : 2,
2, 1
array_tmp1 : array_y1 + array_const_0D0 ,
2 2 2
if not array_y2_set_initial then (if 2 <= glob_max_terms
1, 7
5
then (temporary : array_tmp1 glob_h factorial_3(1, 6),
2
array_y2 : temporary, array_y2_higher : temporary,
7 1, 7
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 6
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 5
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 4
temporary 5.0
temporary : -------------, array_y2_higher : temporary,
glob_h 5, 3
temporary 6.0
temporary : -------------, array_y2_higher : temporary)), kkk : 3,
glob_h 6, 2
array_tmp3 : ats(2, array_m1, array_y2, 1),
2
array_tmp4 : array_const_1D0 + array_tmp3 ,
2 2 2
if not array_y1_set_initial then (if 2 <= glob_max_terms
2, 3
1
then (temporary : array_tmp4 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_tmp1 : array_y1 + array_const_0D0 ,
3 3 3
if not array_y2_set_initial then (if 3 <= glob_max_terms
1, 8
5
then (temporary : array_tmp1 glob_h factorial_3(2, 7),
3
array_y2 : temporary, array_y2_higher : temporary,
8 1, 8
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 7
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 6
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 5
temporary 5.0
temporary : -------------, array_y2_higher : temporary,
glob_h 5, 4
temporary 6.0
temporary : -------------, array_y2_higher : temporary)), kkk : 4,
glob_h 6, 3
array_tmp3 : ats(3, array_m1, array_y2, 1),
3
array_tmp4 : array_const_1D0 + array_tmp3 ,
3 3 3
if not array_y1_set_initial then (if 3 <= glob_max_terms
2, 4
1
then (temporary : array_tmp4 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_tmp1 : array_y1 + array_const_0D0 ,
4 4 4
if not array_y2_set_initial then (if 4 <= glob_max_terms
1, 9
5
then (temporary : array_tmp1 glob_h factorial_3(3, 8),
4
array_y2 : temporary, array_y2_higher : temporary,
9 1, 9
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 8
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 7
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 6
temporary 5.0
temporary : -------------, array_y2_higher : temporary,
glob_h 5, 5
temporary 6.0
temporary : -------------, array_y2_higher : temporary)), kkk : 5,
glob_h 6, 4
array_tmp3 : ats(4, array_m1, array_y2, 1),
4
array_tmp4 : array_const_1D0 + array_tmp3 ,
4 4 4
if not array_y1_set_initial then (if 4 <= glob_max_terms
2, 5
1
then (temporary : array_tmp4 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_tmp1 : array_y1 + array_const_0D0 ,
5 5 5
if not array_y2_set_initial then (if 5 <= glob_max_terms
1, 10
5
then (temporary : array_tmp1 glob_h factorial_3(4, 9),
5
array_y2 : temporary, array_y2_higher : temporary,
10 1, 10
temporary 2.0
temporary : -------------, array_y2_higher : temporary,
glob_h 2, 9
temporary 3.0
temporary : -------------, array_y2_higher : temporary,
glob_h 3, 8
temporary 4.0
temporary : -------------, array_y2_higher : temporary,
glob_h 4, 7
temporary 5.0
temporary : -------------, array_y2_higher : temporary,
glob_h 5, 6
temporary 6.0
temporary : -------------, array_y2_higher : temporary)), kkk : 6,
glob_h 6, 5
array_tmp3 : ats(5, array_m1, array_y2, 1),
5
array_tmp4 : array_const_1D0 + array_tmp3 ,
5 5 5
if not array_y1_set_initial then (if 5 <= glob_max_terms
2, 6
1
then (temporary : array_tmp4 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
while kkk <= glob_max_terms do (array_tmp1 :
kkk
array_y1 + array_const_0D0 , order_d : 5,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y2_set_initial
1, order_d + kkk
order_d
array_tmp1 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y2 : temporary, array_y2_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_y2_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), array_tmp3 :
kkk
ats(kkk, array_m1, array_y2, 1), array_tmp4 :
kkk
array_const_1D0 + array_tmp3 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y1_set_initial
2, order_d + kkk
order_d
array_tmp4 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y1 : temporary, array_y1_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_y1_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk))
log(x)
(%i9) log10(x) := ---------
log(10.0)
log(x)
(%o9) log10(x) := ---------
log(10.0)
(%i10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i11) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o11) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i12) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o12) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i16) dump_series(iolevel, dump_label, series_name, array_series, numb) :=
if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i))
i
(%o16) dump_series(iolevel, dump_label, series_name, array_series, numb) :=
if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i))
i
(%i17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb,
subnum) := if glob_iolevel >= iolevel then (sub : 1,
while sub <= subnum do (i : 1, while i <=
num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))
sub, i
(%o17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb,
subnum) := if glob_iolevel >= iolevel then (sub : 1,
while sub <= subnum do (i : 1, while i <=
num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))
sub, i
(%i18) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o18) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, "
"),
if secs >= 0.0 then (sec_in_millinium :
sec_in_min min_in_hour hours_in_day days_in_year years_in_century
secs
centuries_in_millinium, milliniums : ----------------,
sec_in_millinium
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) centuries_in_millinium,
cent_int : floor(centuries), years : (centuries - cent_int) years_in_century,
years_int : floor(years), days : (years - years_int) days_in_year,
days_int : floor(days), hours : (days - days_int) hours_in_day,
hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour,
minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min,
sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\
Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(fd,
"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds",
minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int))
else printf(fd, "Unknown"), printf(fd, " | "))
(%o19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""),
if secs >= 0.0 then (sec_in_millinium :
sec_in_min min_in_hour hours_in_day days_in_year years_in_century
secs
centuries_in_millinium, milliniums : ----------------,
sec_in_millinium
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) centuries_in_millinium,
cent_int : floor(centuries), years : (centuries - cent_int) years_in_century,
years_int : floor(years), days : (years - years_int) days_in_year,
days_int : floor(days), hours : (days - days_int) hours_in_day,
hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour,
minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min,
sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\
Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(fd,
"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds",
minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int))
else printf(fd, "Unknown"), printf(fd, " | "))
(%i20) omniout_timestr(secs_in) := (secs : convfloat(secs_in),
if secs >= convfloat(0.0) then (sec_in_millinium :
convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day)
convfloat(days_in_year) convfloat(years_in_century)
secs
convfloat(centuries_in_millinium), milliniums : ---------------------------,
convfloat(sec_in_millinium)
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) convfloat(centuries_in_millinium),
cent_int : floor(centuries), years : (centuries - cent_int)
convfloat(years_in_century), years_int : floor(years),
days : (years - years_int) convfloat(days_in_year), days_int : floor(days),
hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours),
minutes : (hours - hours_int) convfloat(min_in_hour),
minutes_int : floor(minutes), seconds :
(minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds),
if millinium_int > 0 then printf(true,
"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(true,
"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o20) omniout_timestr(secs_in) := (secs : convfloat(secs_in),
if secs >= convfloat(0.0) then (sec_in_millinium :
convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day)
convfloat(days_in_year) convfloat(years_in_century)
secs
convfloat(centuries_in_millinium), milliniums : ---------------------------,
convfloat(sec_in_millinium)
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) convfloat(centuries_in_millinium),
cent_int : floor(centuries), years : (centuries - cent_int)
convfloat(years_in_century), years_int : floor(years),
days : (years - years_int) convfloat(days_in_year), days_int : floor(days),
hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours),
minutes : (hours - hours_int) convfloat(min_in_hour),
minutes_int : floor(minutes), seconds :
(minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds),
if millinium_int > 0 then printf(true,
"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(true,
"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i21) mode_declare(ats, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o21) [ats]
(%i22) ats(mmm_ats, array_a, array_b, jjj_ats) :=
(ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats,
iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o22) ats(mmm_ats, array_a, array_b, jjj_ats) :=
(ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats,
iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i23) mode_declare(att, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o23) [att]
(%i24) att(mmm_att, array_aa, array_bb, jjj_att) :=
(ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att,
iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : array_aa array_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o24) att(mmm_att, array_aa, array_bb, jjj_att) :=
(ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att,
iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : array_aa array_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i25) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o25) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i26) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o26) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i27) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o27) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i28) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o28) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i29) log_revs(file, revs) := printf(file, revs)
(%o29) log_revs(file, revs) := printf(file, revs)
(%i30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i31) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o31) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i32) logstart(file) := printf(file, "")
(%o32) logstart(file) := printf(file, "
")
(%i33) logend(file) := printf(file, "
~%")
(%o33) logend(file) := printf(file, "~%")
(%i34) chk_data() := (errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o34) chk_data() := (errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i35) mode_declare(comp_expect_sec, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o35) [comp_expect_sec]
(%i36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) :=
(ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) :=
(ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i37) mode_declare(comp_percent, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o37) [comp_percent]
(%i38) comp_percent(t_end2, t_start2, t2) :=
(sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o38) comp_percent(t_end2, t_start2, t2) :=
(sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i39) mode_declare(factorial_1, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o39) [factorial_1]
(%i40) factorial_1(nnn) := nnn!
(%o40) factorial_1(nnn) := nnn!
(%i41) mode_declare(factorial_3, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o41) [factorial_3]
mmm2!
(%i42) factorial_3(mmm2, nnn2) := -----
nnn2!
mmm2!
(%o42) factorial_3(mmm2, nnn2) := -----
nnn2!
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%i46) arcsin(x) := asin(x)
(%o46) arcsin(x) := asin(x)
(%i47) arccos(x) := acos(x)
(%o47) arccos(x) := acos(x)
(%i48) arctan(x) := atan(x)
(%o48) arctan(x) := atan(x)
(%i49) exact_soln_y1(x) := cos(x) + 1.0
(%o49) exact_soln_y1(x) := cos(x) + 1.0
(%i50) exact_soln_y2(x) := sin(x) + 1.0
(%o50) exact_soln_y2(x) := sin(x) + 1.0
(%i51) exact_soln_y2p(x) := cos(x)
(%o51) exact_soln_y2p(x) := cos(x)
(%i52) exact_soln_y2pp(x) := - sin(x)
(%o52) exact_soln_y2pp(x) := - sin(x)
(%i53) exact_soln_y2ppp(x) := - cos(x)
(%o53) exact_soln_y2ppp(x) := - cos(x)
(%i54) exact_soln_y2pppp(x) := sin(x)
(%o54) exact_soln_y2pppp(x) := sin(x)
(%i55) mainprog() := (define_variable(INFO, 2, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_reached_optimal_h,
false, boolean), define_variable(djd_debug2, true, boolean),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_almost_1, 0.999, float),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(djd_debug, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_hmax, 1.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_warned, false, boolean),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(years_in_century, 100.0, float),
define_variable(glob_dump, false, boolean), 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/mtest7postode.ode#################"),
omniout_str(ALWAYS, "diff ( y2 , x , 5 ) = y1 ;"),
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 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 : 0.0,"), omniout_str(ALWAYS, "x_end : 5.0,"),
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, "array_y2_init[1 + 1] : exact_soln_y2p(x_start),"),
omniout_str(ALWAYS, "array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"),
omniout_str(ALWAYS, "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"),
omniout_str(ALWAYS, "array_y2_init[4 + 1] : exact_soln_y2pppp(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 20,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 1000,"),
omniout_str(ALWAYS, "glob_max_minutes : 15,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y1 (x) := ("),
omniout_str(ALWAYS, "1.0 + 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, "exact_soln_y2p (x) := ("),
omniout_str(ALWAYS, "cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2pp (x) := ("),
omniout_str(ALWAYS, "-sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2ppp (x) := ("),
omniout_str(ALWAYS, "-cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2pppp (x) := ("),
omniout_str(ALWAYS, "sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_x, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y2, 1 + max_terms),
array(array_y1, 1 + max_terms), array(array_type_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_y1_init, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_y2_init, 1 + max_terms), array(array_y2_higher_work, 1 + 6,
1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms),
array(array_y2_higher_work2, 1 + 6, 1 + max_terms),
array(array_complex_pole, 1 + 2, 1 + 3), array(array_real_pole, 1 + 2, 1 + 3),
array(array_y1_higher, 1 + 2, 1 + max_terms),
array(array_y2_higher, 1 + 6, 1 + max_terms),
array(array_y1_set_initial, 1 + 3, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_y1_higher_work2, 1 + 2,
1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms), term : 1,
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_type_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_1st_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y1_init : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_y2_init : 0.0, term : 1 + term), ord : 1,
term
while ord <= 6 do (term : 1, while term <=
max_terms do (array_y2_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_y2_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 6 do (term : 1, while term <=
max_terms do (array_y2_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_complex_pole : 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 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1,
while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_y1_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <= 3 do (array_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_y1_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), 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_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_y1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term),
term
array(array_y2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y2 : 0.0, term : 1 + term),
term
array(array_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_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_5, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_5 : 0.0, term : 1 + term),
term
array_const_5 : 5, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_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, x_start : 0.0, x_end : 5.0,
1
array_y1_init : exact_soln_y1(x_start),
1 + 0
array_y2_init : exact_soln_y2(x_start),
1 + 0
array_y2_init : exact_soln_y2p(x_start),
1 + 1
array_y2_init : exact_soln_y2pp(x_start),
1 + 2
array_y2_init : exact_soln_y2ppp(x_start),
1 + 3
array_y2_init : exact_soln_y2pppp(x_start), glob_h : 1.0E-5,
1 + 4
glob_look_poles : true, glob_max_iter : 20, glob_h : 0.001,
glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_log10_abserr glob_log10_relerr
glob_abserr : 10.0 , glob_relerr : 10.0 ,
chk_data(), array_y2_set_initial : true, array_y2_set_initial : true,
1, 1 1, 2
array_y2_set_initial : true, array_y2_set_initial : true,
1, 3 1, 4
array_y2_set_initial : true, array_y2_set_initial : false,
1, 5 1, 6
array_y2_set_initial : false, array_y2_set_initial : false,
1, 7 1, 8
array_y2_set_initial : false, array_y2_set_initial : false,
1, 9 1, 10
array_y2_set_initial : false, array_y2_set_initial : false,
1, 11 1, 12
array_y2_set_initial : false, array_y2_set_initial : false,
1, 13 1, 14
array_y2_set_initial : false, array_y2_set_initial : false,
1, 15 1, 16
array_y2_set_initial : false, array_y2_set_initial : false,
1, 17 1, 18
array_y2_set_initial : false, array_y2_set_initial : false,
1, 19 1, 20
array_y2_set_initial : false, array_y2_set_initial : false,
1, 21 1, 22
array_y2_set_initial : false, array_y2_set_initial : false,
1, 23 1, 24
array_y2_set_initial : false, array_y2_set_initial : false,
1, 25 1, 26
array_y2_set_initial : false, array_y2_set_initial : false,
1, 27 1, 28
array_y2_set_initial : false, array_y2_set_initial : false,
1, 29 1, 30
array_y1_set_initial : true, array_y1_set_initial : false,
2, 1 2, 2
array_y1_set_initial : false, array_y1_set_initial : false,
2, 3 2, 4
array_y1_set_initial : false, array_y1_set_initial : false,
2, 5 2, 6
array_y1_set_initial : false, array_y1_set_initial : false,
2, 7 2, 8
array_y1_set_initial : false, array_y1_set_initial : false,
2, 9 2, 10
array_y1_set_initial : false, array_y1_set_initial : false,
2, 11 2, 12
array_y1_set_initial : false, array_y1_set_initial : false,
2, 13 2, 14
array_y1_set_initial : false, array_y1_set_initial : false,
2, 15 2, 16
array_y1_set_initial : false, array_y1_set_initial : false,
2, 17 2, 18
array_y1_set_initial : false, array_y1_set_initial : false,
2, 19 2, 20
array_y1_set_initial : false, array_y1_set_initial : false,
2, 21 2, 22
array_y1_set_initial : false, array_y1_set_initial : false,
2, 23 2, 24
array_y1_set_initial : false, array_y1_set_initial : false,
2, 25 2, 26
array_y1_set_initial : false, array_y1_set_initial : false,
2, 27 2, 28
array_y1_set_initial : false, array_y1_set_initial : false,
2, 29 2, 30
if glob_html_log then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, order_diff : 5, term_no : 1,
2
while term_no <= order_diff do (array_y2 :
term_no
term_no - 1
array_y2_init glob_h
term_no
--------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
term_no - 1
array_y2_init glob_h
it
array_y2_higher : ---------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y1 :
term_no
term_no - 1
array_y1_init glob_h
term_no
--------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
term_no - 1
array_y1_init glob_h
it
array_y1_higher : ---------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(), start_array_y2(),
if !array_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), start_array_y1(),
if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
1
convfloat(glob_max_sec)) do (omniout_str
(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop"),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter,
if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2
then (subiter : 1, while subiter <= 6 do (atomall(), subiter : 1 + subiter))
else (subiter : 1, while subiter <= glob_max_terms + 6 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 : 5, ord : 6,
1 1 2
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
6, iii
array_y2_higher
6, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 6, 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 : 5,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
5, iii
array_y2_higher
5, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 5, calc_term : 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 : 5,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
5, iii
array_y2_higher
5, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 5, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_higher
4, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_higher
4, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_higher
4, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 4, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 5, 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 : 5, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 4, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 6, 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 : 6, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 5, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 5, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 4, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y2 : array_y2_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y2_higher :
ord, term_no
array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
order_diff : 1, ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (array_y1_higher_work :
2, iii
array_y1_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y1 : array_y1_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y1_higher :
ord, term_no
array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"),
if glob_iter >= glob_max_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y2 , x , 5 ) = y1 ;"),
omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 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,
"2012-06-15T22:49:49-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mtest7"),
logitem_str(html_log_file, "diff ( y2 , x , 5 ) = y1 ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_integer(html_log_file,
glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 090 | "), logitem_str(html_log_file, "mtest7 diffeq.max"), logitem_str(html_log_file, "\
mtest7 maxima results"),
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs"),
logend(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logitem_str(html_log_file,
"diff ( y1 , x , 1 ) = m1 * y2 + 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))
(%o55) mainprog() := (define_variable(INFO, 2, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_reached_optimal_h,
false, boolean), define_variable(djd_debug2, true, boolean),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_almost_1, 0.999, float),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(djd_debug, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_hmax, 1.0, float),
define_variable(hours_in_day, 24.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_warned, false, boolean),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(years_in_century, 100.0, float),
define_variable(glob_dump, false, boolean), 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/mtest7postode.ode#################"),
omniout_str(ALWAYS, "diff ( y2 , x , 5 ) = y1 ;"),
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 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 : 0.0,"), omniout_str(ALWAYS, "x_end : 5.0,"),
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, "array_y2_init[1 + 1] : exact_soln_y2p(x_start),"),
omniout_str(ALWAYS, "array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"),
omniout_str(ALWAYS, "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"),
omniout_str(ALWAYS, "array_y2_init[4 + 1] : exact_soln_y2pppp(x_start),"),
omniout_str(ALWAYS, "glob_h : 0.00001,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 20,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_h : 0.001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 1000,"),
omniout_str(ALWAYS, "glob_max_minutes : 15,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y1 (x) := ("),
omniout_str(ALWAYS, "1.0 + 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, "exact_soln_y2p (x) := ("),
omniout_str(ALWAYS, "cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2pp (x) := ("),
omniout_str(ALWAYS, "-sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2ppp (x) := ("),
omniout_str(ALWAYS, "-cos(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, "exact_soln_y2pppp (x) := ("),
omniout_str(ALWAYS, "sin(x) "), omniout_str(ALWAYS, ");"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30,
glob_max_terms : max_terms, glob_html_log : true,
array(array_x, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y2, 1 + max_terms),
array(array_y1, 1 + max_terms), array(array_type_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_y1_init, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_y2_init, 1 + max_terms), array(array_y2_higher_work, 1 + 6,
1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms),
array(array_y2_higher_work2, 1 + 6, 1 + max_terms),
array(array_complex_pole, 1 + 2, 1 + 3), array(array_real_pole, 1 + 2, 1 + 3),
array(array_y1_higher, 1 + 2, 1 + max_terms),
array(array_y2_higher, 1 + 6, 1 + max_terms),
array(array_y1_set_initial, 1 + 3, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_y1_higher_work2, 1 + 2,
1 + max_terms), array(array_y1_higher_work, 1 + 2, 1 + max_terms), term : 1,
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_type_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_1st_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y1_init : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_y2_init : 0.0, term : 1 + term), ord : 1,
term
while ord <= 6 do (term : 1, while term <=
max_terms do (array_y2_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_y2_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 6 do (term : 1, while term <=
max_terms do (array_y2_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_complex_pole : 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 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1,
while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1,
while term <= max_terms do (array_y1_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <= 3 do (array_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_y1_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), 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_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_y1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term),
term
array(array_y2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y2 : 0.0, term : 1 + term),
term
array(array_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_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_5, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_5 : 0.0, term : 1 + term),
term
array_const_5 : 5, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_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, x_start : 0.0, x_end : 5.0,
1
array_y1_init : exact_soln_y1(x_start),
1 + 0
array_y2_init : exact_soln_y2(x_start),
1 + 0
array_y2_init : exact_soln_y2p(x_start),
1 + 1
array_y2_init : exact_soln_y2pp(x_start),
1 + 2
array_y2_init : exact_soln_y2ppp(x_start),
1 + 3
array_y2_init : exact_soln_y2pppp(x_start), glob_h : 1.0E-5,
1 + 4
glob_look_poles : true, glob_max_iter : 20, glob_h : 0.001,
glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_log10_abserr glob_log10_relerr
glob_abserr : 10.0 , glob_relerr : 10.0 ,
chk_data(), array_y2_set_initial : true, array_y2_set_initial : true,
1, 1 1, 2
array_y2_set_initial : true, array_y2_set_initial : true,
1, 3 1, 4
array_y2_set_initial : true, array_y2_set_initial : false,
1, 5 1, 6
array_y2_set_initial : false, array_y2_set_initial : false,
1, 7 1, 8
array_y2_set_initial : false, array_y2_set_initial : false,
1, 9 1, 10
array_y2_set_initial : false, array_y2_set_initial : false,
1, 11 1, 12
array_y2_set_initial : false, array_y2_set_initial : false,
1, 13 1, 14
array_y2_set_initial : false, array_y2_set_initial : false,
1, 15 1, 16
array_y2_set_initial : false, array_y2_set_initial : false,
1, 17 1, 18
array_y2_set_initial : false, array_y2_set_initial : false,
1, 19 1, 20
array_y2_set_initial : false, array_y2_set_initial : false,
1, 21 1, 22
array_y2_set_initial : false, array_y2_set_initial : false,
1, 23 1, 24
array_y2_set_initial : false, array_y2_set_initial : false,
1, 25 1, 26
array_y2_set_initial : false, array_y2_set_initial : false,
1, 27 1, 28
array_y2_set_initial : false, array_y2_set_initial : false,
1, 29 1, 30
array_y1_set_initial : true, array_y1_set_initial : false,
2, 1 2, 2
array_y1_set_initial : false, array_y1_set_initial : false,
2, 3 2, 4
array_y1_set_initial : false, array_y1_set_initial : false,
2, 5 2, 6
array_y1_set_initial : false, array_y1_set_initial : false,
2, 7 2, 8
array_y1_set_initial : false, array_y1_set_initial : false,
2, 9 2, 10
array_y1_set_initial : false, array_y1_set_initial : false,
2, 11 2, 12
array_y1_set_initial : false, array_y1_set_initial : false,
2, 13 2, 14
array_y1_set_initial : false, array_y1_set_initial : false,
2, 15 2, 16
array_y1_set_initial : false, array_y1_set_initial : false,
2, 17 2, 18
array_y1_set_initial : false, array_y1_set_initial : false,
2, 19 2, 20
array_y1_set_initial : false, array_y1_set_initial : false,
2, 21 2, 22
array_y1_set_initial : false, array_y1_set_initial : false,
2, 23 2, 24
array_y1_set_initial : false, array_y1_set_initial : false,
2, 25 2, 26
array_y1_set_initial : false, array_y1_set_initial : false,
2, 27 2, 28
array_y1_set_initial : false, array_y1_set_initial : false,
2, 29 2, 30
if glob_html_log then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, order_diff : 5, term_no : 1,
2
while term_no <= order_diff do (array_y2 :
term_no
term_no - 1
array_y2_init glob_h
term_no
--------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
term_no - 1
array_y2_init glob_h
it
array_y2_higher : ---------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y1 :
term_no
term_no - 1
array_y1_init glob_h
term_no
--------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
term_no - 1
array_y1_init glob_h
it
array_y1_higher : ---------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(), start_array_y2(),
if !array_y2_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y2_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), start_array_y1(),
if !array_y1_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y1_higher !, log10norm : log10(tmp),
! 1, 1!
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
1
convfloat(glob_max_sec)) do (omniout_str
(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop"),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter,
if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2
then (subiter : 1, while subiter <= 6 do (atomall(), subiter : 1 + subiter))
else (subiter : 1, while subiter <= glob_max_terms + 6 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 : 5, ord : 6,
1 1 2
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
6, iii
array_y2_higher
6, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 6, 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 : 5,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
5, iii
array_y2_higher
5, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 5, calc_term : 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 : 5,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
5, iii
array_y2_higher
5, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 5, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_higher
4, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_higher
4, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 4,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
4, iii
array_y2_higher
4, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 4, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 4, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 3,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
3, iii
array_y2_higher
3, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 5, 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 : 5, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 4, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 2,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
2, iii
array_y2_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 6, 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 : 6, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 5, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 5, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 4, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 4, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 3, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 3, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y2_higher_work :
1, iii
array_y2_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y2_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y2_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y2 : array_y2_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y2_higher :
ord, term_no
array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
order_diff : 1, ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (array_y1_higher_work :
2, iii
array_y1_higher
2, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 2, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------, ord : 1,
ord, calc_term convfp(calc_term - 1)!
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_y1_higher_work :
1, iii
array_y1_higher
1, iii
---------------------
calc_term - 1
glob_h
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum :
array_y1_higher_work + temp_sum, iii : iii - 1),
ord, iii
calc_term - 1
temp_sum glob_h
array_y1_higher_work2 : ----------------------------,
ord, calc_term convfp(calc_term - 1)!
term_no : glob_max_terms, while term_no >=
1 do (array_y1 : array_y1_higher_work2 , ord : 1,
term_no 1, term_no
while ord <= order_diff do (array_y1_higher :
ord, term_no
array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1),
ord, term_no
display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"),
if glob_iter >= glob_max_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y2 , x , 5 ) = y1 ;"),
omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 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,
"2012-06-15T22:49:49-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mtest7"),
logitem_str(html_log_file, "diff ( y2 , x , 5 ) = y1 ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_integer(html_log_file,
glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 090 | "), logitem_str(html_log_file, "mtest7 diffeq.max"), logitem_str(html_log_file, "\
mtest7 maxima results"),
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs"),
logend(html_log_file), logditto(html_log_file), logditto(html_log_file),
logditto(html_log_file), logitem_str(html_log_file,
"diff ( y1 , x , 1 ) = m1 * y2 + 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))
(%i56) mainprog()
"##############ECHO OF PROBLEM#################"
"##############temp/mtest7postode.ode#################"
"diff ( y2 , x , 5 ) = y1 ;"
"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 32,"
"max_terms : 30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : 0.0,"
"x_end : 5.0,"
"array_y1_init[0 + 1] : exact_soln_y1(x_start),"
"array_y2_init[0 + 1] : exact_soln_y2(x_start),"
"array_y2_init[1 + 1] : exact_soln_y2p(x_start),"
"array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"
"array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"
"array_y2_init[4 + 1] : exact_soln_y2pppp(x_start),"
"glob_h : 0.00001,"
"glob_look_poles : true,"
"glob_max_iter : 20,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_h : 0.001 ,"
"glob_look_poles : true,"
"glob_max_iter : 1000,"
"glob_max_minutes : 15,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y1 (x) := ("
"1.0 + cos(x) "
");"
"exact_soln_y2 (x) := ("
"1.0 + sin(x) "
");"
"exact_soln_y2p (x) := ("
"cos(x) "
");"
"exact_soln_y2pp (x) := ("
"-sin(x) "
");"
"exact_soln_y2ppp (x) := ("
"-cos(x) "
");"
"exact_soln_y2pppp (x) := ("
"sin(x) "
");"
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = 0.0 " "
y2[1] (analytic) = 1. " "
y2[1] (numeric) = 1. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 2. " "
y1[1] (numeric) = 2. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
x[1] = 0.0 " "
y2[1] (analytic) = 1. " "
y2[1] (numeric) = 1. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 2. " "
y1[1] (numeric) = 2. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.000E-3 " "
y2[1] (analytic) = 1.0009999998333334 " "
y2[1] (numeric) = 1.0009999998333334 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9999995000000417 " "
y1[1] (numeric) = 1.9999995000000417 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.000E-3 " "
y2[1] (analytic) = 1.001999998666667 " "
y2[1] (numeric) = 1.0019999986666672 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.216014024156684200000000000000E-14 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9999980000006667 " "
y1[1] (numeric) = 1.9999980000006667 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.000E-3 " "
y2[1] (analytic) = 1.002999995500002 " "
y2[1] (numeric) = 1.0029999955000042 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.21380464527659970000000000000E-13 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.999995500003375 " "
y1[1] (numeric) = 1.9999955000033751 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11022552263070910000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.000E-3 " "
y2[1] (analytic) = 1.0039999893333418 " "
y2[1] (numeric) = 1.0039999893333504 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.6252387291620470000000000000E-13 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9999920000106668 " "
y1[1] (numeric) = 1.9999920000106668 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.000E-3 " "
y2[1] (analytic) = 1.0049999791666928 " "
y2[1] (numeric) = 1.0049999791667188 " "
absolute error = 2.597921877622866300000000000000E-14 " "
relative error = 2.584996946743186000000000000E-12 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9999875000260416 " "
y1[1] (numeric) = 1.9999875000260419 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110229963547972600000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.000E-3 " "
y2[1] (analytic) = 1.0059999640000648 " "
y2[1] (numeric) = 1.0059999640001296 " "
absolute error = 6.48370246381091400000000000000E-14 " "
relative error = 6.445032500826706000000000000E-12 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.999982000054 " "
y1[1] (numeric) = 1.999982000054 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.000E-3 " "
y2[1] (analytic) = 1.0069999428334735 " "
y2[1] (numeric) = 1.0069999428336134 " "
absolute error = 1.39888101102769720000000000000E-13 " "
relative error = 1.38915699150047400000000000E-11 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9999755001000414 " "
y1[1] (numeric) = 1.9999755001000414 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.000E-3 " "
y2[1] (analytic) = 1.0079999146669398 " "
y2[1] (numeric) = 1.0079999146672127 " "
absolute error = 2.7289281945286350000000000000E-13 " "
relative error = 2.70727026344076470000000000E-11 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9999680001706663 " "
y1[1] (numeric) = 1.9999680001706661 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110240788383030400000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.000000000000001000E-3 " "
y2[1] (analytic) = 1.008999878500492 " "
y2[1] (numeric) = 1.0089998785009842 " "
absolute error = 4.9205084451386940000000000000E-13 " "
relative error = 4.876619462483209300000000000E-11 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9999595002733743 " "
y1[1] (numeric) = 1.9999595002733737 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.330736520834747000000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.000000000000000200E-2 " "
y2[1] (analytic) = 1.0099998333341667 " "
y2[1] (numeric) = 1.009999833335 " "
absolute error = 8.3333340228364250000000000000E-13 " "
relative error = 8.250827126700400000000000E-11 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9999500004166653 " "
y1[1] (numeric) = 1.999950000416664 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 6.6615046839802300000000000000E-14 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.100000000000000300E-2 " "
y2[1] (analytic) = 1.0109997781680087 " "
y2[1] (numeric) = 1.010999778169351 " "
absolute error = 1.3422596367718143000000000000E-12 " "
relative error = 1.3276557183860790000000000E-10 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9999395006100391 " "
y1[1] (numeric) = 1.999939500610037 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.11025660954894540000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.200000000000000400E-2 " "
y2[1] (analytic) = 1.0119997120020736 " "
y2[1] (numeric) = 1.0119997120041473 " "
absolute error = 2.0736745653948674000000000000E-12 " "
relative error = 2.04908612206266940000000000E-10 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9999280008639957 " "
y1[1] (numeric) = 1.999928000863992 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 1.88744708914260230000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.300000000000000600E-2 " "
y2[1] (analytic) = 1.0129996338364273 " "
y2[1] (numeric) = 1.0129996338395217 " "
absolute error = 3.0944136142352363000000000000E-12 " "
relative error = 3.05470358613663840000000000E-10 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.999915501190035 " "
y1[1] (numeric) = 1.9999155011900285 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 3.21978280532065200000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.400000000000000700E-2 " "
y2[1] (analytic) = 1.0139995426711486 " "
y2[1] (numeric) = 1.0139995426756305 " "
absolute error = 4.481970350411757000000000000E-12 " "
relative error = 4.42009109649599800000000000E-10 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9999020016006561 " "
y1[1] (numeric) = 1.999902001600646 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 5.1072761657203440000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.500000000000000800E-2 " "
y2[1] (analytic) = 1.014999437506328 " "
y2[1] (numeric) = 1.0149994375126563 " "
absolute error = 6.328271240363392000000000000E-12 " "
relative error = 6.2347534456874410000000000E-10 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9998875021093592 " "
y1[1] (numeric) = 1.9998875021093434 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 7.8830268867869260000000000000E-13 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.600000000000001000E-2 " "
y2[1] (analytic) = 1.0159993173420714 " "
y2[1] (numeric) = 1.0159993173508097 " "
absolute error = 8.738343382219682000000000000E-12 " "
relative error = 8.6007374543123000000000000E-10 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9998720027306434 " "
y1[1] (numeric) = 1.99987200273062 " "
absolute error = 2.331468351712828700000000000000E-14 " "
relative error = 1.165808786027016100000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.700000000000001000E-2 " "
y2[1] (analytic) = 1.0169991811784986 " "
y2[1] (numeric) = 1.016999181190331 " "
absolute error = 1.183231290724506800000000000E-11 " "
relative error = 1.1634535333188552000000000E-9 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.999855503480008 " "
y1[1] (numeric) = 1.9998555034799745 " "
absolute error = 3.35287353436797300000000000000E-14 " "
relative error = 1.6765578955747243000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.80000000000000100E-2 " "
y2[1] (analytic) = 1.0179990280157463 " "
y2[1] (numeric) = 1.0179990280314928 " "
absolute error = 1.57465152028635200000000000E-11 " "
relative error = 1.5468104359152646000000000E-9 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9998380043739528 " "
y1[1] (numeric) = 1.9998380043739055 " "
absolute error = 4.72955008490316700000000000000E-14 " "
relative error = 2.364966599574023000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.90000000000000100E-2 " "
y2[1] (analytic) = 1.0189988568539674 " "
y2[1] (numeric) = 1.0189988568746016 " "
absolute error = 2.06341610464733100000000000E-11 " "
relative error = 2.0249444744402093000000000E-9 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9998195054299763 " "
y1[1] (numeric) = 1.9998195054299108 " "
absolute error = 6.55031584528842400000000000000E-14 " "
relative error = 3.275453523431884000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.00000000000000120E-2 " "
y2[1] (analytic) = 1.0199986666933332 " "
y2[1] (numeric) = 1.0199986667199998 " "
absolute error = 2.66666688730765600000000000E-11 " "
relative error = 2.614382718707416000000000E-9 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9998000066665778 " "
y1[1] (numeric) = 1.9998000066664887 " "
absolute error = 8.90398865749375500000000000000E-14 " "
relative error = 4.452439557861396000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.10000000000000130E-2 " "
y2[1] (analytic) = 1.0209984565340338 " "
y2[1] (numeric) = 1.020998456568068 " "
absolute error = 3.403433090909402400000000000E-11 " "
relative error = 3.3334360783100290000000000E-9 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9997795081032559 " "
y1[1] (numeric) = 1.9997795081031366 " "
absolute error = 1.1923795284474181000000000000E-13 " "
relative error = 5.962554989766659000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.200000000000001400E-2 " "
y2[1] (analytic) = 1.0219982253762798 " "
y2[1] (numeric) = 1.0219982254192268 " "
absolute error = 4.294697930617985500000000000E-11 " "
relative error = 4.202255761292307000000000E-9 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9997580097605092 " "
y1[1] (numeric) = 1.9997580097603516 " "
absolute error = 1.57651669496772230000000000000E-13 " "
relative error = 7.883537344383613000000000000E-12 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.300000000000001500E-2 " "
y2[1] (analytic) = 1.0229979722203022 " "
y2[1] (numeric) = 1.0229979722739384 " "
absolute error = 5.36362065872708600000000000E-11 " "
relative error = 5.243041339647966000000000E-9 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.999735511659836 " "
y1[1] (numeric) = 1.9997355116596303 " "
absolute error = 2.05835348765504020000000000000E-13 " "
relative error = 1.029312864453034300000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.400000000000001600E-2 " "
y2[1] (analytic) = 1.0239976960663544 " "
y2[1] (numeric) = 1.0239976961327095 " "
absolute error = 6.63551436019815800000000000E-11 " "
relative error = 6.480009071981526000000000E-9 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9997120138237345 " "
y1[1] (numeric) = 1.999712013823469 " "
absolute error = 2.65565347490337440000000000000E-13 " "
relative error = 1.32801796285925500000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.500000000000001700E-2 " "
y2[1] (analytic) = 1.0249973959147123 " "
y2[1] (numeric) = 1.0249973959960925 " "
absolute error = 8.13802358834436700000000000E-11 " "
relative error = 7.939555379145093000000000E-9 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9996875162757026 " "
y1[1] (numeric) = 1.9996875162753633 " "
absolute error = 3.39284156325447840000000000000E-13 " "
relative error = 1.696685874987828600000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.600000000000002000E-2 " "
y2[1] (analytic) = 1.0259970707656765 " "
y2[1] (numeric) = 1.025997070864688 " "
absolute error = 9.90114656929108600000000000E-11 " "
relative error = 9.650267872501919000000000E-9 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9996620190402377 " "
y1[1] (numeric) = 1.9996620190398084 " "
absolute error = 4.2921222132008550000000000000E-13 " "
relative error = 2.14642383179379100000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.700000000000002000E-2 " "
y2[1] (analytic) = 1.0269967196195722 " "
y2[1] (numeric) = 1.0269967197391463 " "
absolute error = 1.1957412837659831000000000E-10 " "
relative error = 1.164308766447587600000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.999635522142837 " "
y1[1] (numeric) = 1.9996355221422988 " "
absolute error = 5.3823612233827590000000000000E-13 " "
relative error = 2.691671138955836000000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.800000000000002000E-2 " "
y2[1] (analytic) = 1.0279963414767503 " "
y2[1] (numeric) = 1.02799634162017 " "
absolute error = 1.43419720544102350000000000E-10 " "
relative error = 1.395138433450796300000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9996080256099975 " "
y1[1] (numeric) = 1.999608025609328 " "
absolute error = 6.6946448384896940000000000000E-13 " "
relative error = 3.347978580175700000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.90000000000000200E-2 " "
y2[1] (analytic) = 1.0289959353375895 " "
y2[1] (numeric) = 1.0289959355085156 " "
absolute error = 1.70926162113005380000000000E-10 " "
relative error = 1.66109657232930200000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9995795294692156 " "
y1[1] (numeric) = 1.9995795294683893 " "
absolute error = 8.2622797492604150000000000000E-13 " "
relative error = 4.13200856854821940000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.00000000000000200E-2 " "
y2[1] (analytic) = 1.0299955002024956 " "
y2[1] (numeric) = 1.0299955004049957 " "
absolute error = 2.02500016754925130000000000E-10 " "
relative error = 1.966028169201845300000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9995500337489875 " "
y1[1] (numeric) = 1.999550033747975 " "
absolute error = 1.0125233984581428000000000000E-12 " "
relative error = 5.063756251999091000000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.10000000000000200E-2 " "
y2[1] (analytic) = 1.0309950350719042 " "
y2[1] (numeric) = 1.0309950353104804 " "
absolute error = 2.38576269850909740000000000E-10 " "
relative error = 2.314038979191309400000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.999519538478809 " "
y1[1] (numeric) = 1.9995195384775764 " "
absolute error = 1.2325696019388488000000000000E-12 " "
relative error = 6.16432887110751200000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.20000000000000230E-2 " "
y2[1] (analytic) = 1.0319945389462801 " "
y2[1] (numeric) = 1.0319945392259005 " "
absolute error = 2.7962032689288210000000000E-10 " "
relative error = 2.709513629581692400000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9994880436891753 " "
y1[1] (numeric) = 1.999488043687684 " "
absolute error = 1.4912515666765103000000000000E-12 " "
relative error = 7.45816696120403700000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.30000000000000240E-2 " "
y2[1] (analytic) = 1.0329940108261197 " "
y2[1] (numeric) = 1.0329940111522482 " "
absolute error = 3.2612845757284960000000000E-10 " "
relative error = 3.1571185714042405000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9994555494115813 " "
y1[1] (numeric) = 1.9994555494097876 " "
absolute error = 1.793676318584403000000000000E-12 " "
relative error = 8.97082367803706800000000000E-11 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.40000000000000250E-2 " "
y2[1] (analytic) = 1.0339934497119514 " "
y2[1] (numeric) = 1.03399345009058 " "
absolute error = 3.786286839613240000000000E-10 " "
relative error = 3.66180930901256600000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9994220556785212 " "
y1[1] (numeric) = 1.9994220556763755 " "
absolute error = 2.1456170173905775000000000000E-12 " "
relative error = 1.07311861009877870000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.500000000000002600E-2 " "
y2[1] (analytic) = 1.0349928546043363 " "
y2[1] (numeric) = 1.0349928550420187 " "
absolute error = 4.37682334819555760000000000E-10 " "
relative error = 4.22884402411527500000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9993875625234887 " "
y1[1] (numeric) = 1.9993875625209354 " "
absolute error = 2.553290912032935000000000000E-12 " "
relative error = 1.27703650852481450000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.600000000000002600E-2 " "
y2[1] (analytic) = 1.0359922245038693 " "
y2[1] (numeric) = 1.0359922250077542 " "
absolute error = 5.0388493377795380000000000E-10 " "
relative error = 4.863790691279188400000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9993520699809768 " "
y1[1] (numeric) = 1.9993520699779534 " "
absolute error = 3.0233593406592263000000000000E-12 " "
relative error = 1.51216956035561680000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.700000000000003000E-2 " "
y2[1] (analytic) = 1.0369915584111808 " "
y2[1] (numeric) = 1.0369915589890473 " "
absolute error = 5.7786642138069060000000000E-10 " "
relative error = 5.57252772882803800000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9993155780864782 " "
y1[1] (numeric) = 1.9993155780829148 " "
absolute error = 3.5633718198369024000000000000E-12 " "
relative error = 1.78229583108003600000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.80000000000000300E-2 " "
y2[1] (analytic) = 1.037990855326937 " "
y2[1] (numeric) = 1.0379908559872302 " "
absolute error = 6.6029315348714590000000000E-10 " "
relative error = 6.36126175966331400000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.999278086876485 " "
y1[1] (numeric) = 1.9992780868723032 " "
absolute error = 4.181766044553114600000000000E-12 " "
relative error = 2.0916380127420780000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.90000000000000300E-2 " "
y2[1] (analytic) = 1.0389901142518412 " "
y2[1] (numeric) = 1.0389901150037095 " "
absolute error = 7.5186834536111750000000000E-10 " "
relative error = 7.23653031003596100000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9992395963884881 " "
y1[1] (numeric) = 1.999239596383601 " "
absolute error = 4.887201754399939000000000000E-12 " "
relative error = 2.4445302920312250000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.00000000000000300E-2 " "
y2[1] (analytic) = 1.0399893341866342 " "
y2[1] (numeric) = 1.0399893350399676 " "
absolute error = 8.5333340393844990000000000E-10 " "
relative error = 8.20521303332244000000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.999200106660978 " "
y1[1] (numeric) = 1.9992001066552891 " "
absolute error = 5.688782778179302000000000000E-12 " "
relative error = 2.84552944911582060000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.10000000000000300E-2 " "
y2[1] (analytic) = 1.0409885141320965 " "
y2[1] (numeric) = 1.0409885150975648 " "
absolute error = 9.654683719162449000000000E-10 " "
relative error = 9.27453433740510600000000E-8 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9991596177334445 " "
y1[1] (numeric) = 1.9991596177268471 " "
absolute error = 6.59738930153253000000000000E-12 " "
relative error = 3.3000813156742070000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.20000000000000300E-2 " "
y2[1] (analytic) = 1.041987653089048 " "
y2[1] (numeric) = 1.0419876541781417 " "
absolute error = 1.0890937041097004000000000E-9 " "
relative error = 1.04520787830930930000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9991181296463765 " "
y1[1] (numeric) = 1.999118129638753 " "
absolute error = 7.6234574208911000000000000E-12 " "
relative error = 3.81341017713626160000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.30000000000000300E-2 " "
y2[1] (analytic) = 1.0429867500583498 " "
y2[1] (numeric) = 1.0429867512834203 " "
absolute error = 1.2250704894967157000000000E-9 " "
relative error = 1.17457914918687050000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9990756424412623 " "
y1[1] (numeric) = 1.9990756424324827 " "
absolute error = 8.779643678735738000000000000E-12 " "
relative error = 4.39185166000726050000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.40000000000000340E-2 " "
y2[1] (analytic) = 1.0439858040409051 " "
y2[1] (numeric) = 1.0439858054152074 " "
absolute error = 1.3743022275747308000000000E-9 " "
relative error = 1.31639934399039320000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9990321561605888 " "
y1[1] (numeric) = 1.9990321561505107 " "
absolute error = 1.007816052833732100000000000E-11 " "
relative error = 5.0415199661889320000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.50000000000000340E-2 " "
y2[1] (analytic) = 1.0449848140376603 " "
y2[1] (numeric) = 1.044984815575395 " "
absolute error = 1.5377346063161212000000000E-9 " "
relative error = 1.47153775409859940000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9989876708478425 " "
y1[1] (numeric) = 1.9989876708363095 " "
absolute error = 1.153299677980612600000000000E-11 " "
relative error = 5.7694186652559840000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.600000000000003500E-2 " "
y2[1] (analytic) = 1.045983779049605 " "
y2[1] (numeric) = 1.0459837807659633 " "
absolute error = 1.7163583887480627000000000E-9 " "
relative error = 1.640903447190710000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9989421865475085 " "
y1[1] (numeric) = 1.9989421865343497 " "
absolute error = 1.315880737706720500000000000E-11 " "
relative error = 6.5828854209108270000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.700000000000003600E-2 " "
y2[1] (analytic) = 1.0469826980777746 " "
y2[1] (numeric) = 1.046982699988983 " "
absolute error = 1.9112085247741106000000000E-9 " "
relative error = 1.8254442296735430000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9988957033050712 " "
y1[1] (numeric) = 1.9988957032901 " "
absolute error = 1.49711354424653100000000000E-11 " "
relative error = 7.4897031484490710000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.800000000000003700E-2 " "
y2[1] (analytic) = 1.04798157012325 " "
y2[1] (numeric) = 1.0479815722466164 " "
absolute error = 2.12336637162025000000000E-9 " "
relative error = 2.02614858138252100000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9988482211670138 " "
y1[1] (numeric) = 1.998848221150027 " "
absolute error = 1.698685636597474500000000000E-11 " "
relative error = 8.4983222768445540000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.90000000000000400E-2 " "
y2[1] (analytic) = 1.0489803941871592 " "
y2[1] (numeric) = 1.0489803965411197 " "
absolute error = 2.3539605820133147000000000E-9 " "
relative error = 2.2440463092137838000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9987997401808184 " "
y1[1] (numeric) = 1.9987997401615945 " "
absolute error = 1.922395576059443600000000000E-11 " "
relative error = 9.6177497796029190000000000E-10 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.00000000000000300E-2 " "
y2[1] (analytic) = 1.0499791692706784 " "
y2[1] (numeric) = 1.0499791718748452 " "
absolute error = 2.604166882136383000000000E-9 " "
relative error = 2.4802081396960020000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9987502603949663 " "
y1[1] (numeric) = 1.9987502603732648 " "
absolute error = 2.170152946234793500000000000E-11 " "
relative error = 1.0857549285852035000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.10000000000000300E-2 " "
y2[1] (analytic) = 1.0509778943750323 " "
y2[1] (numeric) = 1.050977897250243 " "
absolute error = 2.8752107361640356000000000E-9 " "
relative error = 2.73574806049920740000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.998699781858937 " "
y1[1] (numeric) = 1.9986997818344974 " "
absolute error = 2.443956148567849600000000000E-11 " "
relative error = 1.2227730101089979000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.20000000000000400E-2 " "
y2[1] (analytic) = 1.0519765685014963 " "
y2[1] (numeric) = 1.0519765716698635 " "
absolute error = 3.1683671242177525000000000E-9 " "
relative error = 3.01182290469737400000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9986483046232089 " "
y1[1] (numeric) = 1.9986483045957495 " "
absolute error = 2.745936811265892000000000000E-11 " "
relative error = 1.3738969507111778000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.30000000000000400E-2 " "
y2[1] (analytic) = 1.052975190651396 " "
y2[1] (numeric) = 1.0529751941363588 " "
absolute error = 3.4849627628119606000000000E-9 " "
relative error = 3.30963425705792570000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9985958287392593 " "
y1[1] (numeric) = 1.9985958287084753 " "
absolute error = 3.078404198220141600000000000E-11 " "
relative error = 1.5402835100291587000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.40000000000000400E-2 " "
y2[1] (analytic) = 1.0539737598261096 " "
y2[1] (numeric) = 1.053973763652485 " "
absolute error = 3.82637543872022000000000E-9 " "
relative error = 3.6304276107893960000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9985423542595644 " "
y1[1] (numeric) = 1.9985423542251268 " "
absolute error = 3.44375639116378800000000000E-11 " "
relative error = 1.7231340550896945000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.50000000000000400E-2 " "
y2[1] (analytic) = 1.0549722750270678 " "
y2[1] (numeric) = 1.0549722792211045 " "
absolute error = 4.194036673510481700000000E-9 " "
relative error = 3.97549468624933600000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9984878812375984 " "
y1[1] (numeric) = 1.9984878811991529 " "
absolute error = 3.844546903053469600000000000E-11 " "
relative error = 1.923727904055474000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.60000000000000400E-2 " "
y2[1] (analytic) = 1.0559707352557555 " "
y2[1] (numeric) = 1.0559707398451872 " "
absolute error = 4.58943172354509000000000E-9 " "
relative error = 4.3461732132505850000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9984324097278345 " "
y1[1] (numeric) = 1.9984324096849995 " "
absolute error = 4.28350688252976400000000000E-11 " "
relative error = 2.143433453980629000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.700000000000004000E-2 " "
y2[1] (analytic) = 1.0569691395137126 " "
y2[1] (numeric) = 1.0569691445278133 " "
absolute error = 5.014100690203804000000000E-9 " "
relative error = 4.7438477650451344000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9983759397857437 " "
y1[1] (numeric) = 1.9983759397381096 " "
absolute error = 4.76341188715423400000000000E-11 " "
relative error = 2.383641532265918000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.800000000000004000E-2 " "
y2[1] (analytic) = 1.057967486802535 " "
y2[1] (numeric) = 1.057967492272175 " "
absolute error = 5.469639852151431000000000E-9 " "
relative error = 5.1699507975260830000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9983184714677966 " "
y1[1] (numeric) = 1.9983184714149231 " "
absolute error = 5.28734833693533800000000000E-11 " "
relative error = 2.64589874558468000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.900000000000004000E-2 " "
y2[1] (analytic) = 1.0589657761238755 " "
y2[1] (numeric) = 1.058965782081578 " "
absolute error = 5.957702553516242000000000E-9 " "
relative error = 5.6259632632540560000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9982600048314612 " "
y1[1] (numeric) = 1.998260004772877 " "
absolute error = 5.85842485634202600000000000E-11 " "
relative error = 2.931763054946467000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.000000000000004000E-2 " "
y2[1] (analytic) = 1.0599640064794447 " "
y2[1] (numeric) = 1.0599640129594448 " "
absolute error = 6.480000092068394000000000E-9 " "
relative error = 6.1134152220800510000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9982005399352043 " "
y1[1] (numeric) = 1.998200539870404 " "
absolute error = 6.48003872782965100000000000E-11 " "
relative error = 3.2429371318455250000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.10000000000000400E-2 " "
y2[1] (analytic) = 1.0609621768710125 " "
y2[1] (numeric) = 1.060962183909315 " "
absolute error = 7.03830260739835000000000E-9 " "
relative error = 6.6338864483894210000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9981400768384905 " "
y1[1] (numeric) = 1.998140076766934 " "
absolute error = 7.15565384723504400000000000E-11 " "
relative error = 3.581157262286089000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.20000000000000400E-2 " "
y2[1] (analytic) = 1.0619602863004083 " "
y2[1] (numeric) = 1.0619602939348487 " "
absolute error = 7.634440413184507000000000E-9 " "
relative error = 7.1890074531703050000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.998078615601783 " "
y1[1] (numeric) = 1.9980786155228933 " "
absolute error = 7.8889561549999600000000000E-11 " "
relative error = 3.948271150794513400000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.30000000000000400E-2 " "
y2[1] (analytic) = 1.062958333769523 " "
y2[1] (numeric) = 1.0629583420398276 " "
absolute error = 8.27030466332701000000000E-9 " "
relative error = 7.7804598737171460000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.998016156286543 " "
y1[1] (numeric) = 1.9980161561997045 " "
absolute error = 8.6838536361710790000000000E-11 " "
relative error = 4.346237946499214600000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.40000000000000500E-2 " "
y2[1] (analytic) = 1.0639563182803093 " "
y2[1] (numeric) = 1.0639563272281578 " "
absolute error = 8.947848462170782000000000E-9 " "
relative error = 8.4099772786098410000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9979526989552299 " "
y1[1] (numeric) = 1.997952698859786 " "
absolute error = 9.54438750255803800000000000E-11 " "
relative error = 4.777083815622358000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.50000000000000500E-2 " "
y2[1] (analytic) = 1.0649542388347826 " "
y2[1] (numeric) = 1.0649542485038712 " "
absolute error = 9.669088640862356000000000E-9 " "
relative error = 9.0793465937482610000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.997888243671301 " "
y1[1] (numeric) = 1.9978882435665524 " "
absolute error = 1.04748654194963820000000000E-10 " "
relative error = 5.242968645857721000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.60000000000000500E-2 " "
y2[1] (analytic) = 1.0659520944350225 " "
y2[1] (numeric) = 1.0659521048711273 " "
absolute error = 1.043610486917145900000000E-8 " "
relative error = 9.7904070207796890000000E-7 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9978227904992116 " "
y1[1] (numeric) = 1.9978227903844143 " "
absolute error = 1.14797282790846110000000000E-10 " "
relative error = 5.746119392409214000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.70000000000000500E-2 " "
y2[1] (analytic) = 1.0669498840831735 " "
y2[1] (numeric) = 1.066949895334216 " "
absolute error = 1.125104254207087700000000E-8 " "
relative error = 1.0545052499573455000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9977563395044151 " "
y1[1] (numeric) = 1.9977563393787783 " "
absolute error = 1.25636834269471360000000000E-10 " "
relative error = 6.288896788115721000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.80000000000000500E-2 " "
y2[1] (analytic) = 1.067947606781446 " "
y2[1] (numeric) = 1.067947618897559 " "
absolute error = 1.21161130017810590000000E-8 " "
relative error = 1.1345231661969168000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.997688890753362 " "
y1[1] (numeric) = 1.997688890616046 " "
absolute error = 1.37316158443923100000000000E-10 " "
relative error = 6.873750916847661000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.90000000000000500E-2 " "
y2[1] (analytic) = 1.0689452615321173 " "
y2[1] (numeric) = 1.0689452745657118 " "
absolute error = 1.303359442594853600000000E-8 " "
relative error = 1.2192948409039682000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9976204443135015 " "
y1[1] (numeric) = 1.997620444163615 " "
absolute error = 1.49886547617938960000000000E-10 " "
relative error = 7.503254586956768000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.00000000000000500E-2 " "
y2[1] (analytic) = 1.0699428473375328 " "
y2[1] (numeric) = 1.0699428613433661 " "
absolute error = 1.400583338195815500000000E-8 " "
relative error = 1.3090263107801087000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9975510002532797 " "
y1[1] (numeric) = 1.997551000089878 " "
absolute error = 1.63401736585910840000000000E-10 " "
relative error = 8.18010336482984900000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.10000000000000500E-2 " "
y2[1] (analytic) = 1.0709403632001069 " "
y2[1] (numeric) = 1.0709403782353515 " "
absolute error = 1.503524460488847600000000E-8 " "
relative error = 1.403929212263626000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9974805586421405 " "
y1[1] (numeric) = 1.9974805584642232 " "
absolute error = 1.77917236499070000000000000E-10 " "
relative error = 8.907082260666188000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.20000000000000500E-2 " "
y2[1] (analytic) = 1.0719378081223236 " "
y2[1] (numeric) = 1.0719378242466373 " "
absolute error = 1.61243136620470300000000E-8 " "
relative error = 1.5042210042289145000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9974091195505261 " "
y1[1] (numeric) = 1.997409119357034 " "
absolute error = 1.93492111222326460000000000E-10 " "
relative error = 9.68715469096625000000000E-9 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.30000000000000500E-2 " "
y2[1] (analytic) = 1.0729351811067382 " "
y2[1] (numeric) = 1.072935198382335 " "
absolute error = 1.727559673092571300000000E-8 " "
relative error = 1.610124920417452000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.997336683049875 " "
y1[1] (numeric) = 1.9973366828396883 " "
absolute error = 2.10186756888219860000000000E-10 " "
relative error = 1.052335135442817700000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.40000000000000500E-2 " "
y2[1] (analytic) = 1.0739324811559778 " "
y2[1] (numeric) = 1.0739324996476998 " "
absolute error = 1.84917219314684200000000E-8 " "
relative error = 1.7218700668745937000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9972632492126245 " "
y1[1] (numeric) = 1.9972632489845594 " "
absolute error = 2.2806512234296860000000000E-10 " "
relative error = 1.141888143352550500000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.50000000000000600E-2 " "
y2[1] (analytic) = 1.0749297072727424 " "
y2[1] (numeric) = 1.074929727048133 " "
absolute error = 1.977539065833866500000000E-8 " "
relative error = 1.8396915188539900000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9971888181122073 " "
y1[1] (numeric) = 1.9971888178650146 " "
absolute error = 2.4719271074502558000000000E-10 " "
relative error = 1.237703258216107500000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.60000000000000600E-2 " "
y2[1] (analytic) = 1.0759268584598058 " "
y2[1] (numeric) = 1.075926879589184 " "
absolute error = 2.11293782470534100000000E-8 " "
relative error = 1.9638303552808606000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9971133898230555 " "
y1[1] (numeric) = 1.9971133895554163 " "
absolute error = 2.67639244100337240000000000E-10 " "
relative error = 1.34013043758146400000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.70000000000000600E-2 " "
y2[1] (analytic) = 1.0769239337200174 " "
y2[1] (numeric) = 1.076923956276552 " "
absolute error = 2.255653464011686500000000E-8 " "
relative error = 2.0945336930343678000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9970369644205967 " "
y1[1] (numeric) = 1.9970369641311208 " "
absolute error = 2.8947599872708450000000000E-10 " "
relative error = 1.449527494405045400000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.80000000000000600E-2 " "
y2[1] (analytic) = 1.0779209320563015 " "
y2[1] (numeric) = 1.0779209561160878 " "
absolute error = 2.405978638542194400000000E-8 " "
relative error = 2.232054844646551800000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9969595419812567 " "
y1[1] (numeric) = 1.996959541668479 " "
absolute error = 3.12777581612522200000000000E-10 " "
relative error = 1.566268995626241600000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.90000000000000600E-2 " "
y2[1] (analytic) = 1.07891785247166 " "
y2[1] (numeric) = 1.0789178781137967 " "
absolute error = 2.564213663625025700000000E-8 " "
relative error = 2.3766532899152112000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9968811225824579 " "
y1[1] (numeric) = 1.996881122244836 " "
absolute error = 3.37621930412979050000000000E-10 " "
relative error = 1.690746267240740600000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.00000000000000600E-2 " "
y2[1] (analytic) = 1.0799146939691728 " "
y2[1] (numeric) = 1.0799147212758393 " "
absolute error = 2.730666648353974300000000E-8 " "
relative error = 2.528594771053207000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9968017063026193 " "
y1[1] (numeric) = 1.9968017059385301 " "
absolute error = 3.64089203230832940000000000E-10 " "
relative error = 1.823361839493813400000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.10000000000000600E-2 " "
y2[1] (analytic) = 1.080911455551998 " "
y2[1] (numeric) = 1.0809114846085346 " "
absolute error = 2.905653651019690600000000E-8 " "
relative error = 2.688151407865167000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9967212932211575 " "
y1[1] (numeric) = 1.996721292828894 " "
absolute error = 3.92263554971350460000000000E-10 " "
relative error = 1.964538347455301300000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.20000000000000600E-2 " "
y2[1] (analytic) = 1.0819081362233747 " "
y2[1] (numeric) = 1.0819081671183615 " "
absolute error = 3.08949867910968100000000E-8 " "
relative error = 2.855601668635397000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.996639883418486 " "
y1[1] (numeric) = 1.996639882996254 " "
absolute error = 4.22232027119662230000000000E-10 " "
relative error = 2.114712976667332500000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.30000000000000600E-2 " "
y2[1] (analytic) = 1.0829047349866219 " "
y2[1] (numeric) = 1.0829047678119603 " "
absolute error = 3.282533844739532500000000E-8 " "
relative error = 3.031230484720417000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9965574769760137 " "
y1[1] (numeric) = 1.9965574765219294 " "
absolute error = 4.540843256961580000000000E-10 " "
relative error = 2.27433635611589900000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.40000000000000600E-2 " "
y2[1] (analytic) = 1.0839012508451409 " "
y2[1] (numeric) = 1.0839012856961359 " "
absolute error = 3.485099497879673400000000E-8 " "
relative error = 3.2153293440359690000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9964740739761475 " "
y1[1] (numeric) = 1.9964740734882331 " "
absolute error = 4.879143755687209700000000E-10 " "
relative error = 2.443880348503590000000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.50000000000000600E-2 " "
y2[1] (analytic) = 1.0848976828024162 " "
y2[1] (numeric) = 1.0848977197778586 " "
absolute error = 3.697544248559836400000000E-8 " "
relative error = 3.4081962817070940000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9963896745022904 " "
y1[1] (numeric) = 1.9963896739784712 " "
absolute error = 5.2381921022970350000000000E-10 " "
relative error = 2.623832495829222500000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.60000000000000700E-2 " "
y2[1] (analytic) = 1.0858940298620157 " "
y2[1] (numeric) = 1.0858940690642669 " "
absolute error = 3.920225122300280400000000E-8 " "
relative error = 3.6101359934711330000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.996304278638842 " "
y1[1] (numeric) = 1.9963042780769424 " "
absolute error = 5.6189963792974140000000000E-10 " "
relative error = 2.814699361927263000000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.70000000000000700E-2 " "
y2[1] (analytic) = 1.0868902910275924 " "
y2[1] (numeric) = 1.0868903325626689 " "
absolute error = 4.15350764892963300000000E-8 " "
relative error = 3.821459887182109000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.996217886471198 " "
y1[1] (numeric) = 1.9962178858689386 " "
absolute error = 6.0225935349933480000000000E-10 " "
relative error = 3.017002089706626000000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.80000000000000700E-2 " "
y2[1] (analytic) = 1.0878864653028855 " "
y2[1] (numeric) = 1.087886509280545 " "
absolute error = 4.39776595140273230000000E-8 " "
relative error = 4.042486134045543000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9961304980857502 " "
y1[1] (numeric) = 1.996130497440744 " "
absolute error = 6.4500627061647720000000000E-10 " "
relative error = 3.23128308111631730000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.90000000000000700E-2 " "
y2[1] (analytic) = 1.0888825516917204 " "
y2[1] (numeric) = 1.088882598225549 " "
absolute error = 4.653382856822929600000000E-8 " "
relative error = 4.273539739977737000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9960421135698874 " "
y1[1] (numeric) = 1.996042112879635 " "
absolute error = 6.9025229976205080000000000E-10 " "
relative error = 3.458104892023276500000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.00000000000000700E-2 " "
y2[1] (analytic) = 1.0898785491980112 " "
y2[1] (numeric) = 1.089878598405511 " "
absolute error = 4.92074998525993100000000E-8 " "
relative error = 4.514952596214387700000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9959527330119942 " "
y1[1] (numeric) = 1.995952732273881 " "
absolute error = 7.3811312617522160000000000E-10 " "
relative error = 3.69804912695187600000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.10000000000000700E-2 " "
y2[1] (analytic) = 1.0908744568257602 " "
y2[1] (numeric) = 1.0908745088284388 " "
absolute error = 5.20026786077210100000000E-8 " "
relative error = 4.767063550010973000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9958623565014508 " "
y1[1] (numeric) = 1.995862355712743 " "
absolute error = 7.8870776576422940000000000E-10 " "
relative error = 3.95171422114877700000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.20000000000000700E-2 " "
y2[1] (analytic) = 1.09187027357906 " "
y2[1] (numeric) = 1.0918703285025202 " "
absolute error = 5.492346022428762000000000E-8 " "
relative error = 5.030218474970757000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9957709841286342 " "
y1[1] (numeric) = 1.9957709832864738 " "
absolute error = 8.4216034146322730000000000E-10 " "
relative error = 4.21972434793624200000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.30000000000000700E-2 " "
y2[1] (analytic) = 1.0928659984620939 " "
y2[1] (numeric) = 1.0928660564361246 " "
absolute error = 5.7974030687191200000000E-8 " "
relative error = 5.304770280050216000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9956786159849162 " "
y1[1] (numeric) = 1.9956786150863182 " "
absolute error = 8.9859808483083730000000000E-10 " "
relative error = 4.502719414004228700000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.40000000000000700E-2 " "
y2[1] (analytic) = 1.0938616304791369 " "
y2[1] (numeric) = 1.0938616916378054 " "
absolute error = 6.11586685739240500000000E-8 " "
relative error = 5.591079060624434000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9955852521626654 " "
y1[1] (numeric) = 1.9955852512045122 " "
absolute error = 9.5815311240698970000000000E-10 " "
relative error = 4.80136396763112700000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.50000000000000700E-2 " "
y2[1] (analytic) = 1.0948571686345574 " "
y2[1] (numeric) = 1.0948572331163022 " "
absolute error = 6.4481744832534100000000E-8 " "
relative error = 5.8895120459367320000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9954908927552453 " "
y1[1] (numeric) = 1.9954908917342837 " "
absolute error = 1.0209615375345038000000000E-9 " "
relative error = 5.11634275676811500000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.60000000000000700E-2 " "
y2[1] (analytic) = 1.0958526119328171 " "
y2[1] (numeric) = 1.095852679880542 " "
absolute error = 6.79477247800264200000000E-8 " "
relative error = 6.2004437494731320000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9953955378570152 " "
y1[1] (numeric) = 1.9953955367698513 " "
absolute error = 1.087163914448297000000000E-9 " "
relative error = 5.448362962743081000000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.70000000000000800E-2 " "
y2[1] (analytic) = 1.096847959378473 " "
y2[1] (numeric) = 1.0968480309396418 " "
absolute error = 7.15611687684969400000000E-8 " "
relative error = 6.524255997070638000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9952991875633304 " "
y1[1] (numeric) = 1.9952991864064245 " "
absolute error = 1.1569059044092000000000E-9 " "
relative error = 5.79815754760076600000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.80000000000000800E-2 " "
y2[1] (analytic) = 1.0978432099761775 " "
y2[1] (numeric) = 1.0978432853029105 " "
absolute error = 7.53267330733109500000000E-8 " "
relative error = 6.861337975114451000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.995201841970541 " "
y1[1] (numeric) = 1.995201840740204 " "
absolute error = 1.2303371654809325000000000E-9 " "
relative error = 6.1664796994463600000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.90000000000000800E-2 " "
y2[1] (analytic) = 1.0988383627306801 " "
y2[1] (numeric) = 1.098838441979851 " "
absolute error = 7.92491707812814600000000E-8 " "
relative error = 7.21208627848981000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9951035011759926 " "
y1[1] (numeric) = 1.9951034998683808 " "
absolute error = 1.3076117966193124000000000E-9 " "
relative error = 6.5541050669729900000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10000000000000007 " "
y2[1] (analytic) = 1.0998334166468282 " "
y2[1] (numeric) = 1.0998334999801616 " "
absolute error = 8.3333333344981500000000E-8 " "
relative error = 7.576905018857141000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9950041652780257 " "
y1[1] (numeric) = 1.9950041638891365 " "
absolute error = 1.3888892258506758000000000E-9 " "
relative error = 6.96183622081369900000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10100000000000008 " "
y2[1] (analytic) = 1.100828370729568 " "
y2[1] (numeric) = 1.1008284583137389 " "
absolute error = 8.75841708047886400000000E-8 " "
relative error = 7.956205811333034000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9949038343759766 " "
y1[1] (numeric) = 1.9949038329016426 " "
absolute error = 1.4743339882272720000000000E-9 " "
relative error = 7.39050155111089200000000E-8 "%"
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10200000000000008 " "
y2[1] (analytic) = 1.1018232239839456 " "
y2[1] (numeric) = 1.1018233159906792 " "
absolute error = 9.20067335652419200000000E-8 " "
relative error = 8.350407902328125000000E-6 "%"
h = 1.000E-3 " "
y1[1] (analytic) = 1.9948025085701762 " "
y1[1] (numeric) = 1.994802507006061 " "
absolute error = 1.5641150596934494000000000E-9 " "
relative error = 7.84095193871882200000000E-8 "%"
h = 1.000E-3 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y2 , x , 5 ) = y1 ;"
"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"
Iterations = 102
"Total Elapsed Time "= 15 Minutes 11 Seconds
"Elapsed Time(since restart) "= 15 Minutes 11 Seconds
"Expected Time Remaining "= 12 Hours 2 Minutes 19 Seconds
"Optimized Time Remaining "= 12 Hours 2 Minutes 4 Seconds
"Time to Timeout " Unknown
Percent Done = 2.0600000000000014 "%"
(%o56) true
(%o56) diffeq.max