(%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(DEBUGL, 3, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_disp_incr, 0.1, float),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_clock_start_sec,
0.0, float), define_variable(glob_display_flag, true, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(djd_debug, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_log10relerr, 0.0, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_clock_sec, 0.0, float),
define_variable(years_in_century, 100.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(days_in_year, 365.0, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_hmax, 1.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3,
DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/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 : 0.0001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 1000,"),
omniout_str(ALWAYS, "glob_max_minutes : 15,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y1 (x) := ("),
omniout_str(ALWAYS, "1.0 + 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_y1_init, 1 + max_terms),
array(array_y2_init, 1 + max_terms), array(array_1st_rel_error,
1 + max_terms), array(array_norms, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_type_pole, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_y2, 1 + max_terms),
array(array_y1, 1 + max_terms), array(array_y1_higher_work2, 1 + 2,
1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3),
array(array_y2_set_initial, 1 + 3, 1 + max_terms),
array(array_y2_higher_work, 1 + 6, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_y2_higher_work2, 1 + 6,
1 + max_terms), array(array_y2_higher, 1 + 6, 1 + max_terms),
array(array_y1_set_initial, 1 + 3, 1 + max_terms),
array(array_real_pole, 1 + 2, 1 + 3), array(array_y1_higher_work, 1 + 2,
1 + max_terms), array(array_y1_higher, 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_y1_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y2_init : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_norms : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_type_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_last_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 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_y2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1 : 0.0, term : 1 + term), ord : 1,
term
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 <= 3 do (array_complex_pole : 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_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1,
while term <= max_terms do (array_y2_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 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_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y1_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_y1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term),
term
array(array_y2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y2 : 0.0, term : 1 + term),
term
array(array_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_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_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_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 : 1.0E-4,
glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_log10_abserr glob_log10_relerr
glob_abserr : 10.0 , glob_relerr : 10.0 ,
chk_data(), array_y2_set_initial : true, array_y2_set_initial : true,
1, 1 1, 2
array_y2_set_initial : true, array_y2_set_initial : true,
1, 3 1, 4
array_y2_set_initial : 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,
"2012-06-13T16:37:57-05:00"), 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(DEBUGL, 3, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_disp_incr, 0.1, float),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_clock_start_sec,
0.0, float), define_variable(glob_display_flag, true, boolean),
define_variable(glob_html_log, true, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(djd_debug, true, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_log10relerr, 0.0, float),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_clock_sec, 0.0, float),
define_variable(years_in_century, 100.0, float),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_start, 0, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(djd_debug2, true, boolean),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(days_in_year, 365.0, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_hmax, 1.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3,
DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/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 : 0.0001 ,"),
omniout_str(ALWAYS, "glob_look_poles : true,"),
omniout_str(ALWAYS, "glob_max_iter : 1000,"),
omniout_str(ALWAYS, "glob_max_minutes : 15,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y1 (x) := ("),
omniout_str(ALWAYS, "1.0 + 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_y1_init, 1 + max_terms),
array(array_y2_init, 1 + max_terms), array(array_1st_rel_error,
1 + max_terms), array(array_norms, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_type_pole, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_pole, 1 + max_terms), array(array_y2, 1 + max_terms),
array(array_y1, 1 + max_terms), array(array_y1_higher_work2, 1 + 2,
1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3),
array(array_y2_set_initial, 1 + 3, 1 + max_terms),
array(array_y2_higher_work, 1 + 6, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_y2_higher_work2, 1 + 6,
1 + max_terms), array(array_y2_higher, 1 + 6, 1 + max_terms),
array(array_y1_set_initial, 1 + 3, 1 + max_terms),
array(array_real_pole, 1 + 2, 1 + 3), array(array_y1_higher_work, 1 + 2,
1 + max_terms), array(array_y1_higher, 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_y1_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y2_init : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_norms : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_type_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_last_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 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_y2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1 : 0.0, term : 1 + term), ord : 1,
term
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 <= 3 do (array_complex_pole : 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_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1,
while term <= max_terms do (array_y2_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 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_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y1_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_y1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term),
term
array(array_y2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y2 : 0.0, term : 1 + term),
term
array(array_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_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_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_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 : 1.0E-4,
glob_look_poles : true, glob_max_iter : 1000, glob_max_minutes : 15,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_log10_abserr glob_log10_relerr
glob_abserr : 10.0 , glob_relerr : 10.0 ,
chk_data(), array_y2_set_initial : true, array_y2_set_initial : true,
1, 1 1, 2
array_y2_set_initial : true, array_y2_set_initial : true,
1, 3 1, 4
array_y2_set_initial : 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,
"2012-06-13T16:37:57-05:00"), 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 : 0.0001 ,"
"glob_look_poles : true,"
"glob_max_iter : 1000,"
"glob_max_minutes : 15,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y1 (x) := ("
"1.0 + 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 = 1.0000E-4 " "
y1[1] (analytic) = 2. " "
y1[1] (numeric) = 2. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
x[1] = 0.0 " "
y2[1] (analytic) = 1. " "
y2[1] (numeric) = 1. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 2. " "
y1[1] (numeric) = 2. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.0000E-4 " "
y2[1] (analytic) = 1.0000999999998332 " "
y2[1] (numeric) = 1.0000999999998332 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999999995 " "
y1[1] (numeric) = 1.999999995 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.0000E-4 " "
y2[1] (analytic) = 1.0001999999986666 " "
y2[1] (numeric) = 1.0001999999986666 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999999800000001 " "
y1[1] (numeric) = 1.9999999800000001 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.00000000000000040000E-4 " "
y2[1] (analytic) = 1.0002999999955 " "
y2[1] (numeric) = 1.0002999999955 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999999550000003 " "
y1[1] (numeric) = 1.9999999550000005 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11022304960517500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.0000E-4 " "
y2[1] (analytic) = 1.0003999999893334 " "
y2[1] (numeric) = 1.0003999999893334 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999999920000001 " "
y1[1] (numeric) = 1.9999999200000012 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110223069034078800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.0000E-4 " "
y2[1] (analytic) = 1.0004999999791666 " "
y2[1] (numeric) = 1.0004999999791666 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999998750000025 " "
y1[1] (numeric) = 1.9999998750000028 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110223094014098500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.0000000000000010000E-4 " "
y2[1] (analytic) = 1.000599999964 " "
y2[1] (numeric) = 1.0005999999639998 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.219114580581851800000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999998200000055 " "
y1[1] (numeric) = 1.9999998200000055 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.0000000000000010000E-4 " "
y2[1] (analytic) = 1.0006999999428334 " "
y2[1] (numeric) = 1.0006999999428332 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.218892824400079400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.99999975500001 " "
y1[1] (numeric) = 1.9999997550000101 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110223160627488300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.0000000000000020000E-4 " "
y2[1] (analytic) = 1.0007999999146666 " "
y2[1] (numeric) = 1.0007999999146666 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999999680000017 " "
y1[1] (numeric) = 1.9999996800000173 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110223202260859500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.0000000000000020000E-4 " "
y2[1] (analytic) = 1.0008999998785 " "
y2[1] (numeric) = 1.0008999998785 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999995950000273 " "
y1[1] (numeric) = 1.9999995950000276 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110223249445349400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.0000000000000002000E-3 " "
y2[1] (analytic) = 1.0009999998333334 " "
y2[1] (numeric) = 1.0009999998333332 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21822782179821900000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999995000000417 " "
y1[1] (numeric) = 1.999999500000042 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11022330218095900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.1000000000000003000E-3 " "
y2[1] (analytic) = 1.0010999997781667 " "
y2[1] (numeric) = 1.0010999997781667 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999999395000061 " "
y1[1] (numeric) = 1.9999993950000612 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110223360467689200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.2000000000000004000E-3 " "
y2[1] (analytic) = 1.001199999712 " "
y2[1] (numeric) = 1.001199999712 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999992800000865 " "
y1[1] (numeric) = 1.9999992800000865 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.3000000000000003000E-3 " "
y2[1] (analytic) = 1.0012999996338334 " "
y2[1] (numeric) = 1.0012999996338334 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999999155000119 " "
y1[1] (numeric) = 1.999999155000119 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.4000000000000004000E-3 " "
y2[1] (analytic) = 1.0013999995426668 " "
y2[1] (numeric) = 1.0013999995426668 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.99999902000016 " "
y1[1] (numeric) = 1.99999902000016 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.5000000000000005000E-3 " "
y2[1] (analytic) = 1.0014999994375 " "
y2[1] (numeric) = 1.0014999994375002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.217120369942529600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999998875000211 " "
y1[1] (numeric) = 1.999998875000211 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.6000000000000006000E-3 " "
y2[1] (analytic) = 1.0015999993173335 " "
y2[1] (numeric) = 1.0015999993173337 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.216899012343965500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999998720000273 " "
y1[1] (numeric) = 1.9999987200002731 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110223735168195500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.7000000000000007000E-3 " "
y2[1] (analytic) = 1.0016999991811668 " "
y2[1] (numeric) = 1.001699999181167 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.216677698977141400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999998555000348 " "
y1[1] (numeric) = 1.999998555000348 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.8000000000000005000E-3 " "
y2[1] (analytic) = 1.0017999990280002 " "
y2[1] (numeric) = 1.0017999990280004 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.216456429831012400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999983800004375 " "
y1[1] (numeric) = 1.9999983800004375 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 1.9000000000000006000E-3 " "
y2[1] (analytic) = 1.0018999988568336 " "
y2[1] (numeric) = 1.0018999988568338 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.216235204894539000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999998195000543 " "
y1[1] (numeric) = 1.9999981950005432 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110224026602039100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.0000000000000004000E-3 " "
y2[1] (analytic) = 1.001999998666667 " "
y2[1] (numeric) = 1.0019999986666672 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.216014024156684200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999980000006667 " "
y1[1] (numeric) = 1.999998000000667 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110224134848921300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.1000000000000002000E-3 " "
y2[1] (analytic) = 1.0020999984565004 " "
y2[1] (numeric) = 1.0020999984565007 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21579288760641500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999977950008103 " "
y1[1] (numeric) = 1.9999977950008105 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110224248646940900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.2000E-3 " "
y2[1] (analytic) = 1.0021999982253338 " "
y2[1] (numeric) = 1.0021999982253342 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.43114359046540340000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999975800009762 " "
y1[1] (numeric) = 1.9999975800009762 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.3000E-3 " "
y2[1] (analytic) = 1.0022999979721672 " "
y2[1] (numeric) = 1.0022999979721678 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.64605224107355300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999997355001166 " "
y1[1] (numeric) = 1.999997355001166 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.4000E-3 " "
y2[1] (analytic) = 1.0023999976960007 " "
y2[1] (numeric) = 1.0023999976960014 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.64538922891252200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999971200013824 " "
y1[1] (numeric) = 1.9999971200013824 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.4999999999999997000E-3 " "
y2[1] (analytic) = 1.0024999973958342 " "
y2[1] (numeric) = 1.002499997395835 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.85963513224260500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999968750016275 " "
y1[1] (numeric) = 1.9999968750016277 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110224759350439500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.5999999999999995000E-3 " "
y2[1] (analytic) = 1.0025999970706676 " "
y2[1] (numeric) = 1.0025999970706687 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10734393364146730000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999996620001904 " "
y1[1] (numeric) = 1.9999966200019041 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110224900904182200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.6999999999999990000E-3 " "
y2[1] (analytic) = 1.0026999967195012 " "
y2[1] (numeric) = 1.0026999967195025 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32868019737600650000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999963550022142 " "
y1[1] (numeric) = 1.9999963550022144 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110225048009077400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.799999999999999000E-3 " "
y2[1] (analytic) = 1.0027999963413348 " "
y2[1] (numeric) = 1.0027999963413363 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54997231765661050000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999996080002561 " "
y1[1] (numeric) = 1.9999960800025611 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110225200665128200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.899999999999998700E-3 " "
y2[1] (analytic) = 1.0028999959351683 " "
y2[1] (numeric) = 1.00289999593517 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.77122030770761080000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999995795002947 " "
y1[1] (numeric) = 1.999995795002947 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 2.9999999999999990000E-3 " "
y2[1] (analytic) = 1.002999995500002 " "
y2[1] (numeric) = 1.002999995500004 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.99242418074893980000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999995500003375 " "
y1[1] (numeric) = 1.999995500003375 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.0999999999999983000E-3 " "
y2[1] (analytic) = 1.0030999950348358 " "
y2[1] (numeric) = 1.003099995034838 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.2135839499961330000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999995195003848 " "
y1[1] (numeric) = 1.999995195003848 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.1999999999999984000E-3 " "
y2[1] (analytic) = 1.0031999945386694 " "
y2[1] (numeric) = 1.0031999945386723 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.87737228841675460000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999994880004369 " "
y1[1] (numeric) = 1.999994880004369 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.2999999999999985000E-3 " "
y2[1] (analytic) = 1.0032999940105032 " "
y2[1] (numeric) = 1.0032999940105065 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.31971403743534950000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999945550049414 " "
y1[1] (numeric) = 1.9999945550049412 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11022604721282710000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.399999999999998000E-3 " "
y2[1] (analytic) = 1.0033999934493372 " "
y2[1] (numeric) = 1.003399993449341 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.7619676184661290000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999994220005568 " "
y1[1] (numeric) = 1.9999942200055678 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110226233175879400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.499999999999998000E-3 " "
y2[1] (analytic) = 1.003499992854171 " "
y2[1] (numeric) = 1.0034999928541755 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.42540321885779850000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999938750062527 " "
y1[1] (numeric) = 1.9999938750062523 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.220452849380222500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.5999999999999976000E-3 " "
y2[1] (analytic) = 1.003599992224005 " "
y2[1] (numeric) = 1.0035999922240102 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 5.0887066090528870000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999935200069983 " "
y1[1] (numeric) = 1.999993520006998 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110226621755526200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.6999999999999980000E-3 " "
y2[1] (analytic) = 1.003699991557839 " "
y2[1] (numeric) = 1.003699991557845 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.9731038989755400000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999931550078092 " "
y1[1] (numeric) = 1.9999931550078087 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22045364874425580000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.7999999999999970000E-3 " "
y2[1] (analytic) = 1.0037999908546733 " "
y2[1] (numeric) = 1.00379999085468 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 6.6361209488348600000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999992780008688 " "
y1[1] (numeric) = 1.9999927800086879 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110227032539921200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.8999999999999974000E-3 " "
y2[1] (analytic) = 1.0038999901135075 " "
y2[1] (numeric) = 1.003899990113515 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 7.5201879089544240000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999923950096394 " "
y1[1] (numeric) = 1.9999923950096392 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110227246258909400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 3.9999999999999974000E-3 " "
y2[1] (analytic) = 1.0039999893333418 " "
y2[1] (numeric) = 1.0039999893333504 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.6252387291620470000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999920000106668 " "
y1[1] (numeric) = 1.9999920000106666 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110227465529097400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.099999999999997500E-3 " "
y2[1] (analytic) = 1.0040999885131763 " "
y2[1] (numeric) = 1.004099988513186 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.7300694437495970000000000000E-13 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999915950117741 " "
y1[1] (numeric) = 1.999991595011774 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110227690350489300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.199999999999998000E-3 " "
y2[1] (analytic) = 1.004199987652011 " "
y2[1] (numeric) = 1.0041999876520218 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.0834680118614863000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999911800129655 " "
y1[1] (numeric) = 1.9999911800129653 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110227920723089600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.299999999999998000E-3 " "
y2[1] (analytic) = 1.0042999867488456 " "
y2[1] (numeric) = 1.0042999867488578 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.2160164723701027000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999907550142448 " "
y1[1] (numeric) = 1.9999907550142448 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.3999999999999984000E-3 " "
y2[1] (analytic) = 1.0043999858026804 " "
y2[1] (numeric) = 1.0043999858026942 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.3706457287880222000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999990320015617 " "
y1[1] (numeric) = 1.9999903200156168 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110228398121934200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.499999999999999000E-3 " "
y2[1] (analytic) = 1.0044999848125153 " "
y2[1] (numeric) = 1.0044999848125309 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.5473491866357006000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999989875017086 " "
y1[1] (numeric) = 1.9999898750170857 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11022864514818800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.599999999999999000E-3 " "
y2[1] (analytic) = 1.0045999837773505 " "
y2[1] (numeric) = 1.0045999837773678 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.7240174660395932000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999989420018656 " "
y1[1] (numeric) = 1.9999894200186559 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110228897725669300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.699999999999999000E-3 " "
y2[1] (analytic) = 1.0046999826961858 " "
y2[1] (numeric) = 1.004699982696205 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.9227511656401924000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999988955020332 " "
y1[1] (numeric) = 1.9999889550203318 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110229155854383100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.8000E-3 " "
y2[1] (analytic) = 1.0047999815680213 " "
y2[1] (numeric) = 1.0047999815680426 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 2.121445308900015100000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999884800221184 " "
y1[1] (numeric) = 1.9999884800221182 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110229419534334700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 4.9000E-3 " "
y2[1] (analytic) = 1.0048999803918568 " "
y2[1] (numeric) = 1.0048999803918806 " "
absolute error = 2.37587727269783500000000000000E-14 " "
relative error = 2.364292286851644000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.99998799502402 " "
y1[1] (numeric) = 1.9999879950240198 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110229688765529500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"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 = 1.0000E-4 " "
y1[1] (analytic) = 1.9999875000260416 " "
y1[1] (numeric) = 1.9999875000260414 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110229963547972600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.1000E-3 " "
y2[1] (analytic) = 1.0050999778915288 " "
y2[1] (numeric) = 1.0050999778915575 " "
absolute error = 2.86437540353290400000000000000E-14 " "
relative error = 2.8498412760307806000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999869950281883 " "
y1[1] (numeric) = 1.999986995028188 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110230243881669500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.200000000000000000E-3 " "
y2[1] (analytic) = 1.005199976565365 " "
y2[1] (numeric) = 1.0051999765653967 " "
absolute error = 3.17523785042794770000000000000E-14 " "
relative error = 3.158812101525623000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999986480030465 " "
y1[1] (numeric) = 1.9999864800304648 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110230529766626200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.300000000000001000E-3 " "
y2[1] (analytic) = 1.0052999751872016 " "
y2[1] (numeric) = 1.0052999751872365 " "
absolute error = 3.486100297322991500000000000000E-14 " "
relative error = 3.4677214596308215000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999985955032877 " "
y1[1] (numeric) = 1.9999859550328767 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110230821202847900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.400000000000001000E-3 " "
y2[1] (analytic) = 1.0053999737560382 " "
y2[1] (numeric) = 1.0053999737560766 " "
absolute error = 3.841371665203041600000000000000E-14 " "
relative error = 3.820739770712543000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999854200354292 " "
y1[1] (numeric) = 1.999985420035429 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110231118190340800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.500000000000002000E-3 " "
y2[1] (analytic) = 1.0054999722708753 " "
y2[1] (numeric) = 1.0054999722709173 " "
absolute error = 4.19664303308309200000000000000E-14 " "
relative error = 4.173687865555249000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999848750381277 " "
y1[1] (numeric) = 1.9999848750381273 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22046284145822100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.600000000000002000E-3 " "
y2[1] (analytic) = 1.0055999707307126 " "
y2[1] (numeric) = 1.0055999707307586 " "
absolute error = 4.59632332194814800000000000000E-14 " "
relative error = 4.570727382388704600000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999984320040977 " "
y1[1] (numeric) = 1.9999843200409768 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110231728819163500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.700000000000002000E-3 " "
y2[1] (analytic) = 1.00569996913455 " "
y2[1] (numeric) = 1.0056999691346005 " "
absolute error = 5.04041253179821100000000000000E-14 " "
relative error = 5.011845169027609000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999837550439832 " "
y1[1] (numeric) = 1.9999837550439832 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.800000000000002000E-3 " "
y2[1] (analytic) = 1.005799967481388 " "
y2[1] (numeric) = 1.0057999674814428 " "
absolute error = 5.48450174164827300000000000000E-14 " "
relative error = 5.4528752425613510000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999831800471521 " "
y1[1] (numeric) = 1.999983180047152 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110232361653143200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 5.9000000000000030000E-3 " "
y2[1] (analytic) = 1.0058999657702263 " "
y2[1] (numeric) = 1.0058999657702858 " "
absolute error = 5.95079541199083900000000000000E-14 " "
relative error = 5.915891852560372000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999982595050489 " "
y1[1] (numeric) = 1.9999825950504888 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110232686397082700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.000000000000003000E-3 " "
y2[1] (analytic) = 1.0059999640000648 " "
y2[1] (numeric) = 1.0059999640001296 " "
absolute error = 6.48370246381091400000000000000E-14 " "
relative error = 6.445032500826706000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999982000054 " "
y1[1] (numeric) = 1.9999820000539998 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110233016692330500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.100000000000003000E-3 " "
y2[1] (analytic) = 1.0060999621699038 " "
y2[1] (numeric) = 1.006099962169974 " "
absolute error = 7.01660951563098900000000000000E-14 " "
relative error = 6.974067964874914000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999981395057691 " "
y1[1] (numeric) = 1.9999813950576908 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110233352538893300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.200000000000003000E-3 " "
y2[1] (analytic) = 1.006199960278743 " "
y2[1] (numeric) = 1.0061999602788192 " "
absolute error = 7.61612994892857400000000000000E-14 " "
relative error = 7.569201202133532000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999980780061568 " "
y1[1] (numeric) = 1.9999807800615679 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110233693936777700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.3000000000000030000E-3 " "
y2[1] (analytic) = 1.0062999583255827 " "
y2[1] (numeric) = 1.0062999583256653 " "
absolute error = 8.26005930321116500000000000000E-14 " "
relative error = 8.208347058818688000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999980155065637 " "
y1[1] (numeric) = 1.999980155065637 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.400000000000003000E-3 " "
y2[1] (analytic) = 1.0063999563094228 " "
y2[1] (numeric) = 1.0063999563095123 " "
absolute error = 8.94839757847876200000000000000E-14 " "
relative error = 8.891492415494037000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999979520069905 " "
y1[1] (numeric) = 1.9999795200699049 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110234393386539400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.500000000000004000E-3 " "
y2[1] (analytic) = 1.0064999542292634 " "
y2[1] (numeric) = 1.00649995422936 " "
absolute error = 9.65894031423886200000000000000E-14 " "
relative error = 9.596563093373695000000000000E-12 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999788750743774 " "
y1[1] (numeric) = 1.9999788750743774 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.600000000000005000E-3 " "
y2[1] (analytic) = 1.0065999520841045 " "
y2[1] (numeric) = 1.0065999520842086 " "
absolute error = 1.04138919709839680000000000000E-13 " "
relative error = 1.03456114312569100000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999782200790612 " "
y1[1] (numeric) = 1.9999782200790612 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.7000000000000050000E-3 " "
y2[1] (analytic) = 1.0066999498729459 " "
y2[1] (numeric) = 1.0066999498730582 " "
absolute error = 1.12354570092065840000000000000E-13 " "
relative error = 1.116068100591898900000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999977555083963 " "
y1[1] (numeric) = 1.999977555083963 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.800000000000005000E-3 " "
y2[1] (analytic) = 1.0067999475947877 " "
y2[1] (numeric) = 1.0067999475949088 " "
absolute error = 1.21014309684142060000000000000E-13 " "
relative error = 1.201969765426004300000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999976880089089 " "
y1[1] (numeric) = 1.999976880089089 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 6.900000000000005000E-3 " "
y2[1] (analytic) = 1.0068999452486302 " "
y2[1] (numeric) = 1.0068999452487604 " "
absolute error = 1.30118138486068350000000000000E-13 " "
relative error = 1.292264828298691800000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999761950944461 " "
y1[1] (numeric) = 1.9999761950944461 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.000000000000005000E-3 " "
y2[1] (analytic) = 1.0069999428334735 " "
y2[1] (numeric) = 1.0069999428336132 " "
absolute error = 1.3966605649784470000000000000E-13 " "
relative error = 1.386951980402854000000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999755001000414 " "
y1[1] (numeric) = 1.9999755001000414 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.100000000000005000E-3 " "
y2[1] (analytic) = 1.007099940348317 " "
y2[1] (numeric) = 1.007099940348467 " "
absolute error = 1.50102152929321160000000000000E-13 " "
relative error = 1.490439497766295500000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999974795105882 " "
y1[1] (numeric) = 1.9999747951058817 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110237016328377700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.200000000000006000E-3 " "
y2[1] (analytic) = 1.0071999377921612 " "
y2[1] (numeric) = 1.0071999377923222 " "
absolute error = 1.6098233857064770000000000000E-13 " "
relative error = 1.59831561272263400000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999740801119743 " "
y1[1] (numeric) = 1.999974080111974 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11023741323987300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.300000000000006000E-3 " "
y2[1] (analytic) = 1.0072999351640062 " "
y2[1] (numeric) = 1.0072999351641785 " "
absolute error = 1.7230661342182430000000000000E-13 " "
relative error = 1.710579018291803500000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999733551183256 " "
y1[1] (numeric) = 1.9999733551183256 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.400000000000007000E-3 " "
y2[1] (analytic) = 1.0073999324628515 " "
y2[1] (numeric) = 1.007399932463036 " "
absolute error = 1.84519066692701020000000000000E-13 " "
relative error = 1.831636679204416000000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999972620124944 " "
y1[1] (numeric) = 1.9999726201249437 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110238223717080300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.500000000000007000E-3 " "
y2[1] (analytic) = 1.0074999296876979 " "
y2[1] (numeric) = 1.007499929687895 " "
absolute error = 1.9717560917342780000000000000E-13 " "
relative error = 1.957078143266449400000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999718751318358 " "
y1[1] (numeric) = 1.9999718751318356 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110238637282808800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.600000000000007000E-3 " "
y2[1] (analytic) = 1.0075999268375446 " "
y2[1] (numeric) = 1.0075999268377553 " "
absolute error = 2.1072033007385470000000000000E-13 " "
relative error = 2.0913095015322403000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999971120139009 " "
y1[1] (numeric) = 1.9999711201390087 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110239056399964500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.700000000000007000E-3 " "
y2[1] (analytic) = 1.0076999239113922 " "
y2[1] (numeric) = 1.0076999239116171 " "
absolute error = 2.24931184789056720000000000000E-13 " "
relative error = 2.2321246578642700000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999703551464707 " "
y1[1] (numeric) = 1.9999703551464705 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110239481068555900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.8000000000000070000E-3 " "
y2[1] (analytic) = 1.0077999209082407 " "
y2[1] (numeric) = 1.0077999209084805 " "
absolute error = 2.3980817331903380000000000000E-13 " "
relative error = 2.379521652501381300000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999695801542292 " "
y1[1] (numeric) = 1.9999695801542288 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22047982257718300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 7.900000000000008000E-3 " "
y2[1] (analytic) = 1.0078999178270898 " "
y2[1] (numeric) = 1.0078999178273456 " "
absolute error = 2.55795384873636070000000000000E-13 " "
relative error = 2.537904610857593000000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999687951622915 " "
y1[1] (numeric) = 1.9999687951622913 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.110240347060080200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.000000000000007000E-3 " "
y2[1] (analytic) = 1.0079999146669398 " "
y2[1] (numeric) = 1.0079999146672123 " "
absolute error = 2.7244873024301340000000000000E-13 " "
relative error = 2.702864616144685600000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999680001706663 " "
y1[1] (numeric) = 1.999968000170666 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.220481576766060700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.100000000000006000E-3 " "
y2[1] (analytic) = 1.0080999114267906 " "
y2[1] (numeric) = 1.0080999114270806 " "
absolute error = 2.8999025403209090000000000000E-13 " "
relative error = 2.876602316348386000000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999967195179361 " "
y1[1] (numeric) = 1.9999671951793605 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.220482470514901800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.200000000000006000E-3 " "
y2[1] (analytic) = 1.0081999081056423 " "
y2[1] (numeric) = 1.0081999081059507 " "
absolute error = 3.0841995624086850000000000000E-13 " "
relative error = 3.059115099706508600000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999663801883836 " "
y1[1] (numeric) = 1.9999663801883831 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.220483375366702000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.300000000000005000E-3 " "
y2[1] (analytic) = 1.008299904702495 " "
y2[1] (numeric) = 1.0082999047028227 " "
absolute error = 3.2773783686934620000000000000E-13 " "
relative error = 3.25040035549787400000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999655551977424 " "
y1[1] (numeric) = 1.999965555197742 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.220484291321478400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.400000000000005000E-3 " "
y2[1] (analytic) = 1.0083999012163485 " "
y2[1] (numeric) = 1.0083999012166966 " "
absolute error = 3.4816594052244910000000000000E-13 " "
relative error = 3.4526574239295904000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999964720207446 " "
y1[1] (numeric) = 1.9999647202074453 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33072782756887500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.500000000000004000E-3 " "
y2[1] (analytic) = 1.0084998976462032 " "
y2[1] (numeric) = 1.0084998976465724 " "
absolute error = 3.69260177990327070000000000000E-13 " "
relative error = 3.661479578254444600000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999638752175022 " "
y1[1] (numeric) = 1.9999638752175015 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33072923481005300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.600000000000003000E-3 " "
y2[1] (analytic) = 1.0085998939910588 " "
y2[1] (numeric) = 1.0085998939914502 " "
absolute error = 3.9146463848283020000000000000E-13 " "
relative error = 3.881267892402738300000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999630202279195 " "
y1[1] (numeric) = 1.9999630202279188 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.3307306587057800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.700000000000003000E-3 " "
y2[1] (analytic) = 1.0086998902499154 " "
y2[1] (numeric) = 1.0086998902503301 " "
absolute error = 4.1477932199995850000000000000E-13 " "
relative error = 4.112019105079835500000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999621552387068 " "
y1[1] (numeric) = 1.9999621552387061 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.330732099256083500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.800000000000002000E-3 " "
y2[1] (analytic) = 1.008799886421773 " "
y2[1] (numeric) = 1.0087998864222123 " "
absolute error = 4.39204228541711900000000000000E-13 " "
relative error = 4.3537299562906900000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999612802498725 " "
y1[1] (numeric) = 1.9999612802498719 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33073355646099300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 8.900000000000001000E-3 " "
y2[1] (analytic) = 1.0088998825056321 " "
y2[1] (numeric) = 1.0088998825060969 " "
absolute error = 4.6473935810809053000000000000E-13 " "
relative error = 4.60639718733931100000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999603952614253 " "
y1[1] (numeric) = 1.9999603952614247 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33073503032053800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.000000000000001000E-3 " "
y2[1] (analytic) = 1.008999878500492 " "
y2[1] (numeric) = 1.0089998785009837 " "
absolute error = 4.9160675530401930000000000000E-13 " "
relative error = 4.87221818137988540000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999595002733743 " "
y1[1] (numeric) = 1.9999595002733737 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.330736520834747000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.1000E-3 " "
y2[1] (analytic) = 1.0090998744053534 " "
y2[1] (numeric) = 1.009099874405873 " "
absolute error = 5.1958437552457330000000000000E-13 " "
relative error = 5.14898860561999500000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999585952857282 " "
y1[1] (numeric) = 1.9999585952857275 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33073802800365200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.2000E-3 " "
y2[1] (analytic) = 1.009199870219216 " "
y2[1] (numeric) = 1.0091998702197646 " "
absolute error = 5.4867221876975240000000000000E-13 " "
relative error = 5.436705205387820000000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999576802984962 " "
y1[1] (numeric) = 1.9999576802984955 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.3307395518272800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.3000E-3 " "
y2[1] (analytic) = 1.0092998659410797 " "
y2[1] (numeric) = 1.009299865941659 " "
absolute error = 5.7931437424940670000000000000E-13 " "
relative error = 5.739764700248415000000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999567553116875 " "
y1[1] (numeric) = 1.9999567553116866 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.440988123074217600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.399999999999998000E-3 " "
y2[1] (analytic) = 1.0093998615699449 " "
y2[1] (numeric) = 1.009399861570556 " "
absolute error = 6.1106675275368620000000000000E-13 " "
relative error = 6.05376299342144500000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999558203253112 " "
y1[1] (numeric) = 1.9999558203253103 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.44099019925177600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.499999999999998000E-3 " "
y2[1] (analytic) = 1.0094998571048115 " "
y2[1] (numeric) = 1.0094998571054556 " "
absolute error = 6.4415139888751580000000000000E-13 " "
relative error = 6.38089638501688900000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999548753393765 " "
y1[1] (numeric) = 1.9999548753393757 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.44099229763575740000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.599999999999997000E-3 " "
y2[1] (analytic) = 1.0095998525446794 " "
y2[1] (numeric) = 1.0095998525453582 " "
absolute error = 6.7879035725582070000000000000E-13 " "
relative error = 6.72336030502521400000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999539203538932 " "
y1[1] (numeric) = 1.9999539203538923 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.440994418226203400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.699999999999996000E-3 " "
y2[1] (analytic) = 1.009699847888549 " "
y2[1] (numeric) = 1.0096998478892638 " "
absolute error = 7.1476158325367580000000000000E-13 " "
relative error = 7.0789510838132900000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999529553688709 " "
y1[1] (numeric) = 1.9999529553688697 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.55124570127894500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.799999999999996000E-3 " "
y2[1] (analytic) = 1.0097998431354198 " "
y2[1] (numeric) = 1.0097998431361725 " "
absolute error = 7.5273121069585610000000000000E-13 " "
relative error = 7.45426151343648600000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9999519803843189 " "
y1[1] (numeric) = 1.9999519803843178 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.55124840753332200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 9.899999999999995000E-3 " "
y2[1] (analytic) = 1.0098998382842925 " "
y2[1] (numeric) = 1.0098998382850843 " "
absolute error = 7.9181106116266160000000000000E-13 " "
relative error = 7.84049101847427400000000000E-11 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.999950995400247 " "
y1[1] (numeric) = 1.999950995400246 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.551251141545942000000000000000E-14 "%"
h = 1.0000E-4 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y2 , x , 5 ) = y1 ;"
"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"
Iterations = 99
"Total Elapsed Time "= 15 Minutes 12 Seconds
"Elapsed Time(since restart) "= 15 Minutes 11 Seconds
"Expected Time Remaining "= 5 Days 6 Hours 27 Minutes 3 Seconds
"Optimized Time Remaining "= 5 Days 6 Hours 20 Minutes 52 Seconds
"Time to Timeout " Unknown
Percent Done = 0.1999999999999999 "%"
(%o56) true
(%o56) diffeq.max