(%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 - 1 + 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 - 1 + 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 - 1 + 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 - 1 + 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_m1 array_y1 ,
1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
array_tmp3 : array_const_1D0 + array_tmp2 ,
1 1 1
if not array_y2_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp3 glob_h factorial_3(0, 1),
1
array_y2 : temporary, array_y2_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp5 : array_y2 - array_const_1D0 ,
1 1 1
if not array_y1_set_initial then (if 1 <= glob_max_terms
2, 2
1
then (temporary : array_tmp5 glob_h factorial_3(0, 1),
1
array_y1 : temporary, array_y1_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : ats(2, array_m1, array_y1, 1),
2
array_tmp2 : array_tmp1 + array_const_0D0 ,
2 2 2
array_tmp3 : array_const_1D0 + array_tmp2 ,
2 2 2
if not array_y2_set_initial then (if 2 <= glob_max_terms
1, 3
1
then (temporary : array_tmp3 glob_h factorial_3(1, 2),
2
array_y2 : temporary, array_y2_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp5 : array_y2 - array_const_1D0 ,
2 2 2
if not array_y1_set_initial then (if 2 <= glob_max_terms
2, 3
1
then (temporary : array_tmp5 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 : ats(3, array_m1, array_y1, 1),
3
array_tmp2 : array_tmp1 + array_const_0D0 ,
3 3 3
array_tmp3 : array_const_1D0 + array_tmp2 ,
3 3 3
if not array_y2_set_initial then (if 3 <= glob_max_terms
1, 4
1
then (temporary : array_tmp3 glob_h factorial_3(2, 3),
3
array_y2 : temporary, array_y2_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp5 : array_y2 - array_const_1D0 ,
3 3 3
if not array_y1_set_initial then (if 3 <= glob_max_terms
2, 4
1
then (temporary : array_tmp5 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 : ats(4, array_m1, array_y1, 1),
4
array_tmp2 : array_tmp1 + array_const_0D0 ,
4 4 4
array_tmp3 : array_const_1D0 + array_tmp2 ,
4 4 4
if not array_y2_set_initial then (if 4 <= glob_max_terms
1, 5
1
then (temporary : array_tmp3 glob_h factorial_3(3, 4),
4
array_y2 : temporary, array_y2_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp5 : array_y2 - array_const_1D0 ,
4 4 4
if not array_y1_set_initial then (if 4 <= glob_max_terms
2, 5
1
then (temporary : array_tmp5 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 : ats(5, array_m1, array_y1, 1),
5
array_tmp2 : array_tmp1 + array_const_0D0 ,
5 5 5
array_tmp3 : array_const_1D0 + array_tmp2 ,
5 5 5
if not array_y2_set_initial then (if 5 <= glob_max_terms
1, 6
1
then (temporary : array_tmp3 glob_h factorial_3(4, 5),
5
array_y2 : temporary, array_y2_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 6,
glob_h 2, 5
array_tmp5 : array_y2 - array_const_1D0 ,
5 5 5
if not array_y1_set_initial then (if 5 <= glob_max_terms
2, 6
1
then (temporary : array_tmp5 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
ats(kkk, array_m1, array_y1, 1), array_tmp2 :
kkk
array_tmp1 + array_const_0D0 , array_tmp3 :
kkk kkk kkk
array_const_1D0 + array_tmp2 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y2_set_initial
1, order_d + kkk
order_d
array_tmp3 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_tmp5 :
kkk
array_y2 - array_const_1D0 , 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_tmp5 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y1 : temporary, array_y1_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_y1_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk))
(%o8) atomall() := (array_tmp1 : array_m1 array_y1 ,
1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
array_tmp3 : array_const_1D0 + array_tmp2 ,
1 1 1
if not array_y2_set_initial then (if 1 <= glob_max_terms
1, 2
1
then (temporary : array_tmp3 glob_h factorial_3(0, 1),
1
array_y2 : temporary, array_y2_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp5 : array_y2 - array_const_1D0 ,
1 1 1
if not array_y1_set_initial then (if 1 <= glob_max_terms
2, 2
1
then (temporary : array_tmp5 glob_h factorial_3(0, 1),
1
array_y1 : temporary, array_y1_higher : temporary,
2 1, 2
temporary 2.0
temporary : -------------, array_y1_higher : temporary)), kkk : 2,
glob_h 2, 1
array_tmp1 : ats(2, array_m1, array_y1, 1),
2
array_tmp2 : array_tmp1 + array_const_0D0 ,
2 2 2
array_tmp3 : array_const_1D0 + array_tmp2 ,
2 2 2
if not array_y2_set_initial then (if 2 <= glob_max_terms
1, 3
1
then (temporary : array_tmp3 glob_h factorial_3(1, 2),
2
array_y2 : temporary, array_y2_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 3,
glob_h 2, 2
array_tmp5 : array_y2 - array_const_1D0 ,
2 2 2
if not array_y1_set_initial then (if 2 <= glob_max_terms
2, 3
1
then (temporary : array_tmp5 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 : ats(3, array_m1, array_y1, 1),
3
array_tmp2 : array_tmp1 + array_const_0D0 ,
3 3 3
array_tmp3 : array_const_1D0 + array_tmp2 ,
3 3 3
if not array_y2_set_initial then (if 3 <= glob_max_terms
1, 4
1
then (temporary : array_tmp3 glob_h factorial_3(2, 3),
3
array_y2 : temporary, array_y2_higher : temporary,
4 1, 4
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 4,
glob_h 2, 3
array_tmp5 : array_y2 - array_const_1D0 ,
3 3 3
if not array_y1_set_initial then (if 3 <= glob_max_terms
2, 4
1
then (temporary : array_tmp5 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 : ats(4, array_m1, array_y1, 1),
4
array_tmp2 : array_tmp1 + array_const_0D0 ,
4 4 4
array_tmp3 : array_const_1D0 + array_tmp2 ,
4 4 4
if not array_y2_set_initial then (if 4 <= glob_max_terms
1, 5
1
then (temporary : array_tmp3 glob_h factorial_3(3, 4),
4
array_y2 : temporary, array_y2_higher : temporary,
5 1, 5
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 5,
glob_h 2, 4
array_tmp5 : array_y2 - array_const_1D0 ,
4 4 4
if not array_y1_set_initial then (if 4 <= glob_max_terms
2, 5
1
then (temporary : array_tmp5 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 : ats(5, array_m1, array_y1, 1),
5
array_tmp2 : array_tmp1 + array_const_0D0 ,
5 5 5
array_tmp3 : array_const_1D0 + array_tmp2 ,
5 5 5
if not array_y2_set_initial then (if 5 <= glob_max_terms
1, 6
1
then (temporary : array_tmp3 glob_h factorial_3(4, 5),
5
array_y2 : temporary, array_y2_higher : temporary,
6 1, 6
temporary 2.0
temporary : -------------, array_y2_higher : temporary)), kkk : 6,
glob_h 2, 5
array_tmp5 : array_y2 - array_const_1D0 ,
5 5 5
if not array_y1_set_initial then (if 5 <= glob_max_terms
2, 6
1
then (temporary : array_tmp5 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
ats(kkk, array_m1, array_y1, 1), array_tmp2 :
kkk
array_tmp1 + array_const_0D0 , array_tmp3 :
kkk kkk kkk
array_const_1D0 + array_tmp2 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y2_set_initial
1, order_d + kkk
order_d
array_tmp3 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_tmp5 :
kkk
array_y2 - array_const_1D0 , 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_tmp5 glob_h
kkk
then (temporary : -----------------------------------------,
factorial_3(kkk - 1, - 1 + order_d + kkk)
array_y1 : temporary, array_y1_higher :
order_d + kkk 1, order_d + kkk
temporary, term : - 1 + order_d + kkk, adj2 : 2,
while (adj2 <= 1 + order_d) and (term >= 1) do (temporary :
temporary convfp(adj2)
----------------------, array_y1_higher : temporary,
glob_h adj2, term
adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk))
log(x)
(%i9) log10(x) := ---------
log(10.0)
log(x)
(%o9) log10(x) := ---------
log(10.0)
(%i10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i11) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o11) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i12) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o12) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i16) dump_series(iolevel, dump_label, series_name, array_series, numb) :=
if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i))
i
(%o16) dump_series(iolevel, dump_label, series_name, array_series, numb) :=
if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i))
i
(%i17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb,
subnum) := if glob_iolevel >= iolevel then (sub : 1,
while sub <= subnum do (i : 1, while i <=
num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))
sub, i
(%o17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb,
subnum) := if glob_iolevel >= iolevel then (sub : 1,
while sub <= subnum do (i : 1, while i <=
num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))
sub, i
(%i18) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o18) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, "
"),
if secs >= 0.0 then (sec_in_millinium :
sec_in_min min_in_hour hours_in_day days_in_year years_in_century
secs
centuries_in_millinium, milliniums : ----------------,
sec_in_millinium
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) centuries_in_millinium,
cent_int : floor(centuries), years : (centuries - cent_int) years_in_century,
years_int : floor(years), days : (years - years_int) days_in_year,
days_int : floor(days), hours : (days - days_int) hours_in_day,
hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour,
minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min,
sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\
Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(fd,
"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds",
minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int))
else printf(fd, "Unknown"), printf(fd, " | "))
(%o19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""),
if secs >= 0.0 then (sec_in_millinium :
sec_in_min min_in_hour hours_in_day days_in_year years_in_century
secs
centuries_in_millinium, milliniums : ----------------,
sec_in_millinium
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) centuries_in_millinium,
cent_int : floor(centuries), years : (centuries - cent_int) years_in_century,
years_int : floor(years), days : (years - years_int) days_in_year,
days_int : floor(days), hours : (days - days_int) hours_in_day,
hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour,
minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min,
sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\
Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(fd,
"~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds",
minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int))
else printf(fd, "Unknown"), printf(fd, " | "))
(%i20) omniout_timestr(secs_in) := (secs : convfloat(secs_in),
if secs >= convfloat(0.0) then (sec_in_millinium :
convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day)
convfloat(days_in_year) convfloat(years_in_century)
secs
convfloat(centuries_in_millinium), milliniums : ---------------------------,
convfloat(sec_in_millinium)
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) convfloat(centuries_in_millinium),
cent_int : floor(centuries), years : (centuries - cent_int)
convfloat(years_in_century), years_int : floor(years),
days : (years - years_int) convfloat(days_in_year), days_int : floor(days),
hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours),
minutes : (hours - hours_int) convfloat(min_in_hour),
minutes_int : floor(minutes), seconds :
(minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds),
if millinium_int > 0 then printf(true,
"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(true,
"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o20) omniout_timestr(secs_in) := (secs : convfloat(secs_in),
if secs >= convfloat(0.0) then (sec_in_millinium :
convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day)
convfloat(days_in_year) convfloat(years_in_century)
secs
convfloat(centuries_in_millinium), milliniums : ---------------------------,
convfloat(sec_in_millinium)
millinium_int : floor(milliniums), centuries :
(milliniums - millinium_int) convfloat(centuries_in_millinium),
cent_int : floor(centuries), years : (centuries - cent_int)
convfloat(years_in_century), years_int : floor(years),
days : (years - years_int) convfloat(days_in_year), days_int : floor(days),
hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours),
minutes : (hours - hours_int) convfloat(min_in_hour),
minutes_int : floor(minutes), seconds :
(minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds),
if millinium_int > 0 then printf(true,
"= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elseif cent_int > 0 then printf(true,
"= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int,
years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0
then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",
years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i21) mode_declare(ats, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o21) [ats]
(%i22) ats(mmm_ats, array_a, array_b, jjj_ats) :=
(ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats,
iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o22) ats(mmm_ats, array_a, array_b, jjj_ats) :=
(ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats,
iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i23) mode_declare(att, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o23) [att]
(%i24) att(mmm_att, array_aa, array_bb, jjj_att) :=
(ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att,
iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : array_aa array_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o24) att(mmm_att, array_aa, array_bb, jjj_att) :=
(ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att,
iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : array_aa array_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i25) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o25) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i26) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o26) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i27) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o27) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i28) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o28) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i29) log_revs(file, revs) := printf(file, revs)
(%o29) log_revs(file, revs) := printf(file, revs)
(%i30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i31) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o31) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i32) logstart(file) := printf(file, "")
(%o32) logstart(file) := printf(file, "
")
(%i33) logend(file) := printf(file, "
~%")
(%o33) logend(file) := printf(file, "~%")
(%i34) chk_data() := (errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o34) chk_data() := (errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i35) mode_declare(comp_expect_sec, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o35) [comp_expect_sec]
(%i36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) :=
(ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) :=
(ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i37) mode_declare(comp_percent, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o37) [comp_percent]
(%i38) comp_percent(t_end2, t_start2, t2) :=
(sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o38) comp_percent(t_end2, t_start2, t2) :=
(sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i39) mode_declare(factorial_1, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o39) [factorial_1]
(%i40) factorial_1(nnn) := nnn!
(%o40) factorial_1(nnn) := nnn!
(%i41) mode_declare(factorial_3, bfloat)
modedeclare: bfloat
is not a built-in type; assuming it is a Maxima extension type.
(%o41) [factorial_3]
mmm2!
(%i42) factorial_3(mmm2, nnn2) := -----
nnn2!
mmm2!
(%o42) factorial_3(mmm2, nnn2) := -----
nnn2!
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := (t : elapsed_real_time(), t)
(%i46) arcsin(x) := asin(x)
(%o46) arcsin(x) := asin(x)
(%i47) arccos(x) := acos(x)
(%o47) arccos(x) := acos(x)
(%i48) arctan(x) := atan(x)
(%o48) arctan(x) := atan(x)
(%i49) exact_soln_y1(x) := cos(x) + 1.0
(%o49) exact_soln_y1(x) := cos(x) + 1.0
(%i50) exact_soln_y2(x) := 1.0 - sin(x)
(%o50) exact_soln_y2(x) := 1.0 - sin(x)
(%i51) mainprog() := (define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_hmax, 1.0, float), define_variable(glob_h, 0.1, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(djd_debug, true, boolean),
define_variable(glob_start, 0, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_clock_sec, 0.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(djd_debug2, true, boolean),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(years_in_century, 100.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_html_log, true, boolean), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/mtest3postode.ode#################"),
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"),
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = 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 : 0.1,"), omniout_str(ALWAYS, "x_end : 0.5,"),
omniout_str(ALWAYS, "glob_h : 0.00001,"),
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, "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, ""), 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_m1, 1 + max_terms), array(array_type_pole, 1 + max_terms),
array(array_y2_init, 1 + max_terms), array(array_y2, 1 + max_terms),
array(array_y1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_y2_set_initial, 1 + 3, 1 + max_terms),
array(array_complex_pole, 1 + 2, 1 + 3),
array(array_y1_higher_work, 1 + 2, 1 + max_terms),
array(array_y1_higher, 1 + 2, 1 + max_terms),
array(array_y2_higher_work2, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_y2_higher_work, 1 + 2,
1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3),
array(array_y1_higher_work2, 1 + 2, 1 + max_terms),
array(array_y1_set_initial, 1 + 3, 1 + max_terms),
array(array_y2_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_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_y2_init : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_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_tmp5 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 3 do (term : 1, while term <=
max_terms do (array_y2_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_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), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y2_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y2_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 3 do (term : 1, while term <=
max_terms do (array_y1_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y2_higher : 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_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_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_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_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 : 0.1, x_end : 0.5, glob_h : 1.0E-5,
1
array_y1_init : exact_soln_y1(x_start),
1 + 0
array_y2_init : exact_soln_y2(x_start), glob_max_iter : 20,
1 + 0
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 : false,
1, 1 1, 2
array_y2_set_initial : false, array_y2_set_initial : false,
1, 3 1, 4
array_y2_set_initial : false, array_y2_set_initial : false,
1, 5 1, 6
array_y2_set_initial : false, array_y2_set_initial : false,
1, 7 1, 8
array_y2_set_initial : false, array_y2_set_initial : false,
1, 9 1, 10
array_y2_set_initial : false, array_y2_set_initial : false,
1, 11 1, 12
array_y2_set_initial : false, array_y2_set_initial : false,
1, 13 1, 14
array_y2_set_initial : false, array_y2_set_initial : false,
1, 15 1, 16
array_y2_set_initial : false, array_y2_set_initial : false,
1, 17 1, 18
array_y2_set_initial : false, array_y2_set_initial : false,
1, 19 1, 20
array_y2_set_initial : false, array_y2_set_initial : false,
1, 21 1, 22
array_y2_set_initial : false, array_y2_set_initial : false,
1, 23 1, 24
array_y2_set_initial : false, array_y2_set_initial : false,
1, 25 1, 26
array_y2_set_initial : false, array_y2_set_initial : false,
1, 27 1, 28
array_y2_set_initial : false, array_y2_set_initial : false,
1, 29 1, 30
array_y1_set_initial : true, array_y1_set_initial : false,
2, 1 2, 2
array_y1_set_initial : false, array_y1_set_initial : false,
2, 3 2, 4
array_y1_set_initial : false, array_y1_set_initial : false,
2, 5 2, 6
array_y1_set_initial : false, array_y1_set_initial : false,
2, 7 2, 8
array_y1_set_initial : false, array_y1_set_initial : false,
2, 9 2, 10
array_y1_set_initial : false, array_y1_set_initial : false,
2, 11 2, 12
array_y1_set_initial : false, array_y1_set_initial : false,
2, 13 2, 14
array_y1_set_initial : false, array_y1_set_initial : false,
2, 15 2, 16
array_y1_set_initial : false, array_y1_set_initial : false,
2, 17 2, 18
array_y1_set_initial : false, array_y1_set_initial : false,
2, 19 2, 20
array_y1_set_initial : false, array_y1_set_initial : false,
2, 21 2, 22
array_y1_set_initial : false, array_y1_set_initial : false,
2, 23 2, 24
array_y1_set_initial : false, array_y1_set_initial : false,
2, 25 2, 26
array_y1_set_initial : false, array_y1_set_initial : false,
2, 27 2, 28
array_y1_set_initial : false, array_y1_set_initial : false,
2, 29 2, 30
if glob_html_log then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, order_diff : 1, 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 <= 2 do (atomall(), subiter : 1 + subiter))
else (subiter : 1, while subiter <= glob_max_terms + 2 do (atomall(),
subiter : 1 + subiter)), if glob_look_poles then check_for_pole(),
array_x : glob_h + array_x , array_x : glob_h, order_diff : 1, ord : 2,
1 1 2
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_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 : 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 , 1 ) = m1 * y1 + 1.0;"),
omniout_str(INFO, "diff ( y1 , x , 1 ) = 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,
"2012-06-13T14:42:20-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mtest3"),
logitem_str(html_log_file, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_integer(html_log_file,
glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 090 | "), logitem_str(html_log_file, "mtest3 diffeq.max"), logitem_str(html_log_file, "\
mtest3 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 ) = 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))
(%o51) mainprog() := (define_variable(glob_max_terms, 30, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(INFO, 2, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_warned2, false, boolean),
define_variable(glob_dump, false, boolean),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_look_poles, false, boolean),
define_variable(hours_in_day, 24.0, float),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_warned, false, boolean),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_hmax, 1.0, float), define_variable(glob_h, 0.1, float),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(centuries_in_millinium, 10.0, float),
define_variable(glob_display_flag, true, boolean),
define_variable(djd_debug, true, boolean),
define_variable(glob_start, 0, fixnum),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_clock_sec, 0.0, float),
define_variable(sec_in_min, 60.0, float),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_max_minutes, 0.0, float),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(djd_debug2, true, boolean),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(min_in_hour, 60.0, float),
define_variable(glob_iter, 0, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(years_in_century, 100.0, float),
define_variable(days_in_year, 365.0, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_html_log, true, boolean), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/mtest3postode.ode#################"),
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"),
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = 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 : 0.1,"), omniout_str(ALWAYS, "x_end : 0.5,"),
omniout_str(ALWAYS, "glob_h : 0.00001,"),
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, "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, ""), 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_m1, 1 + max_terms), array(array_type_pole, 1 + max_terms),
array(array_y2_init, 1 + max_terms), array(array_y2, 1 + max_terms),
array(array_y1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms),
array(array_y2_set_initial, 1 + 3, 1 + max_terms),
array(array_complex_pole, 1 + 2, 1 + 3),
array(array_y1_higher_work, 1 + 2, 1 + max_terms),
array(array_y1_higher, 1 + 2, 1 + max_terms),
array(array_y2_higher_work2, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_y2_higher_work, 1 + 2,
1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3),
array(array_y1_higher_work2, 1 + 2, 1 + max_terms),
array(array_y1_set_initial, 1 + 3, 1 + max_terms),
array(array_y2_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_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_y2_init : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_norms : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_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_tmp5 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 3 do (term : 1, while term <=
max_terms do (array_y2_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_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), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y2_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y2_higher_work : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_real_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y1_higher_work2 : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 3 do (term : 1, while term <=
max_terms do (array_y1_set_initial : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y2_higher : 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_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_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_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_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 : 0.1, x_end : 0.5, glob_h : 1.0E-5,
1
array_y1_init : exact_soln_y1(x_start),
1 + 0
array_y2_init : exact_soln_y2(x_start), glob_max_iter : 20,
1 + 0
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 : false,
1, 1 1, 2
array_y2_set_initial : false, array_y2_set_initial : false,
1, 3 1, 4
array_y2_set_initial : false, array_y2_set_initial : false,
1, 5 1, 6
array_y2_set_initial : false, array_y2_set_initial : false,
1, 7 1, 8
array_y2_set_initial : false, array_y2_set_initial : false,
1, 9 1, 10
array_y2_set_initial : false, array_y2_set_initial : false,
1, 11 1, 12
array_y2_set_initial : false, array_y2_set_initial : false,
1, 13 1, 14
array_y2_set_initial : false, array_y2_set_initial : false,
1, 15 1, 16
array_y2_set_initial : false, array_y2_set_initial : false,
1, 17 1, 18
array_y2_set_initial : false, array_y2_set_initial : false,
1, 19 1, 20
array_y2_set_initial : false, array_y2_set_initial : false,
1, 21 1, 22
array_y2_set_initial : false, array_y2_set_initial : false,
1, 23 1, 24
array_y2_set_initial : false, array_y2_set_initial : false,
1, 25 1, 26
array_y2_set_initial : false, array_y2_set_initial : false,
1, 27 1, 28
array_y2_set_initial : false, array_y2_set_initial : false,
1, 29 1, 30
array_y1_set_initial : true, array_y1_set_initial : false,
2, 1 2, 2
array_y1_set_initial : false, array_y1_set_initial : false,
2, 3 2, 4
array_y1_set_initial : false, array_y1_set_initial : false,
2, 5 2, 6
array_y1_set_initial : false, array_y1_set_initial : false,
2, 7 2, 8
array_y1_set_initial : false, array_y1_set_initial : false,
2, 9 2, 10
array_y1_set_initial : false, array_y1_set_initial : false,
2, 11 2, 12
array_y1_set_initial : false, array_y1_set_initial : false,
2, 13 2, 14
array_y1_set_initial : false, array_y1_set_initial : false,
2, 15 2, 16
array_y1_set_initial : false, array_y1_set_initial : false,
2, 17 2, 18
array_y1_set_initial : false, array_y1_set_initial : false,
2, 19 2, 20
array_y1_set_initial : false, array_y1_set_initial : false,
2, 21 2, 22
array_y1_set_initial : false, array_y1_set_initial : false,
2, 23 2, 24
array_y1_set_initial : false, array_y1_set_initial : false,
2, 25 2, 26
array_y1_set_initial : false, array_y1_set_initial : false,
2, 27 2, 28
array_y1_set_initial : false, array_y1_set_initial : false,
2, 29 2, 30
if glob_html_log then html_log_file : openw("html/entry.html"),
omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, order_diff : 1, 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 <= 2 do (atomall(), subiter : 1 + subiter))
else (subiter : 1, while subiter <= glob_max_terms + 2 do (atomall(),
subiter : 1 + subiter)), if glob_look_poles then check_for_pole(),
array_x : glob_h + array_x , array_x : glob_h, order_diff : 1, ord : 2,
1 1 2
calc_term : 1, iii : glob_max_terms, while iii >=
calc_term do (array_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 : 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 , 1 ) = m1 * y1 + 1.0;"),
omniout_str(INFO, "diff ( y1 , x , 1 ) = 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,
"2012-06-13T14:42:20-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mtest3"),
logitem_str(html_log_file, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_integer(html_log_file,
glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_optimal_expect_sec)), 0)
else (logitem_str(html_log_file, "Done"), 0),
log_revs(html_log_file, " 090 | "), logitem_str(html_log_file, "mtest3 diffeq.max"), logitem_str(html_log_file, "\
mtest3 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 ) = 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))
(%i52) mainprog()
"##############ECHO OF PROBLEM#################"
"##############temp/mtest3postode.ode#################"
"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"
"diff ( y1 , x , 1 ) = y2 - 1.0;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits : 32,"
"max_terms : 30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start : 0.1,"
"x_end : 0.5,"
"glob_h : 0.00001,"
"array_y1_init[0 + 1] : exact_soln_y1(x_start),"
"array_y2_init[0 + 1] : exact_soln_y2(x_start),"
"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) "
");"
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
x[1] = 0.1 " "
y2[1] (analytic) = 0.9001665833531718 " "
y2[1] (numeric) = 0.9001665833531718 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9950041652780257 " "
y1[1] (numeric) = 1.9950041652780257 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
x[1] = 0.1 " "
y2[1] (analytic) = 0.9001665833531718 " "
y2[1] (numeric) = 0.9001665833531718 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9950041652780257 " "
y1[1] (numeric) = 1.9950041652780257 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10010000000000001 " "
y2[1] (analytic) = 0.900067083435977 " "
y2[1] (numeric) = 0.9000670834359769 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.233489197701704600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9949941769613568 " "
y1[1] (numeric) = 1.9949941769613568 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10020000000000001 " "
y2[1] (analytic) = 0.8999675845181112 " "
y2[1] (numeric) = 0.8999675845181111 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.233625570213872600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9949841786947462 " "
y1[1] (numeric) = 1.9949841786947462 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10030000000000001 " "
y2[1] (analytic) = 0.8998680866005697 " "
y2[1] (numeric) = 0.8998680866005695 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.467523943024236600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9949741704782937 " "
y1[1] (numeric) = 1.9949741704782937 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10040000000000002 " "
y2[1] (analytic) = 0.8997685896843473 " "
y2[1] (numeric) = 0.899768589684347 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.467796803208344700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9949641523120998 " "
y1[1] (numeric) = 1.9949641523120996 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113025538166631800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10050000000000002 " "
y2[1] (analytic) = 0.8996690937704389 " "
y2[1] (numeric) = 0.8996690937704387 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.46806972099553520000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9949541241962643 " "
y1[1] (numeric) = 1.9949541241962638 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226062266113408600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10060000000000002 " "
y2[1] (analytic) = 0.8995695988598396 " "
y2[1] (numeric) = 0.8995695988598394 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.234171348200639300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9949440861308871 " "
y1[1] (numeric) = 1.994944086130887 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113036733554160800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10070000000000003 " "
y2[1] (analytic) = 0.8994701049535443 " "
y2[1] (numeric) = 0.8994701049535442 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.234307864720525900000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9949340381160696 " "
y1[1] (numeric) = 1.9949340381160692 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22608467931822700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10080000000000003 " "
y2[1] (analytic) = 0.899370612052548 " "
y2[1] (numeric) = 0.8993706120525479 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.234444410065167900000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9949239801519116 " "
y1[1] (numeric) = 1.9949239801519112 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226095902743350000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10090000000000003 " "
y2[1] (analytic) = 0.8992711201578456 " "
y2[1] (numeric) = 0.8992711201578454 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.469161968484617800000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9949139122385136 " "
y1[1] (numeric) = 1.9949139122385133 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11305356869195800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10100000000000003 " "
y2[1] (analytic) = 0.8991716292704319 " "
y2[1] (numeric) = 0.8991716292704317 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.469435174519389600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9949038343759766 " "
y1[1] (numeric) = 1.9949038343759764 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113059191620075200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10110000000000004 " "
y2[1] (analytic) = 0.899072139391302 " "
y2[1] (numeric) = 0.8990721393913018 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.469708438250149400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9948937465644012 " "
y1[1] (numeric) = 1.994893746564401 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113064820156139800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10120000000000004 " "
y2[1] (analytic) = 0.8989726505214507 " "
y2[1] (numeric) = 0.8989726505214505 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.469981759692399500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9948836488038886 " "
y1[1] (numeric) = 1.9948836488038881 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226140908600528500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10130000000000004 " "
y2[1] (analytic) = 0.8988731626618729 " "
y2[1] (numeric) = 0.8988731626618727 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.470255138861647500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9948735410945393 " "
y1[1] (numeric) = 1.9948735410945388 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226152188105124400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10140000000000005 " "
y2[1] (analytic) = 0.8987736758135634 " "
y2[1] (numeric) = 0.8987736758135633 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.235264287886703700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9948634234364546 " "
y1[1] (numeric) = 1.9948634234364542 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22616347882629300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10150000000000005 " "
y2[1] (analytic) = 0.8986741899775172 " "
y2[1] (numeric) = 0.898674189977517 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.470802070443197400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9948532958297358 " "
y1[1] (numeric) = 1.9948532958297354 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226174780764261200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10160000000000005 " "
y2[1] (analytic) = 0.898574705154729 " "
y2[1] (numeric) = 0.8985747051547289 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.235537811443271200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9948431582744839 " "
y1[1] (numeric) = 1.9948431582744834 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226186093919256300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10170000000000005 " "
y2[1] (analytic) = 0.898475221346194 " "
y2[1] (numeric) = 0.8984752213461937 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.471349233118969600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9948330107708006 " "
y1[1] (numeric) = 1.9948330107708 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22619741829150480000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10180000000000006 " "
y2[1] (analytic) = 0.8983757385529065 " "
y2[1] (numeric) = 0.8983757385529063 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.471622901156015600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9948228533187868 " "
y1[1] (numeric) = 1.9948228533187866 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113104376940617600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10190000000000006 " "
y2[1] (analytic) = 0.8982762567758618 " "
y2[1] (numeric) = 0.8982762567758615 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.471896627013219200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.994812685918545 " "
y1[1] (numeric) = 1.9948126859185447 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226220100688673400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10200000000000006 " "
y2[1] (analytic) = 0.8981767760160544 " "
y2[1] (numeric) = 0.8981767760160542 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.472170410706125700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9948025085701762 " "
y1[1] (numeric) = 1.9948025085701757 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226231458714048300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10210000000000007 " "
y2[1] (analytic) = 0.8980772962744793 " "
y2[1] (numeric) = 0.8980772962744791 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.472444252250285700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9947923212737821 " "
y1[1] (numeric) = 1.9947923212737817 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22624282795758800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10220000000000007 " "
y2[1] (analytic) = 0.8979778175521312 " "
y2[1] (numeric) = 0.897977817552131 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.472718151661254500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.994782124029465 " "
y1[1] (numeric) = 1.9947821240294645 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226254208419520500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10230000000000007 " "
y2[1] (analytic) = 0.897878339850005 " "
y2[1] (numeric) = 0.8978783398500048 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.472992108954593400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9947719168373266 " "
y1[1] (numeric) = 1.9947719168373261 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226265600100074000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10240000000000007 " "
y2[1] (analytic) = 0.8977788631690954 " "
y2[1] (numeric) = 0.8977788631690952 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.473266124145869200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9947616996974689 " "
y1[1] (numeric) = 1.9947616996974686 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113138501499739100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10250000000000008 " "
y2[1] (analytic) = 0.8976793875103971 " "
y2[1] (numeric) = 0.8976793875103969 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.47354019725065300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9947514726099944 " "
y1[1] (numeric) = 1.9947514726099942 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113144208558980400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10260000000000008 " "
y2[1] (analytic) = 0.8975799128749049 " "
y2[1] (numeric) = 0.8975799128749048 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.236907164142261300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9947412355750052 " "
y1[1] (numeric) = 1.994741235575005 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113149921227876100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10270000000000008 " "
y2[1] (analytic) = 0.8974804392636136 " "
y2[1] (numeric) = 0.8974804392636135 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.237044258631529600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9947309885926034 " "
y1[1] (numeric) = 1.9947309885926032 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113155639506540500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10280000000000009 " "
y2[1] (analytic) = 0.897380966677518 " "
y2[1] (numeric) = 0.8973809666775179 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.237181382100925700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.994720731662892 " "
y1[1] (numeric) = 1.9947207316628917 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226322726790176400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10290000000000009 " "
y2[1] (analytic) = 0.8972814951176127 " "
y2[1] (numeric) = 0.8972814951176126 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.23731853455824600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9947104647859732 " "
y1[1] (numeric) = 1.9947104647859728 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226334185787269500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10300000000000009 " "
y2[1] (analytic) = 0.8971820245848924 " "
y2[1] (numeric) = 0.8971820245848923 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.237455716011289800000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.99470018796195 " "
y1[1] (numeric) = 1.9947001879619493 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33951848400688500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1031000000000001 " "
y2[1] (analytic) = 0.8970825550803518 " "
y2[1] (numeric) = 0.8970825550803517 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.237592926467858500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9946899011909245 " "
y1[1] (numeric) = 1.994689901190924 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226357137442367700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1032000000000001 " "
y2[1] (analytic) = 0.8969830866049857 " "
y2[1] (numeric) = 0.8969830866049856 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.23773016593575700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9946796044730002 " "
y1[1] (numeric) = 1.9946796044729997 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226368630100833700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1033000000000001 " "
y2[1] (analytic) = 0.8968836191597888 " "
y2[1] (numeric) = 0.8968836191597886 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.237867434422792500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9946692978082798 " "
y1[1] (numeric) = 1.9946692978082794 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226380133980218300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1034000000000001 " "
y2[1] (analytic) = 0.8967841527457556 " "
y2[1] (numeric) = 0.8967841527457555 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.238004731936774400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9946589811968667 " "
y1[1] (numeric) = 1.994658981196866 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.339587473621129500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1035000000000001 " "
y2[1] (analytic) = 0.896684687363881 " "
y2[1] (numeric) = 0.8966846873638809 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.238142058485515600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9946486546388633 " "
y1[1] (numeric) = 1.9946486546388629 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226403175402668600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10360000000000011 " "
y2[1] (analytic) = 0.8965852230151594 " "
y2[1] (numeric) = 0.8965852230151593 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.238279414076831000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9946383181343736 " "
y1[1] (numeric) = 1.9946383181343732 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226414712946196700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10370000000000011 " "
y2[1] (analytic) = 0.8964857597005856 " "
y2[1] (numeric) = 0.8964857597005855 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.238416798718538900000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.994627971683501 " "
y1[1] (numeric) = 1.9946279716835003 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33963939256735340000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10380000000000011 " "
y2[1] (analytic) = 0.8963862974211543 " "
y2[1] (numeric) = 0.8963862974211542 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.238554212418459300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9946176152863484 " "
y1[1] (numeric) = 1.9946176152863477 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33965673254852600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10390000000000012 " "
y2[1] (analytic) = 0.8962868361778599 " "
y2[1] (numeric) = 0.8962868361778598 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.238691655184415700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9946072489430198 " "
y1[1] (numeric) = 1.994607248943019 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33967408936316100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10400000000000012 " "
y2[1] (analytic) = 0.8961873759716972 " "
y2[1] (numeric) = 0.8961873759716971 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.23882912702423400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9945968726536185 " "
y1[1] (numeric) = 1.9945968726536178 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33969146301160760000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10410000000000012 " "
y2[1] (analytic) = 0.8960879168036607 " "
y2[1] (numeric) = 0.8960879168036606 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.238966627945742400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9945864864182488 " "
y1[1] (numeric) = 1.9945864864182479 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.45294513799228300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10420000000000013 " "
y2[1] (analytic) = 0.8959884586747451 " "
y2[1] (numeric) = 0.895988458674745 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.239104157956772600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9945760902370138 " "
y1[1] (numeric) = 1.994576090237013 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33972626081132760000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10430000000000013 " "
y2[1] (analytic) = 0.8958890015859449 " "
y2[1] (numeric) = 0.8958890015859448 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.239241717065158200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9945656841100181 " "
y1[1] (numeric) = 1.9945656841100174 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33974368496330100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10440000000000013 " "
y2[1] (analytic) = 0.8957895455382545 " "
y2[1] (numeric) = 0.8957895455382545 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9945552680373657 " "
y1[1] (numeric) = 1.994555268037365 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33976112595048300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10450000000000013 " "
y2[1] (analytic) = 0.8956900905326689 " "
y2[1] (numeric) = 0.8956900905326688 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.239516922605344900000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9945448420191605 " "
y1[1] (numeric) = 1.9945448420191598 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.339778583773223600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10460000000000014 " "
y2[1] (analytic) = 0.8955906365701822 " "
y2[1] (numeric) = 0.8955906365701822 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.994534406055507 " "
y1[1] (numeric) = 1.9945344060555064 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33979605843187300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10470000000000014 " "
y2[1] (analytic) = 0.8954911836517893 " "
y2[1] (numeric) = 0.8954911836517893 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9945239601465095 " "
y1[1] (numeric) = 1.9945239601465088 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33981354992678300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10480000000000014 " "
y2[1] (analytic) = 0.8953917317784844 " "
y2[1] (numeric) = 0.8953917317784844 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9945135042922724 " "
y1[1] (numeric) = 1.9945135042922717 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.339831058258304600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10490000000000015 " "
y2[1] (analytic) = 0.8952922809512623 " "
y2[1] (numeric) = 0.8952922809512622 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.240067683198973600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9945030384929 " "
y1[1] (numeric) = 1.9945030384928994 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226565722284526100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10500000000000015 " "
y2[1] (analytic) = 0.8951928311711174 " "
y2[1] (numeric) = 0.8951928311711173 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.240205446208422500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9944925627484973 " "
y1[1] (numeric) = 1.9944925627484968 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226577416955059800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10510000000000015 " "
y2[1] (analytic) = 0.8950933824390441 " "
y2[1] (numeric) = 0.895093382439044 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.240343238377994400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9944820770591694 " "
y1[1] (numeric) = 1.9944820770591687 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.33988368427605600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10520000000000015 " "
y2[1] (analytic) = 0.8949939347560371 " "
y2[1] (numeric) = 0.894993934756037 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.240481059715547600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9944715814250202 " "
y1[1] (numeric) = 1.9944715814250198 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226600839971695500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10530000000000016 " "
y2[1] (analytic) = 0.8948944881230906 " "
y2[1] (numeric) = 0.8948944881230905 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.240618910228943200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9944610758461554 " "
y1[1] (numeric) = 1.994461075846155 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22661256831826910000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10540000000000016 " "
y2[1] (analytic) = 0.8947950425411992 " "
y2[1] (numeric) = 0.8947950425411991 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.240756789926044100000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9944505603226799 " "
y1[1] (numeric) = 1.9944505603226794 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.2266243078906600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10550000000000016 " "
y2[1] (analytic) = 0.8946955980113576 " "
y2[1] (numeric) = 0.8946955980113573 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.481789397629434000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9944400348546987 " "
y1[1] (numeric) = 1.9944400348546982 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226636058689104300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10560000000000017 " "
y2[1] (analytic) = 0.8945961545345598 " "
y2[1] (numeric) = 0.8945961545345597 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.241032636902830200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.994429499442317 " "
y1[1] (numeric) = 1.9944294994423168 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11332391035691900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10570000000000017 " "
y2[1] (analytic) = 0.8944967121118005 " "
y2[1] (numeric) = 0.8944967121118004 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.241170604198255800000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9944189540856407 " "
y1[1] (numeric) = 1.9944189540856403 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22665959396509700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10580000000000017 " "
y2[1] (analytic) = 0.8943972707440742 " "
y2[1] (numeric) = 0.8943972707440739 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.482617201417734500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9944083987847747 " "
y1[1] (numeric) = 1.9944083987847743 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22667137844311800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10590000000000017 " "
y2[1] (analytic) = 0.894297830432375 " "
y2[1] (numeric) = 0.8942978304323749 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.241446626442542100000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.994397833539825 " "
y1[1] (numeric) = 1.9943978335398242 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34002476122220600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10600000000000018 " "
y2[1] (analytic) = 0.8941983911776976 " "
y2[1] (numeric) = 0.8941983911776975 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.241584681407159700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9943872583508964 " "
y1[1] (numeric) = 1.994387258350896 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22669498108039300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10610000000000018 " "
y2[1] (analytic) = 0.8940989529810364 " "
y2[1] (numeric) = 0.8940989529810361 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.48344553122120480000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9943766732180954 " "
y1[1] (numeric) = 1.994376673218095 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22670679924012100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10620000000000018 " "
y2[1] (analytic) = 0.8939995158433854 " "
y2[1] (numeric) = 0.8939995158433853 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.241860879060755600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.994366078141528 " "
y1[1] (numeric) = 1.9943660781415273 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.340077942941338500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10630000000000019 " "
y2[1] (analytic) = 0.8939000797657395 " "
y2[1] (numeric) = 0.8939000797657394 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.241999021765506200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9943554731212996 " "
y1[1] (numeric) = 1.994355473121299 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34009570386441700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10640000000000019 " "
y2[1] (analytic) = 0.8938006447490927 " "
y2[1] (numeric) = 0.8938006447490926 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.242137193732745400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9943448581575165 " "
y1[1] (numeric) = 1.9943448581575158 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34011348162977340000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10650000000000019 " "
y2[1] (analytic) = 0.8937012107944394 " "
y2[1] (numeric) = 0.8937012107944393 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.24227539497036600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9943342332502847 " "
y1[1] (numeric) = 1.9943342332502842 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226754184158510600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1066000000000002 " "
y2[1] (analytic) = 0.8936017779027741 " "
y2[1] (numeric) = 0.893601777902774 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.242413625486263700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9943235983997107 " "
y1[1] (numeric) = 1.9943235983997103 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226766058459166700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1067000000000002 " "
y2[1] (analytic) = 0.8935023460750909 " "
y2[1] (numeric) = 0.8935023460750908 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.242551885288337200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9943129536059008 " "
y1[1] (numeric) = 1.9943129536059003 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226777943988723600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1068000000000002 " "
y2[1] (analytic) = 0.8934029153123842 " "
y2[1] (numeric) = 0.8934029153123842 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9943022988689614 " "
y1[1] (numeric) = 1.994302298868961 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22678984074741900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1069000000000002 " "
y2[1] (analytic) = 0.8933034856156485 " "
y2[1] (numeric) = 0.8933034856156485 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9942916341889987 " "
y1[1] (numeric) = 1.9942916341889985 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113400874367746500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1070000000000002 " "
y2[1] (analytic) = 0.8932040569858779 " "
y2[1] (numeric) = 0.8932040569858779 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9942809595661202 " "
y1[1] (numeric) = 1.9942809595661197 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226813667953183300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10710000000000021 " "
y2[1] (analytic) = 0.8931046294240668 " "
y2[1] (numeric) = 0.8931046294240668 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9942702750004315 " "
y1[1] (numeric) = 1.9942702750004313 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113412799200365500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10720000000000021 " "
y2[1] (analytic) = 0.8930052029312092 " "
y2[1] (numeric) = 0.8930052029312093 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.24324362386797900000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9942595804920404 " "
y1[1] (numeric) = 1.9942595804920402 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113418770039187200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10730000000000021 " "
y2[1] (analytic) = 0.8929057775082997 " "
y2[1] (numeric) = 0.8929057775082998 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.243382059553127700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9942488760410535 " "
y1[1] (numeric) = 1.9942488760410533 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.11342474649317710000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10740000000000022 " "
y2[1] (analytic) = 0.8928063531563324 " "
y2[1] (numeric) = 0.8928063531563325 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.243520524579817800000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9942381616475777 " "
y1[1] (numeric) = 1.9942381616475775 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113430728562454800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10750000000000022 " "
y2[1] (analytic) = 0.8927069298763016 " "
y2[1] (numeric) = 0.8927069298763017 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.243659018955969300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9942274373117206 " "
y1[1] (numeric) = 1.9942274373117201 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226873432494281500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10760000000000022 " "
y2[1] (analytic) = 0.8926075076692015 " "
y2[1] (numeric) = 0.8926075076692016 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.243797542689505400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9942167030335889 " "
y1[1] (numeric) = 1.9942167030335884 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22688541909471100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10770000000000023 " "
y2[1] (analytic) = 0.8925080865360263 " "
y2[1] (numeric) = 0.8925080865360264 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.243936095788351300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.99420595881329 " "
y1[1] (numeric) = 1.9942059588132897 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22689741692643800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10780000000000023 " "
y2[1] (analytic) = 0.8924086664777703 " "
y2[1] (numeric) = 0.8924086664777704 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.244074678260435600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.994195204650932 " "
y1[1] (numeric) = 1.9941952046509315 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226909425989703800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10790000000000023 " "
y2[1] (analytic) = 0.8923092474954275 " "
y2[1] (numeric) = 0.8923092474954276 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.244213290113689900000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9941844405466216 " "
y1[1] (numeric) = 1.9941844405466211 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226921446284749200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10800000000000023 " "
y2[1] (analytic) = 0.8922098295899923 " "
y2[1] (numeric) = 0.8922098295899924 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.244351931356047100000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9941736665004668 " "
y1[1] (numeric) = 1.9941736665004663 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226933477811816600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10810000000000024 " "
y2[1] (analytic) = 0.8921104127624588 " "
y2[1] (numeric) = 0.892110412762459 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.24449060199544410000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9941628825125755 " "
y1[1] (numeric) = 1.994162882512575 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22694552057114700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10820000000000024 " "
y2[1] (analytic) = 0.8920109970138211 " "
y2[1] (numeric) = 0.8920109970138214 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.48925860407964080000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9941520885830553 " "
y1[1] (numeric) = 1.9941520885830548 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.226957574562982200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10830000000000024 " "
y2[1] (analytic) = 0.8919115823450736 " "
y2[1] (numeric) = 0.8919115823450737 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.244768031497117500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9941412847120144 " "
y1[1] (numeric) = 1.9941412847120137 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34045445968134740000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10840000000000025 " "
y2[1] (analytic) = 0.8918121687572101 " "
y2[1] (numeric) = 0.8918121687572103 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.244906790375280600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9941304708995604 " "
y1[1] (numeric) = 1.9941304708995597 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34047257436770550000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10850000000000025 " "
y2[1] (analytic) = 0.891712756251225 " "
y2[1] (numeric) = 0.8917127562512251 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.245045578682256600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9941196471458018 " "
y1[1] (numeric) = 1.9941196471458011 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34049070590391240000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10860000000000025 " "
y2[1] (analytic) = 0.8916133448281124 " "
y2[1] (numeric) = 0.8916133448281125 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.24518439642599610000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9941088134508467 " "
y1[1] (numeric) = 1.994108813450846 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34050885429033100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10870000000000025 " "
y2[1] (analytic) = 0.8915139344888663 " "
y2[1] (numeric) = 0.8915139344888664 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.245323243614451500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9940979698148036 " "
y1[1] (numeric) = 1.994097969814803 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34052701952732730000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10880000000000026 " "
y2[1] (analytic) = 0.8914145252344807 " "
y2[1] (numeric) = 0.891414525234481 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.490924240511157800000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9940871162377807 " "
y1[1] (numeric) = 1.99408711623778 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34054520161526540000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10890000000000026 " "
y2[1] (analytic) = 0.89131511706595 " "
y2[1] (numeric) = 0.8913151170659502 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.491202052714672500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9940762527198865 " "
y1[1] (numeric) = 1.994076252719886 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227042267036340500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10900000000000026 " "
y2[1] (analytic) = 0.8912157099842681 " "
y2[1] (numeric) = 0.8912157099842684 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.491479923855369200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.99406537926123 " "
y1[1] (numeric) = 1.9940653792612295 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22705441089695200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10910000000000027 " "
y2[1] (analytic) = 0.8911163039904291 " "
y2[1] (numeric) = 0.8911163039904294 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.73763678092376430000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9940544958619197 " "
y1[1] (numeric) = 1.994054495861919 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34059984898838500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10920000000000027 " "
y2[1] (analytic) = 0.8910168990854271 " "
y2[1] (numeric) = 0.8910168990854274 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.492035843012025400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9940436025220645 " "
y1[1] (numeric) = 1.9940436025220638 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34061809848374700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10930000000000027 " "
y2[1] (analytic) = 0.8909174952702561 " "
y2[1] (numeric) = 0.8909174952702563 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.492313891059856300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9940326992417732 " "
y1[1] (numeric) = 1.9940326992417725 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.3406363648318800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10940000000000027 " "
y2[1] (analytic) = 0.89081809254591 " "
y2[1] (numeric) = 0.8908180925459104 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.73888799716291900000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9940217860211549 " "
y1[1] (numeric) = 1.9940217860211542 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.340654648033153000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10950000000000028 " "
y2[1] (analytic) = 0.8907186909133832 " "
y2[1] (numeric) = 0.8907186909133835 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.739305246261366000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9940108628603186 " "
y1[1] (numeric) = 1.9940108628603181 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227115298725287400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10960000000000028 " "
y2[1] (analytic) = 0.8906192903736694 " "
y2[1] (numeric) = 0.8906192903736697 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.73972258390905700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.993999929759374 " "
y1[1] (numeric) = 1.9939999297593733 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.340691264996582500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10970000000000028 " "
y2[1] (analytic) = 0.8905198909277626 " "
y2[1] (numeric) = 0.890519890927763 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.740140010129933700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.99398898671843 " "
y1[1] (numeric) = 1.9939889867184293 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34070959875947600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10980000000000029 " "
y2[1] (analytic) = 0.890420492576657 " "
y2[1] (numeric) = 0.8904204925766573 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.74055752494794400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.993978033737596 " "
y1[1] (numeric) = 1.9939780337375954 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.340727949376978700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.10990000000000029 " "
y2[1] (analytic) = 0.8903210953213464 " "
y2[1] (numeric) = 0.8903210953213467 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.74097512838704600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9939670708169817 " "
y1[1] (numeric) = 1.9939670708169812 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22716421123297400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11000000000000029 " "
y2[1] (analytic) = 0.8902216991628249 " "
y2[1] (numeric) = 0.8902216991628252 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.741392820471204400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9939560979566968 " "
y1[1] (numeric) = 1.9939560979566964 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227176467451526500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1101000000000003 " "
y2[1] (analytic) = 0.8901223041020864 " "
y2[1] (numeric) = 0.8901223041020867 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.74181060122439300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9939451151568508 " "
y1[1] (numeric) = 1.9939451151568504 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227188734907224200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1102000000000003 " "
y2[1] (analytic) = 0.8900229101401248 " "
y2[1] (numeric) = 0.8900229101401251 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.742228470670592700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9939341224175537 " "
y1[1] (numeric) = 1.9939341224175533 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22720101360031300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1103000000000003 " "
y2[1] (analytic) = 0.8899235172779342 " "
y2[1] (numeric) = 0.8899235172779345 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.74264642883379400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9939231197389156 " "
y1[1] (numeric) = 1.9939231197389151 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227213303531039300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1104000000000003 " "
y2[1] (analytic) = 0.8898241255165084 " "
y2[1] (numeric) = 0.8898241255165087 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.743064475737995500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9939121071210462 " "
y1[1] (numeric) = 1.9939121071210457 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227225604699650500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1105000000000003 " "
y2[1] (analytic) = 0.8897247348568413 " "
y2[1] (numeric) = 0.8897247348568416 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.495655074271468700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9939010845640555 " "
y1[1] (numeric) = 1.9939010845640552 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113618958553196800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11060000000000031 " "
y2[1] (analytic) = 0.8896253452999269 " "
y2[1] (numeric) = 0.8896253452999271 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.495933890576954600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9938900520680543 " "
y1[1] (numeric) = 1.9938900520680538 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22725024075151600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11070000000000031 " "
y2[1] (analytic) = 0.889525956846759 " "
y2[1] (numeric) = 0.8895259568467592 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.496212766091136500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9938790096331522 " "
y1[1] (numeric) = 1.993879009633152 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113631287817632600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11080000000000031 " "
y2[1] (analytic) = 0.8894265694983315 " "
y2[1] (numeric) = 0.8894265694983318 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.49649170083003500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9938679572594604 " "
y1[1] (numeric) = 1.99386795725946 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227274921757888800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11090000000000032 " "
y2[1] (analytic) = 0.8893271832556383 " "
y2[1] (numeric) = 0.8893271832556386 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.745156042214515000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.993856894947089 " "
y1[1] (numeric) = 1.9938568949470885 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227287279119635200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11100000000000032 " "
y2[1] (analytic) = 0.8892277981196733 " "
y2[1] (numeric) = 0.8892277981196737 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.745574622069140500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9938458226961484 " "
y1[1] (numeric) = 1.993845822696148 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22729964772075300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11110000000000032 " "
y2[1] (analytic) = 0.8891284140914304 " "
y2[1] (numeric) = 0.8891284140914307 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.74599329083298400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9938347405067498 " "
y1[1] (numeric) = 1.9938347405067494 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.2273120275614902000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11120000000000033 " "
y2[1] (analytic) = 0.8890290311719032 " "
y2[1] (numeric) = 0.8890290311719036 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.74641204853011100000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9938236483790037 " "
y1[1] (numeric) = 1.9938236483790033 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227324418642095400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11130000000000033 " "
y2[1] (analytic) = 0.8889296493620858 " "
y2[1] (numeric) = 0.8889296493620862 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.74683089518459240000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9938125463130212 " "
y1[1] (numeric) = 1.9938125463130207 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227336820962818300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11140000000000033 " "
y2[1] (analytic) = 0.888830268662972 " "
y2[1] (numeric) = 0.8888302686629723 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.74724983082050930000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9938014343089132 " "
y1[1] (numeric) = 1.9938014343089128 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227349234523907400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11150000000000033 " "
y2[1] (analytic) = 0.8887308890755553 " "
y2[1] (numeric) = 0.8887308890755558 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.99689180728260300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9937903123667908 " "
y1[1] (numeric) = 1.9937903123667904 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227361659325612400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11160000000000034 " "
y2[1] (analytic) = 0.8886315106008298 " "
y2[1] (numeric) = 0.8886315106008302 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.9974506255106900000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9937791804867655 " "
y1[1] (numeric) = 1.9937791804867648 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34106114305227400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11170000000000034 " "
y2[1] (analytic) = 0.8885321332397893 " "
y2[1] (numeric) = 0.8885321332397896 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.748507171857810600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9937680386689483 " "
y1[1] (numeric) = 1.9937680386689476 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34107981397780300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11180000000000034 " "
y2[1] (analytic) = 0.8884327569934273 " "
y2[1] (numeric) = 0.8884327569934277 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.99856861821392800000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9937568869134505 " "
y1[1] (numeric) = 1.9937568869134499 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34109850176538100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11190000000000035 " "
y2[1] (analytic) = 0.8883333818627378 " "
y2[1] (numeric) = 0.8883333818627382 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.99912779275339400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9937457252203838 " "
y1[1] (numeric) = 1.9937457252203834 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22741147094358800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11200000000000035 " "
y2[1] (analytic) = 0.8882340078487144 " "
y2[1] (numeric) = 0.8882340078487149 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.999687086127653000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.99373455358986 " "
y1[1] (numeric) = 1.9937345535898596 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22742395195212220000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11210000000000035 " "
y2[1] (analytic) = 0.8881346349523511 " "
y2[1] (numeric) = 0.8881346349523515 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.750184873776667400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9937233720219911 " "
y1[1] (numeric) = 1.9937233720219905 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34115466630415900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11220000000000036 " "
y2[1] (analytic) = 0.8880352631746413 " "
y2[1] (numeric) = 0.8880352631746417 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.75060452213197600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.993712180516888 " "
y1[1] (numeric) = 1.9937121805168876 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227448947695792300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11230000000000036 " "
y2[1] (analytic) = 0.8879358925165789 " "
y2[1] (numeric) = 0.8879358925165792 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.751024259685822000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9937009790746631 " "
y1[1] (numeric) = 1.9937009790746627 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227461462431431800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11240000000000036 " "
y2[1] (analytic) = 0.8878365229791576 " "
y2[1] (numeric) = 0.8878365229791579 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.751444086462366600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9936897676954286 " "
y1[1] (numeric) = 1.9936897676954282 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227473988409941500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11250000000000036 " "
y2[1] (analytic) = 0.8877371545633711 " "
y2[1] (numeric) = 0.8877371545633714 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.75186400248578240000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9936785463792965 " "
y1[1] (numeric) = 1.9936785463792959 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.34122978844736100000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11260000000000037 " "
y2[1] (analytic) = 0.8876377872702129 " "
y2[1] (numeric) = 0.8876377872702134 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.003045343707003000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9936673151263786 " "
y1[1] (numeric) = 1.9936673151263782 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227499074096581700000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11270000000000037 " "
y2[1] (analytic) = 0.887538421100677 " "
y2[1] (numeric) = 0.8875384211006774 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.752704102369962500000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.993656073936788 " "
y1[1] (numeric) = 1.9936560739367875 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227511633805215600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11280000000000037 " "
y2[1] (analytic) = 0.8874390560557568 " "
y2[1] (numeric) = 0.8874390560557572 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.00416571503881400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9936448228106363 " "
y1[1] (numeric) = 1.9936448228106358 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22752420475772900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11290000000000038 " "
y2[1] (analytic) = 0.887339692136446 " "
y2[1] (numeric) = 0.8873396921364465 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.00472607937586900000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9936335617480365 " "
y1[1] (numeric) = 1.993633561748036 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227536786954374000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11300000000000038 " "
y2[1] (analytic) = 0.8872403293437384 " "
y2[1] (numeric) = 0.8872403293437389 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.005286562870067000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9936222907491012 " "
y1[1] (numeric) = 1.9936222907491008 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.22754938039540400000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11310000000000038 " "
y2[1] (analytic) = 0.8871409676786275 " "
y2[1] (numeric) = 0.8871409676786279 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.005847165553703000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.993611009813943 " "
y1[1] (numeric) = 1.9936110098139426 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.227561985081071600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11320000000000038 " "
y2[1] (analytic) = 0.8870416071421068 " "
y2[1] (numeric) = 0.8870416071421073 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.25800985932385600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9935997189426744 " "
y1[1] (numeric) = 1.9935997189426742 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113787300505815000000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11330000000000039 " "
y2[1] (analytic) = 0.8869422477351702 " "
y2[1] (numeric) = 0.8869422477351706 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.0069687286185300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9935884181354089 " "
y1[1] (numeric) = 1.9935884181354087 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113793614093666800000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11340000000000039 " "
y2[1] (analytic) = 0.886842889458811 " "
y2[1] (numeric) = 0.8868428894588114 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.00752968906437000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9935771073922592 " "
y1[1] (numeric) = 1.993577107392259 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113799933304217600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11350000000000039 " "
y2[1] (analytic) = 0.8867435323140228 " "
y2[1] (numeric) = 0.8867435323140234 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 6.26011346103617600000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9935657867133385 " "
y1[1] (numeric) = 1.9935657867133383 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113806258137594500000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1136000000000004 " "
y2[1] (analytic) = 0.8866441763017995 " "
y2[1] (numeric) = 0.8866441763017999 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.00865196794460000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9935544560987597 " "
y1[1] (numeric) = 1.9935544560987597 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1137000000000004 " "
y2[1] (analytic) = 0.8865448214231343 " "
y2[1] (numeric) = 0.8865448214231347 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.00921328644370400000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9935431155486367 " "
y1[1] (numeric) = 1.9935431155486365 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113818924673335200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1138000000000004 " "
y2[1] (analytic) = 0.8864454676790209 " "
y2[1] (numeric) = 0.8864454676790213 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.00977472435863300000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9935317650630822 " "
y1[1] (numeric) = 1.9935317650630822 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1139000000000004 " "
y2[1] (analytic) = 0.8863461150704528 " "
y2[1] (numeric) = 0.8863461150704532 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.010336281721768000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9935204046422101 " "
y1[1] (numeric) = 1.9935204046422101 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.1140000000000004 " "
y2[1] (analytic) = 0.8862467635984236 " "
y2[1] (numeric) = 0.886246763598424 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.010897958565504000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9935090342861344 " "
y1[1] (numeric) = 1.9935090342861341 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113837966651324300000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11410000000000041 " "
y2[1] (analytic) = 0.8861474132639268 " "
y2[1] (numeric) = 0.8861474132639272 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.011459754922253000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.993497653994968 " "
y1[1] (numeric) = 1.9934976539949678 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113844325224331600000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11420000000000041 " "
y2[1] (analytic) = 0.8860480640679558 " "
y2[1] (numeric) = 0.8860480640679562 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.012021670824428000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9934862637688249 " "
y1[1] (numeric) = 1.9934862637688249 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11430000000000042 " "
y2[1] (analytic) = 0.8859487160115042 " "
y2[1] (numeric) = 0.8859487160115046 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.012583706304463000000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9934748636078194 " "
y1[1] (numeric) = 1.9934748636078194 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11440000000000042 " "
y2[1] (analytic) = 0.8858493690955653 " "
y2[1] (numeric) = 0.8858493690955658 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.01314586139479800000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9934634535120654 " "
y1[1] (numeric) = 1.9934634535120652 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113863434686174900000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11450000000000042 " "
y2[1] (analytic) = 0.885750023321133 " "
y2[1] (numeric) = 0.8857500233211333 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.76028110209591200000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9934520334816765 " "
y1[1] (numeric) = 1.9934520334816765 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11460000000000042 " "
y2[1] (analytic) = 0.8856506786892002 " "
y2[1] (numeric) = 0.8856506786892006 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.76070289790213700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9934406035167678 " "
y1[1] (numeric) = 1.9934406035167676 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.113876202447702200000000000000E-14 "%"
h = 1.0000E-4 " "
" "
"TOP MAIN SOLVE Loop"
"NO POLE"
"NO POLE"
x[1] = 0.11470000000000043 " "
y2[1] (analytic) = 0.8855513352007607 " "
y2[1] (numeric) = 0.885551335200761 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.761124783489128700000000000000E-14 "%"
h = 1.0000E-4 " "
y1[1] (analytic) = 1.9934291636174526 " "
y1[1] (numeric) = 1.9934291636174526 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
h = 1.0000E-4 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"
"diff ( y1 , x , 1 ) = y2 - 1.0;"
Iterations = 147
"Total Elapsed Time "= 15 Minutes 21 Seconds
"Elapsed Time(since restart) "= 15 Minutes 20 Seconds
"Expected Time Remaining "= 6 Hours 39 Minutes 36 Seconds
"Optimized Time Remaining "= 6 Hours 39 Minutes 20 Seconds
"Time to Timeout " Unknown
Percent Done = 3.700000000000106 "%"
(%o52) true
(%o52) diffeq.max