(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) display_poles() := block([rad_given],
if glob_type_given_pole = 4 then (rad_given :
sqrt(expt(array_given_rad_poles , 2.0)
1, 2
+ expt(array_x - array_given_rad_poles , 2.0)),
1 1, 1
omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " "), omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles , 4, " ")) elseif glob_type_given_pole = 3
1, 1
then omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"),
if array_poles # glob_large_float then (omniout_float(ALWAYS,
1, 1
"Radius of convergence (ratio test) for eq 1 ", 4, array_poles , 4,
1, 1
" "), omniout_str(ALWAYS,
"Order of pole (ratio test) Not computed"))
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"),
if (array_real_poles > 0.0) and (array_real_poles # glob_large_float)
1, 1 1, 1
then (omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4, array_real_poles ,
1, 1
4, " "), omniout_float(ALWAYS,
"Order of pole (three term test) ", 4, array_real_poles ,
1, 2
4, " ")) else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1"),
if (array_complex_poles > 0.0) and (array_complex_poles #
1, 1 1, 1
glob_large_float)
then (omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_complex_poles , 4, " "), omniout_float(ALWAYS,
1, 1
"Order of pole (six term test) ", 4,
array_complex_poles , 4, " ")) else omniout_str(ALWAYS,
1, 2
"NO COMPLEX POLE (six term test) for Equation 1"))
(%o3) display_poles() := block([rad_given],
if glob_type_given_pole = 4 then (rad_given :
sqrt(expt(array_given_rad_poles , 2.0)
1, 2
+ expt(array_x - array_given_rad_poles , 2.0)),
1 1, 1
omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " "), omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles , 4, " ")) elseif glob_type_given_pole = 3
1, 1
then omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"),
if array_poles # glob_large_float then (omniout_float(ALWAYS,
1, 1
"Radius of convergence (ratio test) for eq 1 ", 4, array_poles , 4,
1, 1
" "), omniout_str(ALWAYS,
"Order of pole (ratio test) Not computed"))
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"),
if (array_real_poles > 0.0) and (array_real_poles # glob_large_float)
1, 1 1, 1
then (omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4, array_real_poles ,
1, 1
4, " "), omniout_float(ALWAYS,
"Order of pole (three term test) ", 4, array_real_poles ,
1, 2
4, " ")) else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1"),
if (array_complex_poles > 0.0) and (array_complex_poles #
1, 1 1, 1
glob_large_float)
then (omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_complex_poles , 4, " "), omniout_float(ALWAYS,
1, 1
"Order of pole (six term test) ", 4,
array_complex_poles , 4, " ")) else omniout_str(ALWAYS,
1, 2
"NO COMPLEX POLE (six term test) for Equation 1"))
(%i4) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o4) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i5) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o5) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i6) test_suggested_h() := block([max_estimated_step_error, hn_div_ho,
hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp], max_estimated_step_error : 0.0,
no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25,
hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32,
""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
est_tmp : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if est_tmp >= max_estimated_step_error then max_estimated_step_error :
est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, ""), max_estimated_step_error)
(%o6) test_suggested_h() := block([max_estimated_step_error, hn_div_ho,
hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp], max_estimated_step_error : 0.0,
no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25,
hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32,
""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
est_tmp : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if est_tmp >= max_estimated_step_error then max_estimated_step_error :
est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, ""), max_estimated_step_error)
(%i7) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o7) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i8) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 3 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
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_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o8) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 3 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
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_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i9) adjust_for_pole(h_param) := (block([hnew, sz2, tmp], hnew : h_param,
glob_normmax : glob_small_float, if omniabs(array_y_higher ) >
1, 1
glob_small_float then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
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), return(hnew))
1
(%o9) adjust_for_pole(h_param) := (block([hnew, sz2, tmp], hnew : h_param,
glob_normmax : glob_small_float, if omniabs(array_y_higher ) >
1, 1
glob_small_float then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
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), return(hnew))
1
(%i10) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
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)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_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, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o10) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
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)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_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, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i11) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio,
term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad],
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
tmp_rad : glob_large_float, prev_tmp_rad : glob_large_float,
tmp_ratio : glob_large_float, rad_c : glob_large_float,
array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found_sing : 1, n : - 10 - 1 + glob_max_terms, cnt : 0,
while (cnt < 5) and (found_sing = 1) do (if (omniabs(array_y_higher ) =
1, n
0.0) or (omniabs(array_y_higher ) = 0.0) then found_sing : 0
1, 1 + n
array_y_higher glob_h
1, n tmp_rad
else (tmp_rad : omniabs(-------------------------), tmp_ratio : ------------,
array_y_higher prev_tmp_rad
1, 1 + n
if (cnt > 0) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)
then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt = 0
then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt > 0
then found_sing : 0), prev_tmp_rad : tmp_rad, cnt : 1 + cnt, n : 1 + n),
if found_sing = 1 then (if rad_c < array_pole
1
then (array_pole : rad_c, array_poles : rad_c)), n : glob_max_terms,
1 1, 1
m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) = 0.0)
1, m
or (omniabs(array_y_higher ) = 0.0)
1, m - 1
or (omniabs(array_y_higher ) = 0.0)) do m : m - 1,
1, m - 2
array_y_higher array_y_higher
1, m 1, m - 1
if m > 10 then (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1,
glob_h
if omniabs(hdrc) > 0.0 then (rcs : ------,
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
ord_no : -----------------------------------------------------,
hdrc
array_real_poles : rcs, array_real_poles : ord_no)
1, 1 1, 2
else (array_real_poles : glob_large_float,
1, 1
array_real_poles : glob_large_float))
1, 2
else (array_real_poles : glob_large_float,
1, 1
array_real_poles : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) #
1, n
0.0 then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_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 (omniabs(nr1 dr2 - nr2 dr1) = 0.0)
rm4 rm3 rm2
or (omniabs(dr1) = 0.0) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) # 0.0
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 omniabs(rcs) # 0.0 then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(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_poles : rad_c,
1, 1
array_complex_poles : ord_no), if array_pole glob_ratio_of_radius <
1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_poles())
(%o11) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio,
term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad],
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
tmp_rad : glob_large_float, prev_tmp_rad : glob_large_float,
tmp_ratio : glob_large_float, rad_c : glob_large_float,
array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found_sing : 1, n : - 10 - 1 + glob_max_terms, cnt : 0,
while (cnt < 5) and (found_sing = 1) do (if (omniabs(array_y_higher ) =
1, n
0.0) or (omniabs(array_y_higher ) = 0.0) then found_sing : 0
1, 1 + n
array_y_higher glob_h
1, n tmp_rad
else (tmp_rad : omniabs(-------------------------), tmp_ratio : ------------,
array_y_higher prev_tmp_rad
1, 1 + n
if (cnt > 0) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)
then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt = 0
then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt > 0
then found_sing : 0), prev_tmp_rad : tmp_rad, cnt : 1 + cnt, n : 1 + n),
if found_sing = 1 then (if rad_c < array_pole
1
then (array_pole : rad_c, array_poles : rad_c)), n : glob_max_terms,
1 1, 1
m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) = 0.0)
1, m
or (omniabs(array_y_higher ) = 0.0)
1, m - 1
or (omniabs(array_y_higher ) = 0.0)) do m : m - 1,
1, m - 2
array_y_higher array_y_higher
1, m 1, m - 1
if m > 10 then (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1,
glob_h
if omniabs(hdrc) > 0.0 then (rcs : ------,
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
ord_no : -----------------------------------------------------,
hdrc
array_real_poles : rcs, array_real_poles : ord_no)
1, 1 1, 2
else (array_real_poles : glob_large_float,
1, 1
array_real_poles : glob_large_float))
1, 2
else (array_real_poles : glob_large_float,
1, 1
array_real_poles : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) #
1, n
0.0 then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_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 (omniabs(nr1 dr2 - nr2 dr1) = 0.0)
rm4 rm3 rm2
or (omniabs(dr1) = 0.0) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) # 0.0
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 omniabs(rcs) # 0.0 then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(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_poles : rad_c,
1, 1
array_complex_poles : ord_no), if array_pole glob_ratio_of_radius <
1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_poles())
(%i12) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o12) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i13) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_2D0 array_x ,
1 1 1
array_tmp2 : array_const_3D0 + array_tmp1 , array_tmp3 : cosh(array_tmp2 ),
1 1 1 1 1
array_tmp3_g : sinh(array_tmp2 ), array_tmp4 :
1 1 1
array_tmp3 + array_const_0D0 , if not array_y_set_initial
1 1 1, 2
then (if 1 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(0, 1), array_y : temporary,
1 2
temporary 1.0
array_y_higher : temporary, temporary : -------------,
1, 2 glob_h
array_y_higher : temporary, 0)), kkk : 2,
2, 1
array_tmp1 : array_const_2D0 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp3_g array_tmp2
1 2
array_tmp3 : -------------------------,
2 1
array_tmp3 array_tmp2
1 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
2 1 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp3_g array_tmp2
2 2
array_tmp3 : -------------------------,
3 2
array_tmp3 array_tmp2
2 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
3 2 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp3_g array_tmp2
3 2
array_tmp3 : -------------------------,
4 3
array_tmp3 array_tmp2
3 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
4 3 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp3_g array_tmp2
4 2
array_tmp3 : -------------------------,
5 4
array_tmp3 array_tmp2
4 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
5 4 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp3 :
kkk
array_tmp3_g array_tmp2
kkk - 1 2
-------------------------------, array_tmp3_g :
kkk - 1 kkk
- array_tmp3 array_tmp2
kkk - 1 2
-------------------------------, array_tmp4 : array_tmp3 , order_d : 1,
kkk - 1 kkk kkk
if order_d + kkk < glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp4 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o13) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_2D0 array_x ,
1 1 1
array_tmp2 : array_const_3D0 + array_tmp1 , array_tmp3 : cosh(array_tmp2 ),
1 1 1 1 1
array_tmp3_g : sinh(array_tmp2 ), array_tmp4 :
1 1 1
array_tmp3 + array_const_0D0 , if not array_y_set_initial
1 1 1, 2
then (if 1 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(0, 1), array_y : temporary,
1 2
temporary 1.0
array_y_higher : temporary, temporary : -------------,
1, 2 glob_h
array_y_higher : temporary, 0)), kkk : 2,
2, 1
array_tmp1 : array_const_2D0 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp3_g array_tmp2
1 2
array_tmp3 : -------------------------,
2 1
array_tmp3 array_tmp2
1 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
2 1 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp3_g array_tmp2
2 2
array_tmp3 : -------------------------,
3 2
array_tmp3 array_tmp2
2 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
3 2 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp3_g array_tmp2
3 2
array_tmp3 : -------------------------,
4 3
array_tmp3 array_tmp2
3 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
4 3 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp3_g array_tmp2
4 2
array_tmp3 : -------------------------,
5 4
array_tmp3 array_tmp2
4 2
array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 ,
5 4 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp3 :
kkk
array_tmp3_g array_tmp2
kkk - 1 2
-------------------------------, array_tmp3_g :
kkk - 1 kkk
- array_tmp3 array_tmp2
kkk - 1 2
-------------------------------, array_tmp4 : array_tmp3 , order_d : 1,
kkk - 1 kkk kkk
if order_d + kkk < glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp4 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i14) log10(x) := ---------
log(10.0)
log(x)
(%o14) log10(x) := ---------
log(10.0)
(%i15) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o15) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i16) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o16) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i17) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o17) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i18) 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))
(%o18) 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))
(%i19) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o19) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i20) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o20) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i21) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], 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
(%o21) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], 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
(%i22) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], 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
(%o22) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], 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
(%i23) 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))
(%o23) 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))
(%i24) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "| ~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if 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, " | ~%"))
(%o24) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if 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, " | ~%"))
(%i25) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if 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~%"))
(%o25) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if 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~%"))
(%i26) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_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 : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o26) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_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 : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i27) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_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 : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o27) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_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 : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i28) display_pole_debug(typ, m, radius, order2) :=
(if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex"), omniout_int(ALWAYS, "m", 4, m, 4, " "),
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "),
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " "))
(%o28) display_pole_debug(typ, m, radius, order2) :=
(if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex"), omniout_int(ALWAYS, "m", 4, m, 4, " "),
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "),
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " "))
(%i29) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o29) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i30) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o30) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i31) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o31) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i32) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o32) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i33) log_revs(file, revs) := printf(file, revs)
(%o33) log_revs(file, revs) := printf(file, revs)
(%i34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i35) 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") elseif pole = 4
then printf(file, "Yes") else printf(file, "No"), printf(file, " | "))
(%o35) 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") elseif pole = 4
then printf(file, "Yes") else printf(file, "No"), printf(file, " | "))
(%i36) logstart(file) := printf(file, "")
(%o36) logstart(file) := printf(file, "
")
(%i37) logend(file) := printf(file, "
~%")
(%o37) logend(file) := printf(file, "~%")
(%i38) chk_data() := block([errflag], 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())
(%o38) chk_data() := block([errflag], 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())
(%i39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i40) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o40) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i41) factorial_2(nnn) := nnn!
(%o41) factorial_2(nnn) := nnn!
(%i42) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o42) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i43) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o43) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i44) convfp(mmm) := mmm
(%o44) convfp(mmm) := mmm
(%i45) convfloat(mmm) := mmm
(%o45) convfloat(mmm) := mmm
(%i46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i47) Si(x) := 0.0
(%o47) Si(x) := 0.0
(%i48) Ci(x) := 0.0
(%o48) Ci(x) := 0.0
(%i49) ln(x) := log(x)
(%o49) ln(x) := log(x)
(%i50) arcsin(x) := asin(x)
(%o50) arcsin(x) := asin(x)
(%i51) arccos(x) := acos(x)
(%o51) arccos(x) := acos(x)
(%i52) arctan(x) := atan(x)
(%o52) arctan(x) := atan(x)
(%i53) omniabs(x) := abs(x)
(%o53) omniabs(x) := abs(x)
(%i54) expt(x, y) := (if (x <= 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o54) expt(x, y) := (if (x <= 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i55) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%o55) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
sinh(3.0 + 2.0 x)
(%i56) exact_soln_y(x) := block(-----------------)
2
sinh(3.0 + 2.0 x)
(%o56) exact_soln_y(x) := block(-----------------)
2
(%i57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms,
opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value,
est_answer, best_h, found_h, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_yes_pole, 4, fixnum),
define_variable(glob_no_pole, 3, fixnum),
define_variable(glob_not_given, 0, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_estimated_step_error, 0.0, float),
define_variable(glob_ratio_of_radius, 0.1, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float),
define_variable(glob_min_h, 1.0E-6, float),
define_variable(glob_type_given_pole, 0, fixnum),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 0.0, float),
define_variable(glob_smallish_float, 0.0, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
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/lin_coshpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = cosh (2.0 * x + 3.0) ;"),
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:2.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.01,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (sinh(2.0*x+3.0)/2) "), 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 : 0.0, glob_smallish_float : 0.0,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32,
max_terms : 30, glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + 4),
array(array_real_pole, 1 + 4), array(array_complex_pole, 1 + 4),
array(array_1st_rel_error, 1 + 2), array(array_last_rel_error, 1 + 2),
array(array_type_pole, 1 + 2), array(array_type_real_pole, 1 + 2),
array(array_type_complex_pole, 1 + 2), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3_g, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_given_rad_poles, 1 + 2, 1 + 3),
array(array_given_ord_poles, 1 + 2, 1 + 3),
array(array_real_poles, 1 + 2, 1 + 3),
array(array_complex_poles, 1 + 2, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= 4 do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= 4 do (array_real_pole : 0.0, term : 1 + term), term : 1,
term
while term <= 4 do (array_complex_pole : 0.0, term : 1 + term), term : 1,
term
while term <= 2 do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= 2 do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <= 2 do (array_type_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
2 do (array_type_real_pole : 0.0, term : 1 + term), term : 1,
term
while term <= 2 do (array_type_complex_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3_g : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + term), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_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_y_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_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_real_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_complex_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 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_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_g : 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_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 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_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_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term),
term
array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 2.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 100, glob_desired_digits_correct : 10,
glob_display_interval : 0.01, glob_look_poles : true,
glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3,
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),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), found_h : false, glob_h : glob_min_h,
if glob_max_h < glob_h then glob_h : glob_max_h,
if glob_display_interval < glob_h then glob_h : glob_display_interval,
best_h : glob_h, min_value : glob_large_float, est_answer : est_size_answer(),
opt_iter : 1, est_needed_step_err : estimated_needed_step_error(x_start,
x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), estimated_step_error : 0.0,
while (opt_iter <= 100) and (not found_h) do (omniout_int(ALWAYS, "opt_iter",
32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
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,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
estimated_step_error : test_suggested_h(),
omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32,
""), if ((estimated_step_error > est_needed_step_err) and (opt_iter = 1))
or (glob_h >= glob_max_h) then (found_h : true, glob_h : glob_max_h,
best_h : glob_h) elseif (estimated_step_error > est_needed_step_err)
glob_h
and (not found_h) then (glob_h : ------, best_h : glob_h, found_h : true)
2.0
else (glob_h : glob_h 2.0, best_h : glob_h),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter),
if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS,
"Beginning glob_h too large."), found_h : false),
if opt_iter > 100 then (glob_h : glob_max_h, found_h : false),
if glob_display_interval < glob_h then glob_h : glob_display_interval,
if glob_html_log then html_log_file : openw("entry.html"),
if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1,
2
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
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,
array_y_init expt(glob_h, term_no - 1)
it
array_y_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(),
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 (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (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, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, 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_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, 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_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, 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_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
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 ( y , x , 1 ) = cosh (2.0 * x + 3.0) ;"),
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,
"2013-05-26T02:32:54-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_cosh"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = cosh (2.0 * x + 3.0) ;"),
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_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
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_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 189 | "), logitem_str(html_log_file, "lin_cosh diffeq.max"),
logitem_str(html_log_file,
"lin_cosh maxima results"),
logitem_str(html_log_file, "All Tests - All Languages"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%o57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms,
opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value,
est_answer, best_h, found_h, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum),
define_variable(glob_yes_pole, 4, fixnum),
define_variable(glob_no_pole, 3, fixnum),
define_variable(glob_not_given, 0, fixnum),
define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum),
define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_estimated_step_error, 0.0, float),
define_variable(glob_ratio_of_radius, 0.1, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float),
define_variable(glob_min_h, 1.0E-6, float),
define_variable(glob_type_given_pole, 0, fixnum),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 0.0, float),
define_variable(glob_smallish_float, 0.0, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
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/lin_coshpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = cosh (2.0 * x + 3.0) ;"),
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:2.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.01,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (sinh(2.0*x+3.0)/2) "), 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 : 0.0, glob_smallish_float : 0.0,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32,
max_terms : 30, glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + 4),
array(array_real_pole, 1 + 4), array(array_complex_pole, 1 + 4),
array(array_1st_rel_error, 1 + 2), array(array_last_rel_error, 1 + 2),
array(array_type_pole, 1 + 2), array(array_type_real_pole, 1 + 2),
array(array_type_complex_pole, 1 + 2), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3_g, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 2, 1 + 3), array(array_given_rad_poles, 1 + 2, 1 + 3),
array(array_given_ord_poles, 1 + 2, 1 + 3),
array(array_real_poles, 1 + 2, 1 + 3),
array(array_complex_poles, 1 + 2, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= 4 do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= 4 do (array_real_pole : 0.0, term : 1 + term), term : 1,
term
while term <= 4 do (array_complex_pole : 0.0, term : 1 + term), term : 1,
term
while term <= 2 do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= 2 do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <= 2 do (array_type_pole : 0.0,
term
term : 1 + term), term : 1, while term <=
2 do (array_type_real_pole : 0.0, term : 1 + term), term : 1,
term
while term <= 2 do (array_type_complex_pole : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_y : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3_g : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + term), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_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_y_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_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_real_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_complex_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 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_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_g : 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_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 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_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_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term),
term
array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 2.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 100, glob_desired_digits_correct : 10,
glob_display_interval : 0.01, glob_look_poles : true,
glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3,
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),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), found_h : false, glob_h : glob_min_h,
if glob_max_h < glob_h then glob_h : glob_max_h,
if glob_display_interval < glob_h then glob_h : glob_display_interval,
best_h : glob_h, min_value : glob_large_float, est_answer : est_size_answer(),
opt_iter : 1, est_needed_step_err : estimated_needed_step_error(x_start,
x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), estimated_step_error : 0.0,
while (opt_iter <= 100) and (not found_h) do (omniout_int(ALWAYS, "opt_iter",
32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
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,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
estimated_step_error : test_suggested_h(),
omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32,
""), if ((estimated_step_error > est_needed_step_err) and (opt_iter = 1))
or (glob_h >= glob_max_h) then (found_h : true, glob_h : glob_max_h,
best_h : glob_h) elseif (estimated_step_error > est_needed_step_err)
glob_h
and (not found_h) then (glob_h : ------, best_h : glob_h, found_h : true)
2.0
else (glob_h : glob_h 2.0, best_h : glob_h),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter),
if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS,
"Beginning glob_h too large."), found_h : false),
if opt_iter > 100 then (glob_h : glob_max_h, found_h : false),
if glob_display_interval < glob_h then glob_h : glob_display_interval,
if glob_html_log then html_log_file : openw("entry.html"),
if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1,
2
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
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,
array_y_init expt(glob_h, term_no - 1)
it
array_y_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(),
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 (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (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, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, 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_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, 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_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, 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_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
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 ( y , x , 1 ) = cosh (2.0 * x + 3.0) ;"),
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,
"2013-05-26T02:32:54-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_cosh"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = cosh (2.0 * x + 3.0) ;"),
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_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
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_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 189 | "), logitem_str(html_log_file, "lin_cosh diffeq.max"),
logitem_str(html_log_file,
"lin_cosh maxima results"),
logitem_str(html_log_file, "All Tests - All Languages"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i58) main()
"##############ECHO OF PROBLEM#################"
"##############temp/lin_coshpostode.ode#################"
"diff ( y , x , 1 ) = cosh (2.0 * x + 3.0) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.1,"
"x_end:2.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_iter:100,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.01,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (sinh(2.0*x+3.0)/2) "
"));"
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1.9 ""
estimated_steps = 1900000. ""
step_error = 5.26315789473684200000000000000000E-17 ""
est_needed_step_err = 5.26315789473684200000000000000000E-17 ""
opt_iter = 1
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.0188751961806015000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-174 ""
estimated_step_error = 1.0188751961806015000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-174 ""
best_h = 2.000000E-6 ""
opt_iter = 2
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 6.83755544325993400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-167 ""
estimated_step_error = 6.83755544325993400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-167 ""
best_h = 4.000000E-6 ""
opt_iter = 3
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 4.588605442313688500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-159 ""
estimated_step_error = 4.588605442313688500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-159 ""
best_h = 8.000000E-6 ""
opt_iter = 4
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 3.0793605280584670000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-151 ""
estimated_step_error = 3.0793605280584670000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-151 ""
best_h = 1.600000E-5 ""
opt_iter = 5
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.066523254502221600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-143 ""
estimated_step_error = 2.066523254502221600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-143 ""
best_h = 3.200000E-5 ""
opt_iter = 6
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.3868194558353997000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-135 ""
estimated_step_error = 1.3868194558353997000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-135 ""
best_h = 6.400000E-5 ""
opt_iter = 7
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 9.30677675838730800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 ""
estimated_step_error = 9.30677675838730800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 ""
best_h = 1.280000E-4 ""
opt_iter = 8
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 6.245657303597564000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-120 ""
estimated_step_error = 6.245657303597564000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-120 ""
best_h = 2.560000E-4 ""
opt_iter = 9
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 4.1913697289771160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-112 ""
estimated_step_error = 4.1913697289771160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-112 ""
best_h = 5.120000E-4 ""
opt_iter = 10
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.81275385207035040000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-104 ""
estimated_step_error = 2.81275385207035040000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-104 ""
best_h = 1.024000E-3 ""
opt_iter = 11
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.8875712408214815000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-96 ""
estimated_step_error = 1.8875712408214815000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-96 ""
best_h = 2.048000E-3 ""
opt_iter = 12
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.2666794080686720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-88 ""
estimated_step_error = 1.2666794080686720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-88 ""
best_h = 4.096000E-3 ""
opt_iter = 13
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 8.499894493959363000000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 ""
estimated_step_error = 8.499894493959363000000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 ""
best_h = 8.192000E-3 ""
opt_iter = 14
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 5.7033138980216660000000000000000000000000000000000000000000000000000000000000000000000000E-73 ""
estimated_step_error = 5.7033138980216660000000000000000000000000000000000000000000000000000000000000000000000000E-73 ""
best_h = 1.638400E-2 ""
opt_iter = 15
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 3.82626265702556300000000000000000000000000000000000000000000000000000000000000000E-65 ""
estimated_step_error = 3.82626265702556300000000000000000000000000000000000000000000000000000000000000000E-65 ""
best_h = 3.276800E-2 ""
opt_iter = 16
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.5661943707276186000000000000000000000000000000000000000000000000000000000E-57 ""
estimated_step_error = 2.5661943707276186000000000000000000000000000000000000000000000000000000000E-57 ""
best_h = 6.553600E-2 ""
opt_iter = 17
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.72003698199871070000000000000000000000000000000000000000000000000E-49 ""
estimated_step_error = 1.72003698199871070000000000000000000000000000000000000000000000000E-49 ""
best_h = 0.131072 ""
opt_iter = 18
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.15145957392865600000000000000000000000000000000000000000E-41 ""
estimated_step_error = 1.15145957392865600000000000000000000000000000000000000000E-41 ""
best_h = 0.1 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (analytic) = 6.122941998282747 " "
y[1] (numeric) = 6.122941998282747 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.468482779476682 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11 " "
y[1] (analytic) = 6.24704128076929 " "
y[1] (numeric) = 6.247041280769287 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 4.265275575019495400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.469716617662243 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12 " "
y[1] (analytic) = 6.373639463063135 " "
y[1] (numeric) = 6.373639463063129 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 9.75462916271216500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.470902227566933 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13 " "
y[1] (analytic) = 6.502787186125196 " "
y[1] (numeric) = 6.502787186125189 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 1.09267413406387360000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.472041488649596 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14 " "
y[1] (analytic) = 6.634536110766698 " "
y[1] (numeric) = 6.634536110766684 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 2.14195152124355140000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.473136207563249 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000002 " "
y[1] (analytic) = 6.768938938314161 " "
y[1] (numeric) = 6.768938938314147 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 2.09942131916192040000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.474188120941847 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000003 " "
y[1] (analytic) = 6.906049431690678 " "
y[1] (numeric) = 6.906049431690658 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 2.95800136607215800000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.475198898082992 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000004 " "
y[1] (analytic) = 7.045922436921752 " "
y[1] (numeric) = 7.045922436921732 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 2.8992802342041650000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.476170143530158 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000005 " "
y[1] (analytic) = 7.1886139050744875 " "
y[1] (numeric) = 7.188613905074459 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 3.95371205154597950000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.477103399558205 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000006 " "
y[1] (analytic) = 7.334180914638709 " "
y[1] (numeric) = 7.33418091463868 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 3.8752397522231147000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.478000148565418 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20000000000000007 " "
y[1] (analytic) = 7.482681694359174 " "
y[1] (numeric) = 7.482681694359140 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 4.6292171420865720000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.478861815375652 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21000000000000008 " "
y[1] (analytic) = 7.6341756465277975 " "
y[1] (numeric) = 7.634175646527762 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 4.653696539476870300000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.479689769453605 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22000000000000008 " "
y[1] (analytic) = 7.788723370745403 " "
y[1] (numeric) = 7.788723370745360 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 5.4736266928845810000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.480485327036478 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2300000000000001 " "
y[1] (analytic) = 7.94638668816233 " "
y[1] (numeric) = 7.9463866881622875 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 5.3650251137558420000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.481249753185104 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2400000000000001 " "
y[1] (analytic) = 8.107228666207765 " "
y[1] (numeric) = 8.107228666207714 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 6.3541254926393490000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.481984263757282 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (analytic) = 8.271313643817498 " "
y[1] (numeric) = 8.271313643817447 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 6.2280733824079250000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.482690027306397 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (analytic) = 8.43870725717042 " "
y[1] (numeric) = 8.438707257170359 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 7.1570361074309770000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.483368166907844 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (analytic) = 8.609476465943798 " "
y[1] (numeric) = 8.609476465943736 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 7.2214018616512030000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.484019761916134 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (analytic) = 8.78368958009811 " "
y[1] (numeric) = 8.783689580098041 " "
absolute error = 6.92779167366097700000000000000E-14 " "
relative error = 7.8871089540297670000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.484645849654935 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (analytic) = 8.961416287201878 " "
y[1] (numeric) = 8.961416287201809 " "
absolute error = 6.92779167366097700000000000000E-14 " "
relative error = 7.7306883774106170000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.485247427042857 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (analytic) = 9.14272768030768 " "
y[1] (numeric) = 9.1427276803076 " "
absolute error = 7.99360577730112700000000000000E-14 " "
relative error = 8.7431301213513990000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.485825452157101 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (analytic) = 9.327696286390255 " "
y[1] (numeric) = 9.327696286390175 " "
absolute error = 7.99360577730112700000000000000E-14 " "
relative error = 8.5697534866828200000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.486380845737436 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (analytic) = 9.516396095358337 " "
y[1] (numeric) = 9.516396095358248 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 9.3331384150071070000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.486914492632614 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (analytic) = 9.708902589651528 " "
y[1] (numeric) = 9.708902589651437 " "
absolute error = 9.05941988094127700000000000000E-14 " "
relative error = 9.3310441600243080000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.487427243191423 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (analytic) = 9.905292774434349 " "
y[1] (numeric) = 9.905292774434248 " "
absolute error = 1.01252339845814280000000000000E-13 " "
relative error = 1.0222044128483258000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.487919914600486 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3500000000000002 " "
y[1] (analytic) = 10.105645208399265 " "
y[1] (numeric) = 10.105645208399164 " "
absolute error = 1.01252339845814280000000000000E-13 " "
relative error = 1.0019383993578047000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.488393292170745 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3600000000000002 " "
y[1] (analytic) = 10.310040035191282 " "
y[1] (numeric) = 10.310040035191172 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 1.0682220793216562000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.488848130574466 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (analytic) = 10.518559015466401 " "
y[1] (numeric) = 10.51855901546629 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 1.0639335741489261000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.489285155034842 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000002 " "
y[1] (analytic) = 10.731285559597039 " "
y[1] (numeric) = 10.731285559596918 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 1.1256085247977764000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.489705062469838 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39000000000000024 " "
y[1] (analytic) = 10.948304761037221 " "
y[1] (numeric) = 10.9483047610371 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 1.103296516818677000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.490108522591893 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (analytic) = 11.169703430361173 " "
y[1] (numeric) = 11.16970343036104 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 1.1927511216894582000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.490496178965493 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (analytic) = 11.395570129988622 " "
y[1] (numeric) = 11.395570129988489 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 1.16911011415233000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.490868650023767 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (analytic) = 11.62599520961104 " "
y[1] (numeric) = 11.625995209610894 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 1.252892833728372000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.491226530046037 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000027 " "
y[1] (analytic) = 11.861070842332625 " "
y[1] (numeric) = 11.861070842332479 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 1.2280616376638592000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.491570390097593 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (analytic) = 12.100891061540876 " "
y[1] (numeric) = 12.100891061540718 " "
absolute error = 1.5809575870662230000000000000E-13 " "
relative error = 1.3064803071327796000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.491900778933095 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (analytic) = 12.345551798521097 " "
y[1] (numeric) = 12.345551798520939 " "
absolute error = 1.5809575870662230000000000000E-13 " "
relative error = 1.2805888411205804000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49221822386527 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (analytic) = 12.595150920830289 " "
y[1] (numeric) = 12.59515092083012 " "
absolute error = 1.6875389974302380000000000000E-13 " "
relative error = 1.3398322958078485000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.492523231599803 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (analytic) = 12.849788271445387 " "
y[1] (numeric) = 12.849788271445217 " "
absolute error = 1.70530256582424040000000000000E-13 " "
relative error = 1.3271055754387323000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.492816289038082 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000003 " "
y[1] (analytic) = 13.10956570870187 " "
y[1] (numeric) = 13.109565708701687 " "
absolute error = 1.8296475445822580000000000000E-13 " "
relative error = 1.3956583957375293000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.493097864048858 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000003 " "
y[1] (analytic) = 13.374587147038362 " "
y[1] (numeric) = 13.374587147038179 " "
absolute error = 1.8296475445822580000000000000E-13 " "
relative error = 1.3680030078441793000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.493368406209905 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000003 " "
y[1] (analytic) = 13.644958598563889 " "
y[1] (numeric) = 13.644958598563692 " "
absolute error = 1.9717560917342780000000000000E-13 " "
relative error = 1.4450436602583772000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49362834752114 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000003 " "
y[1] (analytic) = 13.920788215464034 " "
y[1] (numeric) = 13.920788215463837 " "
absolute error = 1.9717560917342780000000000000E-13 " "
relative error = 1.4164112413864144000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.4938781030899 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000004 " "
y[1] (analytic) = 14.202186333263363 " "
y[1] (numeric) = 14.202186333263151 " "
absolute error = 2.1138646388862980000000000000E-13 " "
relative error = 1.4884079037432094000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.494118071789845 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000004 " "
y[1] (analytic) = 14.489265514960993 " "
y[1] (numeric) = 14.489265514960781 " "
absolute error = 2.1138646388862980000000000000E-13 " "
relative error = 1.4589177323747793000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.494348636894102 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000004 " "
y[1] (analytic) = 14.782140596057404 " "
y[1] (numeric) = 14.782140596057177 " "
absolute error = 2.27373675443232060000000000000E-13 " "
relative error = 1.5381647466123793000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.494570166684008 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000004 " "
y[1] (analytic) = 15.08092873049006 " "
y[1] (numeric) = 15.080928730489832 " "
absolute error = 2.27373675443232060000000000000E-13 " "
relative error = 1.5076901396897158000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.494783015034065 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000004 " "
y[1] (analytic) = 15.385749437496656 " "
y[1] (numeric) = 15.385749437496415 " "
absolute error = 2.41584530158434060000000000000E-13 " "
relative error = 1.5701837023919530000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.494987521974364 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000004 " "
y[1] (analytic) = 15.696724649424299 " "
y[1] (numeric) = 15.696724649424056 " "
absolute error = 2.4336088699783430000000000000E-13 " "
relative error = 1.5503927885156600000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.495184014230887 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000004 " "
y[1] (analytic) = 16.013978760504177 " "
y[1] (numeric) = 16.013978760503917 " "
absolute error = 2.59348098552436570000000000000E-13 " "
relative error = 1.6195106939449405000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.495372805745097 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000004 " "
y[1] (analytic) = 16.33763867661081 " "
y[1] (numeric) = 16.337638676610545 " "
absolute error = 2.62900812231237070000000000000E-13 " "
relative error = 1.6091726438264886000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.495554198173117 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000004 " "
y[1] (analytic) = 16.667833866026182 " "
y[1] (numeric) = 16.667833866025905 " "
absolute error = 2.77111666946439100000000000000E-13 " "
relative error = 1.6625535697909252000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.495728481365564 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000004 " "
y[1] (analytic) = 17.004696411228704 " "
y[1] (numeric) = 17.004696411228423 " "
absolute error = 2.80664380625239600000000000000E-13 " "
relative error = 1.6505109755438420000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.495895933828763 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000004 " "
y[1] (analytic) = 17.34836106172804 " "
y[1] (numeric) = 17.34836106172774 " "
absolute error = 2.9842794901924210000000000000E-13 " "
relative error = 1.7202083122284073000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.496056823167892 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000004 " "
y[1] (analytic) = 17.69896528796661 " "
y[1] (numeric) = 17.698965287966313 " "
absolute error = 2.9842794901924210000000000000E-13 " "
relative error = 1.6861321787107010000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.496211406512996 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000005 " "
y[1] (analytic) = 18.056649336309743 " "
y[1] (numeric) = 18.056649336309423 " "
absolute error = 3.1974423109204510000000000000E-13 " "
relative error = 1.7707838543947244000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.496359930928302 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (analytic) = 18.42155628514591 " "
y[1] (numeric) = 18.42155628514559 " "
absolute error = 3.1974423109204510000000000000E-13 " "
relative error = 1.7357069410572468000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.496502633805703 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000005 " "
y[1] (analytic) = 18.793832102120184 " "
y[1] (numeric) = 18.793832102119843 " "
absolute error = 3.4106051316484810000000000000E-13 " "
relative error = 1.8147470473910007000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.496639743242799 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (analytic) = 19.173625702523054 " "
y[1] (numeric) = 19.173625702522713 " "
absolute error = 3.4106051316484810000000000000E-13 " "
relative error = 1.7788003085924847000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49677147840631 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000005 " "
y[1] (analytic) = 19.561089008858705 " "
y[1] (numeric) = 19.561089008858342 " "
absolute error = 3.6237679523765110000000000000E-13 " "
relative error = 1.8525389617804006000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.496898049881205 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000005 " "
y[1] (analytic) = 19.956377011615874 " "
y[1] (numeric) = 19.956377011615515 " "
absolute error = 3.5882408155885060000000000000E-13 " "
relative error = 1.7980422065086876000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.497019660006327 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000005 " "
y[1] (analytic) = 20.359647831266287 " "
y[1] (numeric) = 20.359647831265907 " "
absolute error = 3.8014036363165360000000000000E-13 " "
relative error = 1.8671264197795823000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.497136503196861 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000005 " "
y[1] (analytic) = 20.77106278151478 " "
y[1] (numeric) = 20.771062781514395 " "
absolute error = 3.8369307731045410000000000000E-13 " "
relative error = 1.847248170911707000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.497248766254254 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000005 " "
y[1] (analytic) = 21.19078643382709 " "
y[1] (numeric) = 21.190786433826688 " "
absolute error = 4.0145664570445660000000000000E-13 " "
relative error = 1.8944867712111285000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.497356628664026 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000005 " "
y[1] (analytic) = 21.6189866832605 " "
y[1] (numeric) = 21.618986683260097 " "
absolute error = 4.0145664570445660000000000000E-13 " "
relative error = 1.8569632868838526000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49746026288196 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000005 " "
y[1] (analytic) = 22.05583481562423 " "
y[1] (numeric) = 22.055834815623808 " "
absolute error = 4.2277292777725960000000000000E-13 " "
relative error = 1.9168303141161067000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.497559834609147 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000006 " "
y[1] (analytic) = 22.501505575995914 " "
y[1] (numeric) = 22.501505575995488 " "
absolute error = 4.2632564145606010000000000000E-13 " "
relative error = 1.894653848900024000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.497655503056258 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000006 " "
y[1] (analytic) = 22.956177238622086 " "
y[1] (numeric) = 22.95617723862164 " "
absolute error = 4.4764192352886310000000000000E-13 " "
relative error = 1.9499846114436611000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.497747421197525 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000006 " "
y[1] (analytic) = 23.420031678230135 " "
y[1] (numeric) = 23.420031678229684 " "
absolute error = 4.5119463720766360000000000000E-13 " "
relative error = 1.9265329928100278000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.497835736014755 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000006 " "
y[1] (analytic) = 23.893254442780748 " "
y[1] (numeric) = 23.89325444278027 " "
absolute error = 4.7606363295926710000000000000E-13 " "
relative error = 1.9924603996468465000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.497920588731906 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000006 " "
y[1] (analytic) = 24.376034827689423 " "
y[1] (numeric) = 24.376034827688947 " "
absolute error = 4.7606363295926710000000000000E-13 " "
relative error = 1.9529986575933714000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498002115040425 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000006 " "
y[1] (analytic) = 24.86856595154733 " "
y[1] (numeric) = 24.86856595154683 " "
absolute error = 4.9737991503207013000000000000E-13 " "
relative error = 2.0000345657290428000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498080445315743 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000006 " "
y[1] (analytic) = 25.371044833371133 " "
y[1] (numeric) = 25.371044833370632 " "
absolute error = 5.0093262871087060000000000000E-13 " "
relative error = 1.974426484998293000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498155704825491 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000006 " "
y[1] (analytic) = 25.883672471413416 " "
y[1] (numeric) = 25.88367247141289 " "
absolute error = 5.2580162446247410000000000000E-13 " "
relative error = 2.0314027116638214000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498228013929301 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000006 " "
y[1] (analytic) = 26.406653923564473 " "
y[1] (numeric) = 26.406653923563947 " "
absolute error = 5.2580162446247410000000000000E-13 " "
relative error = 1.9911709601089037000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498297488271078 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000006 " "
y[1] (analytic) = 26.940198389378395 " "
y[1] (numeric) = 26.940198389377844 " "
absolute error = 5.5067062021407760000000000000E-13 " "
relative error = 2.044048125611385200000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498364238963578 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000006 " "
y[1] (analytic) = 27.48451929375548 " "
y[1] (numeric) = 27.484519293754925 " "
absolute error = 5.5422333389287810000000000000E-13 " "
relative error = 2.016492731669491000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498428372765813 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000007 " "
y[1] (analytic) = 28.039834372315234 " "
y[1] (numeric) = 28.03983437231465 " "
absolute error = 5.8264504332328220000000000000E-13 " "
relative error = 2.0779189904864387000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498489992253575 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000007 " "
y[1] (analytic) = 28.606365758493332 " "
y[1] (numeric) = 28.606365758492746 " "
absolute error = 5.8619775700208270000000000000E-13 " "
relative error = 2.049186401205258000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498549195983168 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000007 " "
y[1] (analytic) = 29.18434007239815 " "
y[1] (numeric) = 29.184340072397536 " "
absolute error = 6.1461946643248670000000000000E-13 " "
relative error = 2.105990626849154000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498606078648876 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000007 " "
y[1] (analytic) = 29.773988511461624 " "
y[1] (numeric) = 29.773988511461006 " "
absolute error = 6.1817218011128720000000000000E-13 " "
relative error = 2.0762155526234555000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498660731234228 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000007 " "
y[1] (analytic) = 30.375546942921513 " "
y[1] (numeric) = 30.375546942920867 " "
absolute error = 6.4659388954169120000000000000E-13 " "
relative error = 2.1286658335953634000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498713241157226 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000007 " "
y[1] (analytic) = 30.989255998171238 " "
y[1] (numeric) = 30.989255998170588 " "
absolute error = 6.5014660322049170000000000000E-13 " "
relative error = 2.097974224546916000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498763692410101 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000007 " "
y[1] (analytic) = 31.61536116901585 " "
y[1] (numeric) = 31.615361169015166 " "
absolute error = 6.8212102632969620000000000000E-13 " "
relative error = 2.157562023989144000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498812165693469 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000007 " "
y[1] (analytic) = 32.25411290587180 " "
y[1] (numeric) = 32.254112905871125 " "
absolute error = 6.8212102632969620000000000000E-13 " "
relative error = 2.1148342486440455000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498858738545188 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000007 " "
y[1] (analytic) = 32.90576671795072 " "
y[1] (numeric) = 32.90576671795 " "
absolute error = 7.1764816311770120000000000000E-13 " "
relative error = 2.1809191357520033000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498903485464355 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000007 " "
y[1] (analytic) = 33.570583275466184 " "
y[1] (numeric) = 33.57058327546547 " "
absolute error = 7.1764816311770120000000000000E-13 " "
relative error = 2.1377292054444813000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498946478030268 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000007 " "
y[1] (analytic) = 34.24882851390561 " "
y[1] (numeric) = 34.24882851390486 " "
absolute error = 7.4606987254810520000000000000E-13 " "
relative error = 2.1783807064968314000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.498987785016839 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000008 " "
y[1] (analytic) = 34.94077374040770 " "
y[1] (numeric) = 34.940773740406954 " "
absolute error = 7.5317529990570620000000000000E-13 " "
relative error = 2.1555770501861754000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499027472502497 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000008 " "
y[1] (analytic) = 35.64669574228919 " "
y[1] (numeric) = 35.6466957422884 " "
absolute error = 7.8870243669371120000000000000E-13 " "
relative error = 2.212554123938169000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499065603975762 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000008 " "
y[1] (analytic) = 36.36687689776317 " "
y[1] (numeric) = 36.36687689776238 " "
absolute error = 7.8870243669371120000000000000E-13 " "
relative error = 2.168738434457709000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499102240436759 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0000000000000007 " "
y[1] (analytic) = 37.10160528889445 " "
y[1] (numeric) = 37.10160528889362 " "
absolute error = 8.2422957348171620000000000000E-13 " "
relative error = 2.2215469305540567000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499137440494652 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0100000000000007 " "
y[1] (analytic) = 37.851174816835915 " "
y[1] (numeric) = 37.85117481683509 " "
absolute error = 8.2422957348171620000000000000E-13 " "
relative error = 2.1775534774553554000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499171260461404 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0200000000000007 " "
y[1] (analytic) = 38.61588531939317 " "
y[1] (numeric) = 38.61588531939235 " "
absolute error = 8.2422957348171620000000000000E-13 " "
relative error = 2.13443137885999000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499203754441703 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0300000000000007 " "
y[1] (analytic) = 39.39604269096356 " "
y[1] (numeric) = 39.3960426909627 " "
absolute error = 8.5975671026972120000000000000E-13 " "
relative error = 2.182342823145857200000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49923497441951 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0400000000000007 " "
y[1] (analytic) = 40.19195900489791 " "
y[1] (numeric) = 40.19195900489701 " "
absolute error = 9.0238927441532720000000000000E-13 " "
relative error = 2.245198534128081000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499264970341121 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0500000000000007 " "
y[1] (analytic) = 41.00395263833411 " "
y[1] (numeric) = 41.00395263833321 " "
absolute error = 9.0238927441532720000000000000E-13 " "
relative error = 2.2007372859261723000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499293790195042 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0600000000000007 " "
y[1] (analytic) = 41.83234839955231 " "
y[1] (numeric) = 41.8323483995514 " "
absolute error = 9.0949470177292820000000000000E-13 " "
relative error = 2.1741421090828877000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499321480088689 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0700000000000007 " "
y[1] (analytic) = 42.67747765790244 " "
y[1] (numeric) = 42.67747765790149 " "
absolute error = 9.5212726591853420000000000000E-13 " "
relative error = 2.230982987210895200000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499348084322099 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0800000000000007 " "
y[1] (analytic) = 43.539678476356364 " "
y[1] (numeric) = 43.53967847635537 " "
absolute error = 9.9475983006414030000000000000E-13 " "
relative error = 2.2847202020665613000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499373645458785 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0900000000000007 " "
y[1] (analytic) = 44.419295746737575 " "
y[1] (numeric) = 44.41929574673658 " "
absolute error = 9.9475983006414030000000000000E-13 " "
relative error = 2.2394768159673076000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49939820439374 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1000000000000008 " "
y[1] (analytic) = 45.31668132768265 " "
y[1] (numeric) = 45.31668132768166 " "
absolute error = 9.9475983006414030000000000000E-13 " "
relative error = 2.1951294775340713000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499421800418888 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1100000000000008 " "
y[1] (analytic) = 46.23219418538932 " "
y[1] (numeric) = 46.23219418538828 " "
absolute error = 1.0373923942097463000000000000E-12 " "
relative error = 2.243874452615946800000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49944447128587 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1200000000000008 " "
y[1] (analytic) = 47.166200537207615 " "
y[1] (numeric) = 47.166200537206535 " "
absolute error = 1.0800249583553523000000000000E-12 " "
relative error = 2.2898281948815485000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49946625326641 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1300000000000008 " "
y[1] (analytic) = 48.11907399813181 " "
y[1] (numeric) = 48.11907399813073 " "
absolute error = 1.0800249583553523000000000000E-12 " "
relative error = 2.244484086284128000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499487181210307 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1400000000000008 " "
y[1] (analytic) = 49.09119573025147 " "
y[1] (numeric) = 49.091195730250384 " "
absolute error = 1.0871303857129533000000000000E-12 " "
relative error = 2.2145119293621746000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499507288601219 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1500000000000008 " "
y[1] (analytic) = 50.082954595221274 " "
y[1] (numeric) = 50.08295459522014 " "
absolute error = 1.1368683772161603000000000000E-12 " "
relative error = 2.2699706644795994000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499526607610148 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1600000000000008 " "
y[1] (analytic) = 51.0947473098108 " "
y[1] (numeric) = 51.09474730980961 " "
absolute error = 1.1866063687193673000000000000E-12 " "
relative error = 2.322364687556689000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499545169146911 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1700000000000008 " "
y[1] (analytic) = 52.12697860459659 " "
y[1] (numeric) = 52.126978604595394 " "
absolute error = 1.1937117960769683000000000000E-12 " "
relative error = 2.2900076467729633000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49956300290957 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1800000000000008 " "
y[1] (analytic) = 53.18006138585986 " "
y[1] (numeric) = 53.180061385858664 " "
absolute error = 1.1937117960769683000000000000E-12 " "
relative error = 2.244660432818467000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499580137431924 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1900000000000008 " "
y[1] (analytic) = 54.254416900754464 " "
y[1] (numeric) = 54.25441690075321 " "
absolute error = 1.2505552149377763000000000000E-12 " "
relative error = 2.3049832370797926000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499596600129165 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2000000000000008 " "
y[1] (analytic) = 55.35047490581124 " "
y[1] (numeric) = 55.35047490580994 " "
absolute error = 1.3002932064409833000000000000E-12 " "
relative error = 2.3491997289159045000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499612417341677 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2100000000000009 " "
y[1] (analytic) = 56.46867383884646 " "
y[1] (numeric) = 56.468673838845156 " "
absolute error = 1.3073986337985843000000000000E-12 " "
relative error = 2.315263569903755000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499627614377228 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2200000000000009 " "
y[1] (analytic) = 57.60946099434291 " "
y[1] (numeric) = 57.6094609943416 " "
absolute error = 1.3073986337985843000000000000E-12 " "
relative error = 2.2694165354662274000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49964221555139 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2300000000000009 " "
y[1] (analytic) = 58.77329270237354 " "
y[1] (numeric) = 58.773292702372174 " "
absolute error = 1.3642420526593924000000000000E-12 " "
relative error = 2.3211938449116326000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499656244226474 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2400000000000009 " "
y[1] (analytic) = 59.96063451113947 " "
y[1] (numeric) = 59.960634511138046 " "
absolute error = 1.4210854715202004000000000000E-12 " "
relative error = 2.3700307428471118000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499669722848841 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2500000000000009 " "
y[1] (analytic) = 61.17196137319560 " "
y[1] (numeric) = 61.17196137319416 " "
absolute error = 1.4352963262354024000000000000E-12 " "
relative error = 2.3463304004247973000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499682672984878 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.260000000000001 " "
y[1] (analytic) = 62.40775783543801 " "
y[1] (numeric) = 62.40775783543658 " "
absolute error = 1.4352963262354024000000000000E-12 " "
relative error = 2.29986843946567000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499695115355461 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.270000000000001 " "
y[1] (analytic) = 63.6685182329292 " "
y[1] (numeric) = 63.6685182329277 " "
absolute error = 1.4992451724538114000000000000E-12 " "
relative error = 2.3547668676203076000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499707069869059 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.280000000000001 " "
y[1] (analytic) = 64.95474688663846 " "
y[1] (numeric) = 64.9547468866369 " "
absolute error = 1.5631940186722204000000000000E-12 " "
relative error = 2.4065893465805774000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499718555653642 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.290000000000001 " "
y[1] (analytic) = 66.26695830517714 " "
y[1] (numeric) = 66.26695830517558 " "
absolute error = 1.5631940186722204000000000000E-12 " "
relative error = 2.3589343145543096000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499729591087242 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.300000000000001 " "
y[1] (analytic) = 67.60567739060913 " "
y[1] (numeric) = 67.60567739060755 " "
absolute error = 1.5774048733874224000000000000E-12 " "
relative error = 2.3332432042261203000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499740193827389 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.310000000000001 " "
y[1] (analytic) = 68.97143964841847 " "
y[1] (numeric) = 68.97143964841683 " "
absolute error = 1.6342482922482304000000000000E-12 " "
relative error = 2.3694565469110143000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499750380839291 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.320000000000001 " "
y[1] (analytic) = 70.36479140171863 " "
y[1] (numeric) = 70.36479140171693 " "
absolute error = 1.7053025658242404000000000000E-12 " "
relative error = 2.423516835413497800000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499760168423041 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.330000000000001 " "
y[1] (analytic) = 71.78629000978916 " "
y[1] (numeric) = 71.78629000978745 " "
absolute error = 1.7053025658242404000000000000E-12 " "
relative error = 2.3755268110271427000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499769572239629 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.340000000000001 " "
y[1] (analytic) = 73.23650409102689 " "
y[1] (numeric) = 73.23650409102517 " "
absolute error = 1.7195134205394424000000000000E-12 " "
relative error = 2.347891180608826000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499778607336072 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.350000000000001 " "
y[1] (analytic) = 74.71601375040083 " "
y[1] (numeric) = 74.71601375039904 " "
absolute error = 1.7905676941154525000000000000E-12 " "
relative error = 2.3964978914655313000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499787288169397 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.360000000000001 " "
y[1] (analytic) = 76.22541081150175 " "
y[1] (numeric) = 76.22541081149988 " "
absolute error = 1.8616219676914625000000000000E-12 " "
relative error = 2.4422590155598872000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499795628629863 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.370000000000001 " "
y[1] (analytic) = 77.76529905327955 " "
y[1] (numeric) = 77.76529905327769 " "
absolute error = 1.8616219676914625000000000000E-12 " "
relative error = 2.3938980372415264000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499803642063092 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.380000000000001 " "
y[1] (analytic) = 79.33629445156313 " "
y[1] (numeric) = 79.33629445156127 " "
absolute error = 1.8616219676914625000000000000E-12 " "
relative error = 2.346494729254126000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49981134129147 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.390000000000001 " "
y[1] (analytic) = 80.9390254254588 " "
y[1] (numeric) = 80.93902542545685 " "
absolute error = 1.9468870959826745000000000000E-12 " "
relative error = 2.405375016253031000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499818738634671 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.400000000000001 " "
y[1] (analytic) = 82.57413308872603 " "
y[1] (numeric) = 82.574133088724 " "
absolute error = 2.0321522242738865000000000000E-12 " "
relative error = 2.461003401743662200000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499825845929319 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.410000000000001 " "
y[1] (analytic) = 84.2422715062318 " "
y[1] (numeric) = 84.24227150622976 " "
absolute error = 2.0463630789890885000000000000E-12 " "
relative error = 2.4291404331823000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49983267454797 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.420000000000001 " "
y[1] (analytic) = 85.94410795558532 " "
y[1] (numeric) = 85.94410795558328 " "
absolute error = 2.0463630789890885000000000000E-12 " "
relative error = 2.3810394076655253000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499839235417275 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.430000000000001 " "
y[1] (analytic) = 87.68032319405788 " "
y[1] (numeric) = 87.68032319405575 " "
absolute error = 2.1316282072803006000000000000E-12 " "
relative error = 2.431136348074914000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499845539035482 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.440000000000001 " "
y[1] (analytic) = 89.45161173089461 " "
y[1] (numeric) = 89.4516117308924 " "
absolute error = 2.2168933355715126000000000000E-12 " "
relative error = 2.478315697922574800000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499851595489227 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.450000000000001 " "
y[1] (analytic) = 91.25868210512769 " "
y[1] (numeric) = 91.25868210512547 " "
absolute error = 2.2168933355715126000000000000E-12 " "
relative error = 2.429241015137286200000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499857414469654 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.460000000000001 " "
y[1] (analytic) = 93.10225716900148 " "
y[1] (numeric) = 93.10225716899924 " "
absolute error = 2.2311041902867146000000000000E-12 " "
relative error = 2.396401825400173000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49986300528796 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.470000000000001 " "
y[1] (analytic) = 94.98307437712292 " "
y[1] (numeric) = 94.9830743771206 " "
absolute error = 2.3163693185779266000000000000E-12 " "
relative error = 2.438717986091882000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499868376890241 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.480000000000001 " "
y[1] (analytic) = 96.9018860814531 " "
y[1] (numeric) = 96.90188608145068 " "
absolute error = 2.4158453015843406000000000000E-12 " "
relative error = 2.4930838802803554000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49987353787184 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.490000000000001 " "
y[1] (analytic) = 98.85945983225814 " "
y[1] (numeric) = 98.85945983225572 " "
absolute error = 2.4158453015843406000000000000E-12 " "
relative error = 2.44371687411956030000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499878496491101 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.500000000000001 " "
y[1] (analytic) = 100.8565786851398 " "
y[1] (numeric) = 100.85657868513736 " "
absolute error = 2.4300561562995426000000000000E-12 " "
relative error = 2.40941759871296000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499883260682555 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5100000000000011 " "
y[1] (analytic) = 102.8940415142679 " "
y[1] (numeric) = 102.89404151426538 " "
absolute error = 2.5153212845907547000000000000E-12 " "
relative error = 2.4445742897969125000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499887838069647 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5200000000000011 " "
y[1] (analytic) = 104.97266333194057 " "
y[1] (numeric) = 104.97266333193795 " "
absolute error = 2.6147972675971687000000000000E-12 " "
relative error = 2.4909316241017493000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.4998922359769 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5300000000000011 " "
y[1] (analytic) = 107.09327561460009 " "
y[1] (numeric) = 107.09327561459746 " "
absolute error = 2.6290081223123707000000000000E-12 " "
relative error = 2.4548769352928043000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499896461441661 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5400000000000011 " "
y[1] (analytic) = 109.25672663543483 " "
y[1] (numeric) = 109.25672663543219 " "
absolute error = 2.6432189770275727000000000000E-12 " "
relative error = 2.419273447434866800000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499900521225337 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5500000000000012 " "
y[1] (analytic) = 111.46388180369962 " "
y[1] (numeric) = 111.46388180369686 " "
absolute error = 2.7569058147491887000000000000E-12 " "
relative error = 2.47336246516554000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499904421824269 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5600000000000012 " "
y[1] (analytic) = 113.71562401089079 " "
y[1] (numeric) = 113.71562401088794 " "
absolute error = 2.8563817977556030000000000000E-12 " "
relative error = 2.5118639787634110000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499908169480022 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5700000000000012 " "
y[1] (analytic) = 116.01285398391477 " "
y[1] (numeric) = 116.0128539839119 " "
absolute error = 2.8705926524708050000000000000E-12 " "
relative error = 2.4743746523715499000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499911770189494 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5800000000000012 " "
y[1] (analytic) = 118.35649064539098 " "
y[1] (numeric) = 118.35649064538809 " "
absolute error = 2.8848035071860070000000000000E-12 " "
relative error = 2.437385133215207000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49991522971442 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5900000000000012 " "
y[1] (analytic) = 120.74747148123303 " "
y[1] (numeric) = 120.74747148123004 " "
absolute error = 2.9984903449076230000000000000E-12 " "
relative error = 2.4832738177657473000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499918553590616 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6000000000000012 " "
y[1] (analytic) = 123.18675291565533 " "
y[1] (numeric) = 123.18675291565222 " "
absolute error = 3.112177182629239000000000000E-12 " "
relative error = 2.5263894931625590000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499921747136849 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6100000000000012 " "
y[1] (analytic) = 125.67531069375573 " "
y[1] (numeric) = 125.6753106937526 " "
absolute error = 3.126388037344441000000000000E-12 " "
relative error = 2.487670824194571000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499924815463356 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6200000000000012 " "
y[1] (analytic) = 128.21414027182678 " "
y[1] (numeric) = 128.21414027182365 " "
absolute error = 3.126388037344441000000000000E-12 " "
relative error = 2.4384112631541155000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499927763479999 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6300000000000012 " "
y[1] (analytic) = 130.80425721555133 " "
y[1] (numeric) = 130.8042572155481 " "
absolute error = 3.240074875066057000000000000E-12 " "
relative error = 2.4770408425826407000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499930595904114 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6400000000000012 " "
y[1] (analytic) = 133.44669760624214 " "
y[1] (numeric) = 133.44669760623876 " "
absolute error = 3.382183422218077000000000000E-12 " "
relative error = 2.5344826682768890000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49993331726809 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6500000000000012 " "
y[1] (analytic) = 136.14251845528835 " "
y[1] (numeric) = 136.14251845528494 " "
absolute error = 3.410605131648481000000000000E-12 " "
relative error = 2.505172645802483000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49993593192659 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6600000000000013 " "
y[1] (analytic) = 138.89279812697444 " "
y[1] (numeric) = 138.89279812697103 " "
absolute error = 3.410605131648481000000000000E-12 " "
relative error = 2.455566579147277800000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499938444063542 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6700000000000013 " "
y[1] (analytic) = 141.6986367698401 " "
y[1] (numeric) = 141.69863676983658 " "
absolute error = 3.524291969370097000000000000E-12 " "
relative error = 2.4871742239091363000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499940857698823 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6800000000000013 " "
y[1] (analytic) = 144.5611567567541 " "
y[1] (numeric) = 144.56115675675042 " "
absolute error = 3.666400516522117000000000000E-12 " "
relative error = 2.5362279873641214000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499943176694687 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6900000000000013 " "
y[1] (analytic) = 147.4815031338784 " "
y[1] (numeric) = 147.48150313387472 " "
absolute error = 3.666400516522117000000000000E-12 " "
relative error = 2.4860070168893594000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499945404761943 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7000000000000013 " "
y[1] (analytic) = 150.46084407870254 " "
y[1] (numeric) = 150.46084407869884 " "
absolute error = 3.694822225952521000000000000E-12 " "
relative error = 2.4556702765935876000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499947545465945 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7100000000000013 " "
y[1] (analytic) = 153.50037136732962 " "
y[1] (numeric) = 153.50037136732578 " "
absolute error = 3.836930773104541000000000000E-12 " "
relative error = 2.4996231207302327000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499949602232194 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7200000000000013 " "
y[1] (analytic) = 156.60130085120255 " "
y[1] (numeric) = 156.60130085119857 " "
absolute error = 3.979039320256561000000000000E-12 " "
relative error = 2.540872456760314000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499951578351894 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7300000000000013 " "
y[1] (analytic) = 159.76487294346103 " "
y[1] (numeric) = 159.76487294345702 " "
absolute error = 4.007461029686965000000000000E-12 " "
relative error = 2.5083492734383234000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499953476987228 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7400000000000013 " "
y[1] (analytic) = 162.99235311512356 " "
y[1] (numeric) = 162.99235311511956 " "
absolute error = 4.007461029686965000000000000E-12 " "
relative error = 2.4586803939547056000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499955301176353 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7500000000000013 " "
y[1] (analytic) = 166.28503240129265 " "
y[1] (numeric) = 166.2850324012885 " "
absolute error = 4.149569576838985000000000000E-12 " "
relative error = 2.4954558548750821000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499957053838342 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7600000000000013 " "
y[1] (analytic) = 169.6442279175856 " "
y[1] (numeric) = 169.64422791758128 " "
absolute error = 4.320099833421409000000000000E-12 " "
relative error = 2.5465645878150040000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499958737777767 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7700000000000014 " "
y[1] (analytic) = 173.07128338699863 " "
y[1] (numeric) = 173.07128338699428 " "
absolute error = 4.348521542851813000000000000E-12 " "
relative error = 2.5125609851336433000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49996035568927 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7800000000000014 " "
y[1] (analytic) = 176.56756967741433 " "
y[1] (numeric) = 176.56756967740998 " "
absolute error = 4.348521542851813000000000000E-12 " "
relative error = 2.4628087427359857000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499961910161812 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7900000000000014 " "
y[1] (analytic) = 180.1344853499668 " "
y[1] (numeric) = 180.1344853499623 " "
absolute error = 4.519051799434237000000000000E-12 " "
relative error = 2.508709973359396000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499963403682846 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8000000000000014 " "
y[1] (analytic) = 183.77345721848442 " "
y[1] (numeric) = 183.77345721847973 " "
absolute error = 4.689582056016661000000000000E-12 " "
relative error = 2.55182773780074000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499964838642317 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8100000000000014 " "
y[1] (analytic) = 187.48594092023473 " "
y[1] (numeric) = 187.48594092023 " "
absolute error = 4.718003765447065000000000000E-12 " "
relative error = 2.5164573633040166000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49996621733642 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8200000000000014 " "
y[1] (analytic) = 191.27342149819899 " "
y[1] (numeric) = 191.27342149819424 " "
absolute error = 4.746425474877469000000000000E-12 " "
relative error = 2.4814872017763123000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49996754197135 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8300000000000014 " "
y[1] (analytic) = 195.13741399510897 " "
y[1] (numeric) = 195.13741399510405 " "
absolute error = 4.916955731459893300000000000E-12 " "
relative error = 2.5197401312201130000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499968814666762 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8400000000000014 " "
y[1] (analytic) = 199.0794640594839 " "
y[1] (numeric) = 199.0794640594788 " "
absolute error = 5.115907697472721000000000000E-12 " "
relative error = 2.569781730949464000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499970037459242 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8500000000000014 " "
y[1] (analytic) = 203.1011485639107 " "
y[1] (numeric) = 203.10114856390555 " "
absolute error = 5.144329406903125000000000000E-12 " "
relative error = 2.5328903569860106000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49997121230549 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8600000000000014 " "
y[1] (analytic) = 207.20407623581445 " "
y[1] (numeric) = 207.2040762358093 " "
absolute error = 5.144329406903125000000000000E-12 " "
relative error = 2.482735620050483800000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499972341085494 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8700000000000014 " "
y[1] (analytic) = 211.3898883009706 " "
y[1] (numeric) = 211.38988830096525 " "
absolute error = 5.343281372915953000000000000E-12 " "
relative error = 2.527690144435078000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49997342560553 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8800000000000014 " "
y[1] (analytic) = 215.66025914001654 " "
y[1] (numeric) = 215.660259140011 " "
absolute error = 5.5422333389287810000000000000E-12 " "
relative error = 2.569890883480071000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499974467601035 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8900000000000015 " "
y[1] (analytic) = 220.01689695822677 " "
y[1] (numeric) = 220.0168969582212 " "
absolute error = 5.5706550483591850000000000000E-12 " "
relative error = 2.5319214684756014000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499975468739429 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9000000000000015 " "
y[1] (analytic) = 224.46154446881803 " "
y[1] (numeric) = 224.46154446881243 " "
absolute error = 5.5990767577895900000000000000E-12 " "
relative error = 2.4944481118312037000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499976430622722 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9100000000000015 " "
y[1] (analytic) = 228.9959795900575 " "
y[1] (numeric) = 228.9959795900517 " "
absolute error = 5.7980287238024180000000000000E-12 " "
relative error = 2.5319347239990386000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49997735479012 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9200000000000015 " "
y[1] (analytic) = 233.62201615645344 " "
y[1] (numeric) = 233.62201615644742 " "
absolute error = 6.0254023992456500000000000000E-12 " "
relative error = 2.579124390061988000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499978242720484 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9300000000000015 " "
y[1] (analytic) = 238.34150464431352 " "
y[1] (numeric) = 238.34150464430746 " "
absolute error = 6.0538241086760540000000000000E-12 " "
relative error = 2.5399789758441005000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.49997909583468 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9400000000000015 " "
y[1] (analytic) = 243.1563329119604 " "
y[1] (numeric) = 243.15633291195434 " "
absolute error = 6.0538241086760540000000000000E-12 " "
relative error = 2.489683914943709000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499979915497859 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9500000000000015 " "
y[1] (analytic) = 248.06842695489996 " "
y[1] (numeric) = 248.06842695489365 " "
absolute error = 6.30961949354969000000000000E-12 " "
relative error = 2.54349961863418000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499980703021658 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9600000000000015 " "
y[1] (analytic) = 253.0797516762446 " "
y[1] (numeric) = 253.07975167623806 " "
absolute error = 6.536993168992922000000000000E-12 " "
relative error = 2.582977549841858000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499981459666255 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9700000000000015 " "
y[1] (analytic) = 258.1923116727012 " "
y[1] (numeric) = 258.19231167269464 " "
absolute error = 6.536993168992922000000000000E-12 " "
relative error = 2.531831070663163000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499982186642452 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9800000000000015 " "
y[1] (analytic) = 263.40815203643695 " "
y[1] (numeric) = 263.40815203643035 " "
absolute error = 6.59383658785373000000000000E-12 " "
relative error = 2.503277342358642000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499982885113571 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9900000000000015 " "
y[1] (analytic) = 268.729359173143 " "
y[1] (numeric) = 268.7293591731362 " "
absolute error = 6.821210263296962000000000000E-12 " "
relative error = 2.5383196998962960000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 9.499983556197288 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
"Finished!"
"diff ( y , x , 1 ) = cosh (2.0 * x + 3.0) ;"
Iterations = 190
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 1 Minutes 44 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 1 Minutes 41 Seconds
"Time to Timeout "= 0 Years 0 Days 0 Hours 1 Minutes 15 Seconds
Percent Done = 100.52631578947374 "%"
(%o58) true
(%o58) diffeq.max