(%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_0D2 array_x ,
1 1 1
array_tmp2 : array_const_0D3 + array_tmp1 , array_tmp3 : sin(array_tmp2 ),
1 1 1 1 1
array_tmp3_g : cos(array_tmp2 ), array_tmp4 :
1 1 1
expt(array_tmp3 , array_const_2D0 ), array_tmp5 :
1 1 1
array_tmp4 + array_const_0D0 , if not array_y_set_initial
1 1 1, 2
then (if 1 <= glob_max_terms then (temporary :
array_tmp5 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_0D2 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 : -------------------------,
2 1
array_const_2D0 array_tmp4 array_tmp3
1 1 2
array_tmp4 : ----------------------------------------,
2 array_tmp3
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp3_g array_tmp2
2 2
array_tmp3 : -------------------------,
3 2
- array_tmp3 array_tmp2
2 2
array_tmp3_g : -------------------------,
3 2
array_tmp4 : (array_const_2D0 att(2, array_tmp4, array_tmp3, 1)
3 1
- att(2, array_tmp3, array_tmp4, 2))/array_tmp3 , array_tmp5 : array_tmp4 ,
1 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp5 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 : -------------------------,
4 3
array_tmp4 : (array_const_2D0 att(3, array_tmp4, array_tmp3, 1)
4 1
- att(3, array_tmp3, array_tmp4, 2))/array_tmp3 , array_tmp5 : array_tmp4 ,
1 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp5 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 : -------------------------,
5 4
array_tmp4 : (array_const_2D0 att(4, array_tmp4, array_tmp3, 1)
5 1
- att(4, array_tmp3, array_tmp4, 2))/array_tmp3 , array_tmp5 : array_tmp4 ,
1 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp5 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 :
kkk - 1 kkk
(array_const_2D0 att(kkk - 1, array_tmp4, array_tmp3, 1)
1
- att(kkk - 1, array_tmp3, array_tmp4, 2))/array_tmp3 ,
1
array_tmp5 : array_tmp4 , order_d : 1,
kkk kkk
if order_d + kkk < glob_max_terms then (if not subscript(array_y_set_initial,
1, order_d + kkk) then (temporary : array_tmp5 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_0D2 array_x ,
1 1 1
array_tmp2 : array_const_0D3 + array_tmp1 , array_tmp3 : sin(array_tmp2 ),
1 1 1 1 1
array_tmp3_g : cos(array_tmp2 ), array_tmp4 :
1 1 1
expt(array_tmp3 , array_const_2D0 ), array_tmp5 :
1 1 1
array_tmp4 + array_const_0D0 , if not array_y_set_initial
1 1 1, 2
then (if 1 <= glob_max_terms then (temporary :
array_tmp5 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_0D2 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 : -------------------------,
2 1
array_const_2D0 array_tmp4 array_tmp3
1 1 2
array_tmp4 : ----------------------------------------,
2 array_tmp3
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp3_g array_tmp2
2 2
array_tmp3 : -------------------------,
3 2
- array_tmp3 array_tmp2
2 2
array_tmp3_g : -------------------------,
3 2
array_tmp4 : (array_const_2D0 att(2, array_tmp4, array_tmp3, 1)
3 1
- att(2, array_tmp3, array_tmp4, 2))/array_tmp3 , array_tmp5 : array_tmp4 ,
1 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp5 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 : -------------------------,
4 3
array_tmp4 : (array_const_2D0 att(3, array_tmp4, array_tmp3, 1)
4 1
- att(3, array_tmp3, array_tmp4, 2))/array_tmp3 , array_tmp5 : array_tmp4 ,
1 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp5 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 : -------------------------,
5 4
array_tmp4 : (array_const_2D0 att(4, array_tmp4, array_tmp3, 1)
5 1
- att(4, array_tmp3, array_tmp4, 2))/array_tmp3 , array_tmp5 : array_tmp4 ,
1 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp5 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 :
kkk - 1 kkk
(array_const_2D0 att(kkk - 1, array_tmp4, array_tmp3, 1)
1
- att(kkk - 1, array_tmp3, array_tmp4, 2))/array_tmp3 ,
1
array_tmp5 : array_tmp4 , order_d : 1,
kkk kkk
if order_d + kkk < glob_max_terms then (if not subscript(array_y_set_initial,
1, order_d + kkk) then (temporary : array_tmp5 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)
(%i56) exact_soln_y(x) := block(0.75 + 0.5 x
- 2.5 sin(0.3 + 0.2 x) cos(0.3 + 0.2 x))
(%o56) exact_soln_y(x) := block(0.75 + 0.5 x
- 2.5 sin(0.3 + 0.2 x) cos(0.3 + 0.2 x))
(%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/expt_sin_cpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0);"),
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:5.0,"),
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:1000000,"),
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, " (-2.\
5000000000000000000000000000000*sin(0.20000000000000000000000000000000*x+0.300\
00000000000000000000000000000)*cos(0.20000000000000000000000000000000*x+0.3000\
0000000000000000000000000000)+0.50000000000000000000000000000000*x+0.750000000\
00000000000000000000000) "), 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_c1, 1 + max_terms), array(array_tmp4_a1, 1 + max_terms),
array(array_tmp4_a2, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5, 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_c1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4_a1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4_a2 : 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_tmp5 : 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_c1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_c1 : 0.0, term : 1 + term),
term
array(array_tmp4_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_a1 : 0.0, term : 1 + term),
term
array(array_tmp4_a2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_a2 : 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_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 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_0D2, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term),
term
array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term),
term
array_const_0D3 : 0.3, 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_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 : 5.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
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 ) = expt(sin(0.2 * x + 0.3) , 2.0);"),
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,
"2013-05-26T01:46:37-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "expt_sin_c"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0);"),
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, "expt_sin_c diffeq.max"),
logitem_str(html_log_file,
"expt_sin_c 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/expt_sin_cpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0);"),
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:5.0,"),
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:1000000,"),
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, " (-2.\
5000000000000000000000000000000*sin(0.20000000000000000000000000000000*x+0.300\
00000000000000000000000000000)*cos(0.20000000000000000000000000000000*x+0.3000\
0000000000000000000000000000)+0.50000000000000000000000000000000*x+0.750000000\
00000000000000000000000) "), 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_c1, 1 + max_terms), array(array_tmp4_a1, 1 + max_terms),
array(array_tmp4_a2, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5, 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_c1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4_a1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4_a2 : 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_tmp5 : 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_c1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_c1 : 0.0, term : 1 + term),
term
array(array_tmp4_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_a1 : 0.0, term : 1 + term),
term
array(array_tmp4_a2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_a2 : 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_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 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_0D2, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term),
term
array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term),
term
array_const_0D3 : 0.3, 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_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 : 5.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 1000000,
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 ) = expt(sin(0.2 * x + 0.3) , 2.0);"),
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,
"2013-05-26T01:46:37-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "expt_sin_c"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0);"),
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, "expt_sin_c diffeq.max"),
logitem_str(html_log_file,
"expt_sin_c 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/expt_sin_cpostode.ode#################"
"diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0);"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.1,"
"x_end:5.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"/* 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("
" (-2.5000000000000000000000000000000*sin(0.20000000000000000000000000000000*x+0.30000000000000000000000000000000)*cos(0.20000000000000000000000000000000*x+0.30000000000000000000000000000000)+0.50000000000000000000000000000000*x+0.75000000000000000000000000000000) "
"));"
"/* 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 = 4.9 ""
estimated_steps = 4900000.000000001 ""
step_error = 2.04081632653061200000000000000000E-17 ""
est_needed_step_err = 2.04081632653061200000000000000000E-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 = 9.6231357696947530000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-184 ""
estimated_step_error = 9.6231357696947530000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-184 ""
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 = 6.4579753769509400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-176 ""
estimated_step_error = 6.4579753769509400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-176 ""
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 = 4.33387160530974000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-168 ""
estimated_step_error = 4.33387160530974000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-168 ""
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 = 2.90840890438994900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-160 ""
estimated_step_error = 2.90840890438994900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-160 ""
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 = 1.951796019297282200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 ""
estimated_step_error = 1.951796019297282200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 ""
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 = 1.3098225568684294000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 ""
estimated_step_error = 1.3098225568684294000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 ""
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 = 8.78999550044665600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-137 ""
estimated_step_error = 8.78999550044665600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-137 ""
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 = 5.898765622519023000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-129 ""
estimated_step_error = 5.898765622519023000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-129 ""
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 = 3.9584597127433580000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-121 ""
estimated_step_error = 3.9584597127433580000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-121 ""
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 = 2.656296322079278500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-113 ""
estimated_step_error = 2.656296322079278500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-113 ""
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 = 1.7823673712041604000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
estimated_step_error = 1.7823673712041604000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
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 = 1.1958005943093329000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 ""
estimated_step_error = 1.1958005943093329000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 ""
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 = 8.020511381323849000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 ""
estimated_step_error = 8.020511381323849000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 ""
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 = 5.3766176735542190000000000000000000000000000000000000000000000000000000000000000000000000000000000E-82 ""
estimated_step_error = 5.3766176735542190000000000000000000000000000000000000000000000000000000000000000000000000000000000E-82 ""
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 = 3.60035267228840300000000000000000000000000000000000000000000000000000000000000000000000000E-74 ""
estimated_step_error = 3.60035267228840300000000000000000000000000000000000000000000000000000000000000000000000000E-74 ""
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 = 2.405710347770160800000000000000000000000000000000000000000000000000000000000000000E-66 ""
estimated_step_error = 2.405710347770160800000000000000000000000000000000000000000000000000000000000000000E-66 ""
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 = 1.60061231949650400000000000000000000000000000000000000000000000000000000000E-58 ""
estimated_step_error = 1.60061231949650400000000000000000000000000000000000000000000000000000000000E-58 ""
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 = 1.056089107012379400000000000000000000000000000000000000000000000000E-50 ""
estimated_step_error = 1.056089107012379400000000000000000000000000000000000000000000000000E-50 ""
best_h = 0.1 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (analytic) = 5.35056982970100200E-2 " "
y[1] (numeric) = 5.35056982970100200E-2 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 5.45012021486411800E-2 " "
y[1] (numeric) = 5.450120214864113000E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.01853076708037020000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 5.55087139650272100E-2 " "
y[1] (numeric) = 5.550871396502722000E-2 " "
absolute error = 1.387778780781445700000000000000000E-17 " "
relative error = 2.500109769532408700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 5.652829762589406000E-2 " "
y[1] (numeric) = 5.65282976258940800E-2 " "
absolute error = 1.387778780781445700000000000000000E-17 " "
relative error = 2.455016052253698500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 5.75600168178178600E-2 " "
y[1] (numeric) = 5.756001681781819000E-2 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 5.7864282500425750000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 5.86039350332077100E-2 " "
y[1] (numeric) = 5.86039350332078400E-2 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 2.36806415814068750000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 5.966011556928708000E-2 " "
y[1] (numeric) = 5.9660115569287200E-2 " "
absolute error = 1.2490009027033011000000000000000E-16 " "
relative error = 2.09352746099319450000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 6.07286215270834700E-2 " "
y[1] (numeric) = 6.07286215270835400E-2 " "
absolute error = 6.24500451351650600000000000000000E-17 " "
relative error = 1.0283461663511310000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 6.18095158104174900E-2 " "
y[1] (numeric) = 6.18095158104176500E-2 " "
absolute error = 1.59594559789866250000000000000000E-16 " "
relative error = 2.58203866665734140000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 6.29028611248971800E-2 " "
y[1] (numeric) = 6.29028611248974100E-2 " "
absolute error = 2.35922392732845760000000000000000E-16 " "
relative error = 3.75058285925036900000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 6.40087199769143700E-2 " "
y[1] (numeric) = 6.40087199769144400E-2 " "
absolute error = 6.93889390390722800000000000000000E-17 " "
relative error = 1.08405447045493740000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 6.51271546726439600E-2 " "
y[1] (numeric) = 6.51271546726440500E-2 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 1.27852548242618270000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 6.62582273170482200E-2 " "
y[1] (numeric) = 6.62582273170482700E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 6.28350094913135600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 6.74019998128820900E-2 " "
y[1] (numeric) = 6.74019998128822600E-2 " "
absolute error = 1.80411241501587940000000000000000E-16 " "
relative error = 2.67664523311528200000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 6.85585338597036700E-2 " "
y[1] (numeric) = 6.85585338597038400E-2 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 2.4290696477635160000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 6.97278909528862300E-2 " "
y[1] (numeric) = 6.97278909528862500E-2 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 3.98055573405809900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 7.09101323826342200E-2 " "
y[1] (numeric) = 7.0910132382634300E-2 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 1.17425710612942870000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 7.21053192330034500E-2 " "
y[1] (numeric) = 7.21053192330036500E-2 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 2.69451728909999740000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 7.33135123809234300E-2 " "
y[1] (numeric) = 7.33135123809235200E-2 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 1.13576234643142260000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 7.45347724952225600E-2 " "
y[1] (numeric) = 7.45347724952226600E-2 " "
absolute error = 9.7144514654701200000000000000000E-17 " "
relative error = 1.30334488725953880000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 7.57691600356584800E-2 " "
y[1] (numeric) = 7.57691600356586300E-2 " "
absolute error = 1.52655665885959020000000000000000E-16 " "
relative error = 2.01474670979744560000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 7.70167352519504100E-2 " "
y[1] (numeric) = 7.70167352519504500E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 5.405755422798063000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 7.82775581828145700E-2 " "
y[1] (numeric) = 7.82775581828146100E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 5.31868448504871200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 7.95516886550042800E-2 " "
y[1] (numeric) = 7.95516886550044400E-2 " "
absolute error = 1.52655665885959020000000000000000E-16 " "
relative error = 1.91894940845301680000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 8.08391862823527600E-2 " "
y[1] (numeric) = 8.0839186282352890E-2 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 1.71671542552921360000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 8.21401104648187300E-2 " "
y[1] (numeric) = 8.21401104648187500E-2 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 3.37905262831571800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 8.34545203875360900E-2 " "
y[1] (numeric) = 8.34545203875361800E-2 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 9.97749749926339500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 8.47824750198675800E-2 " "
y[1] (numeric) = 8.47824750198677500E-2 " "
absolute error = 1.80411241501587940000000000000000E-16 " "
relative error = 2.12793081894944800000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 8.61240331144610400E-2 " "
y[1] (numeric) = 8.61240331144610500E-2 " "
absolute error = 1.387778780781445700000000000000000E-17 " "
relative error = 1.611372262301107000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 8.74792532063084500E-2 " "
y[1] (numeric) = 8.74792532063085200E-2 " "
absolute error = 6.93889390390722800000000000000000E-17 " "
relative error = 7.93204519881159600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 8.33928572811425 " "
Order of pole (six term test) = -15.931575676952273 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (analytic) = 8.88481936118108400E-2 " "
y[1] (numeric) = 8.88481936118109100E-2 " "
absolute error = 6.93889390390722800000000000000000E-17 " "
relative error = 7.80983115337622500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 9.0230912427844200E-2 " "
y[1] (numeric) = 9.02309124278442900E-2 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 9.2281818510339710000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 11.769009376208933 " "
Order of pole (six term test) = -20.47801483941086 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (analytic) = 9.1627467530830400E-2 " "
y[1] (numeric) = 9.16274675308304200E-2 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 3.02917633364578600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 9.30379165758106200E-2 " "
y[1] (numeric) = 9.3037916575810800E-2 " "
absolute error = 1.80411241501587940000000000000000E-16 " "
relative error = 1.9391152353952640000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 9.4462316995524100E-2 " "
y[1] (numeric) = 9.44623169955241100E-2 " "
absolute error = 1.387778780781445700000000000000000E-17 " "
relative error = 1.46913480943644700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 9.59007259994872900E-2 " "
y[1] (numeric) = 9.59007259994873600E-2 " "
absolute error = 6.93889390390722800000000000000000E-17 " "
relative error = 7.235496740602699000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 9.73532005730806100E-2 " "
y[1] (numeric) = 9.73532005730805100E-2 " "
absolute error = 9.7144514654701200000000000000000E-17 " "
relative error = 9.97856404133084900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 9.88197974766347200E-2 " "
y[1] (numeric) = 9.8819797476634710E-2 " "
absolute error = 1.387778780781445700000000000000000E-17 " "
relative error = 1.404352990208846400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.10030057324452413 " "
y[1] (numeric) = 0.10030057324452411 " "
absolute error = 1.387778780781445700000000000000000E-17 " "
relative error = 1.383619989287759000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.10179558418426127 " "
y[1] (numeric) = 0.10179558418426136 " "
absolute error = 9.7144514654701200000000000000000E-17 " "
relative error = 9.54309712284364700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.10330488637559654 " "
y[1] (numeric) = 0.10330488637559665 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.07470523764829560000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.10482853566962036 " "
y[1] (numeric) = 0.10482853566962043 " "
absolute error = 6.93889390390722800000000000000000E-17 " "
relative error = 6.6192796260895790000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.10636658768786966 " "
y[1] (numeric) = 0.10636658768786986 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 1.82659830998376240000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.1079190978214386 " "
y[1] (numeric) = 0.10791909782143877 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 1.54313237467308460000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.1094861212300915 " "
y[1] (numeric) = 0.1094861212300915 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 11.4497891100404 " "
Order of pole (six term test) = -18.35086865887306 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000004 " "
y[1] (analytic) = 0.11106771284138017 " "
y[1] (numeric) = 0.11106771284138026 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 7.49693360173923500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.11266392734976627 " "
y[1] (numeric) = 0.11266392734976634 " "
absolute error = 6.93889390390722800000000000000000E-17 " "
relative error = 6.15893131646774800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 17.599619565499815 " "
Order of pole (six term test) = -27.77788740742004 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000004 " "
y[1] (analytic) = 0.11427481921574478 " "
y[1] (numeric) = 0.114274819215745 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.94307553010276830000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.1159004426649739 " "
y[1] (numeric) = 0.11590044266497408 " "
absolute error = 1.80411241501587940000000000000000E-16 " "
relative error = 1.55660528427049530000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.11754085168740636 " "
y[1] (numeric) = 0.11754085168740641 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 4.722711332642610700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.11919610003642589 " "
y[1] (numeric) = 0.11919610003642596 " "
absolute error = 6.93889390390722800000000000000000E-17 " "
relative error = 5.82141018186562200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.12086624122798773 " "
y[1] (numeric) = 0.12086624122798778 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 4.59277550681403100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.282966525217671 " "
Order of pole (six term test) = -11.30641653419429 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000004 " "
y[1] (analytic) = 0.1225513285397617 " "
y[1] (numeric) = 0.12255132853976178 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 6.79443689750543300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 22.216525099244905 " "
Order of pole (six term test) = -35.32247009288179 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000004 " "
y[1] (analytic) = 0.12425141501028025 " "
y[1] (numeric) = 0.12425141501028025 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.12596655343808916 " "
y[1] (numeric) = 0.12596655343808927 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 8.81363341556229900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 17.845130632193147 " "
Order of pole (six term test) = -26.22112287572063 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (analytic) = 0.12769679638090392 " "
y[1] (numeric) = 0.1276967963809039 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 2.173553010119175500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.12944219615476737 " "
y[1] (numeric) = 0.12944219615476732 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 4.288489602330757000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.9611300200270536 " "
Order of pole (six term test) = -11.76907982228754 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (analytic) = 0.13120280483321367 " "
y[1] (numeric) = 0.1312028048332137 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 2.115471208935821300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.13297867424643495 " "
y[1] (numeric) = 0.13297867424643509 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 1.04361002893563650000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.970118272041615 " "
Order of pole (six term test) = -11.749086485254342 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000005 " "
y[1] (analytic) = 0.1347698559804522 " "
y[1] (numeric) = 0.13476985598045207 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 1.02973975202788450000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.991455881419660 " "
Order of pole (six term test) = -12.140319625507885 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000005 " "
y[1] (analytic) = 0.13657640137628868 " "
y[1] (numeric) = 0.1365764013762885 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 1.42256661730386870000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.13839836152914997 " "
y[1] (numeric) = 0.13839836152914986 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 8.02193763248647400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.1368319296305631 " "
Order of pole (six term test) = -11.099164825879443 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000005 " "
y[1] (analytic) = 0.1402357872876061 " "
y[1] (numeric) = 0.14023578728760594 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 1.18752464627473560000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.14208872925277705 " "
y[1] (numeric) = 0.14208872925277713 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 5.8601922393685800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.1439572377775249 " "
y[1] (numeric) = 0.14395723777752484 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 3.856086160603202600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.14584136296564587 " "
y[1] (numeric) = 0.14584136296564587 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.2903875195891796 " "
Order of pole (six term test) = -11.475013263581873 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000006 " "
y[1] (analytic) = 0.14774115467107074 " "
y[1] (numeric) = 0.14774115467107074 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.1829986766389973 " "
Order of pole (six term test) = -11.229648127433002 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000006 " "
y[1] (analytic) = 0.14965666249706588 " "
y[1] (numeric) = 0.14965666249706605 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 1.11277006258935160000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.1515879357954406 " "
y[1] (numeric) = 0.15158793579544075 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 9.1549421363859400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.15353502366575644 " "
y[1] (numeric) = 0.1535350236657566 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 1.08466100904972950000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.6057624312875834 " "
Order of pole (six term test) = -11.05570401716818 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000006 " "
y[1] (analytic) = 0.15549797495454265 " "
y[1] (numeric) = 0.15549797495454257 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 5.35484316572151100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.1574768382545133 " "
y[1] (numeric) = 0.15747683825451322 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 5.287553888547817000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.3388853605696244 " "
Order of pole (six term test) = -11.045607603856213 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000006 " "
y[1] (analytic) = 0.15947166190379147 " "
y[1] (numeric) = 0.15947166190379133 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 8.70235353550580200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.663859426691291 " "
Order of pole (six term test) = -11.13898346474495 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000006 " "
y[1] (analytic) = 0.16148249398513426 " "
y[1] (numeric) = 0.1614824939851344 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 8.59398902341204600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.29070480842418 " "
Order of pole (six term test) = -11.224077942921948 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000006 " "
y[1] (analytic) = 0.1635093823251652 " "
y[1] (numeric) = 0.16350938232516532 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 6.78996525359808500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.6986373734118585 " "
Order of pole (six term test) = -11.79906925082956 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000006 " "
y[1] (analytic) = 0.16555237449360716 " "
y[1] (numeric) = 0.16555237449360727 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 6.70617397075164300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.16761151780252237 " "
y[1] (numeric) = 0.16761151780252243 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 3.311893595323223000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.117207138036505 " "
Order of pole (six term test) = -11.362575803898498 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000007 " "
y[1] (analytic) = 0.16968685930555494 " "
y[1] (numeric) = 0.16968685930555513 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 1.14498571135403220000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.17177844579717916 " "
y[1] (numeric) = 0.17177844579717896 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 1.13104428444300710000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.1738863238119479 " "
y[1] (numeric) = 0.173886323811948 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 4.78857250078717200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.17601053962375235 " "
y[1] (numeric) = 0.17601053962375227 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 4.730780726249760300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.17815113924507742 " "
y[1] (numeric) = 0.17815113924507747 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 3.115958251318995400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.513129369261686 " "
Order of pole (six term test) = -11.230728056749648 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000007 " "
y[1] (analytic) = 0.18030816842626884 " "
y[1] (numeric) = 0.18030816842626865 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 1.07753869946746520000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.1824816726547982 " "
y[1] (numeric) = 0.18248167265479828 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 4.563018610882801400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.7621780874459816 " "
Order of pole (three term test) = -445.7193818052369 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000007 " "
y[1] (analytic) = 0.18467169715453857 " "
y[1] (numeric) = 0.18467169715453838 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 1.05207799734907820000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.18687828688503694 " "
y[1] (numeric) = 0.18687828688503702 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 4.455666211137222500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.18910148654079895 " "
y[1] (numeric) = 0.18910148654079892 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.46776083696415600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.5293480900801426 " "
Order of pole (six term test) = -11.215041989056154 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000008 " "
y[1] (analytic) = 0.1913413405505704 " "
y[1] (numeric) = 0.19134134055057034 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.90115826885756300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.19359789307662822 " "
y[1] (numeric) = 0.19359789307662822 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.1786231937363945 " "
Order of pole (six term test) = -11.163722603031179 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000008 " "
y[1] (analytic) = 0.19587118801407355 " "
y[1] (numeric) = 0.19587118801407366 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 5.668128303512336000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.6697880707429085 " "
Order of pole (six term test) = -11.22377194800248 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0000000000000007 " "
y[1] (analytic) = 0.19816126899012965 " "
y[1] (numeric) = 0.19816126899012948 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 8.40393556937044300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.127491411266623 " "
Order of pole (six term test) = -11.15276486781826 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0100000000000007 " "
y[1] (analytic) = 0.2004681793634422 " "
y[1] (numeric) = 0.20046817936344224 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.769075441674857500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.20279196222338858 " "
y[1] (numeric) = 0.20279196222338852 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.73734474594750800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.2051326603893855 " "
y[1] (numeric) = 0.20513266038938546 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.353054923723161200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.2507161368593056 " "
Order of pole (six term test) = -11.074226133001623 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0400000000000007 " "
y[1] (analytic) = 0.20749031641020588 " "
y[1] (numeric) = 0.20749031641020568 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 9.36376370091871200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.000397542574652 " "
Order of pole (six term test) = -11.130361343408843 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0500000000000007 " "
y[1] (analytic) = 0.20986497256329661 " "
y[1] (numeric) = 0.20986497256329648 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 6.6127222843863700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.2745004688341637 " "
Order of pole (six term test) = -11.155719478158808 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0600000000000007 " "
y[1] (analytic) = 0.2122566708541035 " "
y[1] (numeric) = 0.21225667085410338 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 5.23056834990254900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.6972074739035339 " "
Order of pole (six term test) = -11.100132898098385 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0700000000000007 " "
y[1] (analytic) = 0.2146654530153982 " "
y[1] (numeric) = 0.2146654530153981 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 3.878906721004330400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.21709136050661082 " "
y[1] (numeric) = 0.2170913605066108 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.278520506336948700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.21953443451316668 " "
y[1] (numeric) = 0.21953443451316668 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.2219947159458272 " "
y[1] (numeric) = 0.2219947159458271 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 5.00112365240297600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.115850886285423 " "
Order of pole (six term test) = -11.059995529723027 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1100000000000008 " "
y[1] (analytic) = 0.2244722454400352 " "
y[1] (numeric) = 0.22447224544003494 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.1128332594124250000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.140065502161895 " "
Order of pole (six term test) = -11.060386566383936 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1200000000000008 " "
y[1] (analytic) = 0.2269670633552644 " "
y[1] (numeric) = 0.2269670633552645 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.89156007137193900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.4760494113920164 " "
Order of pole (six term test) = -11.058871397627554 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1300000000000008 " "
y[1] (analytic) = 0.22947920977437586 " "
y[1] (numeric) = 0.2294792097743757 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 7.25701704557503500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.6705290504519903 " "
Order of pole (six term test) = -11.041242159466975 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1400000000000008 " "
y[1] (analytic) = 0.23200872450297283 " "
y[1] (numeric) = 0.23200872450297272 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.785264118853990700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.225252479921726 " "
Order of pole (six term test) = -11.064570224640207 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1500000000000008 " "
y[1] (analytic) = 0.2345556470687673 " "
y[1] (numeric) = 0.23455564706876725 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.366651663474254600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.9746534562505386 " "
Order of pole (six term test) = -11.04995465407764 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1600000000000008 " "
y[1] (analytic) = 0.23712001672094607 " "
y[1] (numeric) = 0.23712001672094588 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 8.19370005097675100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.3809357142506544 " "
Order of pole (six term test) = -11.065275167723236 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1700000000000008 " "
y[1] (analytic) = 0.23970187242954233 " "
y[1] (numeric) = 0.2397018724295422 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 5.78960342159766700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.9830776988669019 " "
Order of pole (six term test) = -11.10227866805159 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1800000000000008 " "
y[1] (analytic) = 0.24230125288481352 " "
y[1] (numeric) = 0.2423012528848133 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 9.16398913672097600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.7726563733272795 " "
Order of pole (six term test) = -11.041383133629978 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1900000000000008 " "
y[1] (analytic) = 0.24491819649662094 " "
y[1] (numeric) = 0.2449181964966207 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.01993312099252960000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.806282237069342 " "
Order of pole (six term test) = -11.041765195015142 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2000000000000008 " "
y[1] (analytic) = 0.247552741393816 " "
y[1] (numeric) = 0.24755274139381575 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.00907862758533920000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.5833422038030416 " "
Order of pole (six term test) = -11.072075114448001 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2100000000000009 " "
y[1] (analytic) = 0.2502049254236298 " "
y[1] (numeric) = 0.25020492542362965 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 6.65588230974312100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.073202847033717 " "
Order of pole (six term test) = -11.049533891164177 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2200000000000009 " "
y[1] (analytic) = 0.25287478615106795 " "
y[1] (numeric) = 0.2528747861510678 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 6.5856092743974090000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.0441690043889036 " "
Order of pole (six term test) = -11.047649180922587 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2300000000000009 " "
y[1] (analytic) = 0.2555623608583091 " "
y[1] (numeric) = 0.25556236085830886 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 8.68847056269522600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.975134078454191 " "
Order of pole (six term test) = -11.044466669044118 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2400000000000009 " "
y[1] (analytic) = 0.25826768654410814 " "
y[1] (numeric) = 0.2582676865441082 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.149364946658837100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.8886121881737162 " "
Order of pole (six term test) = -11.062110054222455 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2500000000000009 " "
y[1] (analytic) = 0.26099079992320595 " "
y[1] (numeric) = 0.2609907999232059 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.126939005037398000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.9246261820329059 " "
Order of pole (six term test) = -11.041555177412853 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.260000000000001 " "
y[1] (analytic) = 0.2637317374257394 " "
y[1] (numeric) = 0.2637317374257393 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.20966788245487100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.979155848652091 " "
Order of pole (six term test) = -11.054863978321489 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.270000000000001 " "
y[1] (analytic) = 0.26649053519666044 " "
y[1] (numeric) = 0.2664905351966602 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 8.33217602873476800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.2497613172924018 " "
Order of pole (six term test) = -11.047555535077151 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.280000000000001 " "
y[1] (analytic) = 0.26926722909515666 " "
y[1] (numeric) = 0.26926722909515644 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 8.24625431290648100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.283405579718395 " "
Order of pole (six term test) = -11.048897161164586 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.290000000000001 " "
y[1] (analytic) = 0.2720618546940783 " "
y[1] (numeric) = 0.2720618546940782 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.08077429992364800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.8624851640644079 " "
Order of pole (six term test) = -11.037382596994732 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.300000000000001 " "
y[1] (analytic) = 0.27487444727936905 " "
y[1] (numeric) = 0.2748744472793688 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 8.07803734114855500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.3498585108920307 " "
Order of pole (six term test) = -11.049801970164946 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.310000000000001 " "
y[1] (analytic) = 0.2777050418495004 " "
y[1] (numeric) = 0.27770504184950034 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.998924861484566400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.2572074706922955 " "
Order of pole (six term test) = -11.045260170712636 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.320000000000001 " "
y[1] (analytic) = 0.2805536731149135 " "
y[1] (numeric) = 0.2805536731149133 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 7.91451426957731700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.3662972085645382 " "
Order of pole (six term test) = -11.048435306562915 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.330000000000001 " "
y[1] (analytic) = 0.2834203754974618 " "
y[1] (numeric) = 0.2834203754974616 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 7.83446160267400700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.3321640730393691 " "
Order of pole (six term test) = -11.046241135127588 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.340000000000001 " "
y[1] (analytic) = 0.28630518312986164 " "
y[1] (numeric) = 0.28630518312986153 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 3.877760830203287300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.2338964778083887 " "
Order of pole (six term test) = -11.041919165324686 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.350000000000001 " "
y[1] (analytic) = 0.2892081298551461 " "
y[1] (numeric) = 0.28920812985514593 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 5.75825630410818900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.2260854588076535 " "
Order of pole (six term test) = -11.040837349070811 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.360000000000001 " "
y[1] (analytic) = 0.2921292492261228 " "
y[1] (numeric) = 0.2921292492261225 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 1.14013543070360730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.2849344901925255 " "
Order of pole (six term test) = -11.041890972006806 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.370000000000001 " "
y[1] (analytic) = 0.29506857450483714 " "
y[1] (numeric) = 0.2950685745048368 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 1.12877797287113990000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.1542467749792615 " "
Order of pole (six term test) = -11.031314315272269 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.380000000000001 " "
y[1] (analytic) = 0.29802613866204075 " "
y[1] (numeric) = 0.29802613866204053 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 7.45050772800932500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.30100197437666365 " "
y[1] (numeric) = 0.3010019743766636 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.84421219648855400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.0989994707496906 " "
Order of pole (six term test) = -11.030977712186466 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.400000000000001 " "
y[1] (analytic) = 0.3039961140352919 " "
y[1] (numeric) = 0.30399611403529136 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 1.8260480535225970000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.8374224546123951 " "
Order of pole (six term test) = -11.034012450020013 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.410000000000001 " "
y[1] (analytic) = 0.3070085897316468 " "
y[1] (numeric) = 0.30700858973164646 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 1.08487813868230050000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.1740009378917415 " "
Order of pole (six term test) = -11.034532036512884 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.420000000000001 " "
y[1] (analytic) = 0.31003943326607575 " "
y[1] (numeric) = 0.3100394332660754 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 1.07427272679120490000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.0472432360450297 " "
Order of pole (six term test) = -11.028720920596639 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.430000000000001 " "
y[1] (analytic) = 0.31308867614504 " "
y[1] (numeric) = 0.3130886761450396 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 1.24111182621882460000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.03097958735334 " "
Order of pole (six term test) = -11.028208604541916 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.440000000000001 " "
y[1] (analytic) = 0.31615634958061156 " "
y[1] (numeric) = 0.3161563495806114 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 5.26743979409819900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.0158104321938528 " "
Order of pole (six term test) = -11.027484280847236 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.450000000000001 " "
y[1] (analytic) = 0.31924248448997505 " "
y[1] (numeric) = 0.31924248448997455 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 1.56495574791521540000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.0054284714987702 " "
Order of pole (six term test) = -11.02705578805318 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.460000000000001 " "
y[1] (analytic) = 0.32234711149493 " "
y[1] (numeric) = 0.32234711149492973 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 8.61046202241693300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.9923478474290395 " "
Order of pole (six term test) = -11.026310806277744 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.470000000000001 " "
y[1] (analytic) = 0.32547026092140485 " "
y[1] (numeric) = 0.3254702609214044 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.3644540321221610000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.6521524693608156 " "
Order of pole (six term test) = -11.027906805001994 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.480000000000001 " "
y[1] (analytic) = 0.3286119627989682 " "
y[1] (numeric) = 0.32861196279896776 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.35140913942240980000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.943488316708116 " "
Order of pole (six term test) = -11.02344667212123 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.490000000000001 " "
y[1] (analytic) = 0.33177224686035034 " "
y[1] (numeric) = 0.33177224686035006 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 8.36585214052331400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.2969028814726418 " "
Order of pole (six term test) = -11.007277785563419 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.500000000000001 " "
y[1] (analytic) = 0.33495114254096736 " "
y[1] (numeric) = 0.3349511425409671 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 8.28645497521602700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.905172069742944 " "
Order of pole (six term test) = -11.021812995549126 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5100000000000011 " "
y[1] (analytic) = 0.33814867897844914 " "
y[1] (numeric) = 0.3381486789784491 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.64161963899896400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.5556333519484644 " "
Order of pole (six term test) = -11.022840821508604 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5200000000000011 " "
y[1] (analytic) = 0.34136488501217477 " "
y[1] (numeric) = 0.3413648850121746 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 4.87845882823694900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.9741519587034948 " "
Order of pole (six term test) = -11.015008912627689 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5300000000000011 " "
y[1] (analytic) = 0.3445997891828092 " "
y[1] (numeric) = 0.34459978918280904 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 4.83266266902525500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.4320006499551372 " "
Order of pole (six term test) = -11.019958004909714 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5400000000000011 " "
y[1] (analytic) = 0.34785341973184847 " "
y[1] (numeric) = 0.347853419731848 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.27665615647073380000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.42534843971449854 " "
Order of pole (six term test) = -11.020016906545568 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5500000000000012 " "
y[1] (analytic) = 0.3511258046011658 " "
y[1] (numeric) = 0.35112580460116555 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 7.90473820263814300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.8146907728368054 " "
Order of pole (six term test) = -11.01861500709235 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5600000000000012 " "
y[1] (analytic) = 0.354416971432567 " "
y[1] (numeric) = 0.3544169714325668 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 6.2650669359178390000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.22477718046633197 " "
Order of pole (six term test) = -11.01775163588275 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5700000000000012 " "
y[1] (analytic) = 0.35772694756734613 " "
y[1] (numeric) = 0.357726947567346 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 3.10354876023463300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.20866389154975637 " "
Order of pole (six term test) = -11.01763520970919 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5800000000000012 " "
y[1] (analytic) = 0.3610557600458494 " "
y[1] (numeric) = 0.36105576004584905 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 9.2248052584800700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.12031569532298768 " "
Order of pole (six term test) = -11.01828697490764 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5900000000000012 " "
y[1] (analytic) = 0.3644034356070409 " "
y[1] (numeric) = 0.3644034356070405 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 1.06634027193375020000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.36777000068807675 " "
y[1] (numeric) = 0.36777000068807625 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 1.35845871100578250000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.6680686861438855 " "
Order of pole (six term test) = -11.014557639167764 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6100000000000012 " "
y[1] (analytic) = 0.3711554814238802 " "
y[1] (numeric) = 0.3711554814238801 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.99126129126790430000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.3745599036467261 " "
y[1] (numeric) = 0.3745599036467258 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 7.41018334995279100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.6528052463068843 " "
Order of pole (six term test) = -10.978264409988384 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6300000000000012 " "
y[1] (analytic) = 0.3779832928858242 " "
y[1] (numeric) = 0.37798329288582383 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 1.02802971965266440000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.3814256743669132 " "
y[1] (numeric) = 0.38142567436691266 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 1.45535958803493540000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.6279994166021001 " "
Order of pole (six term test) = -11.008593565276156 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6500000000000012 " "
y[1] (analytic) = 0.38488707301185565 " "
y[1] (numeric) = 0.3848870730118554 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 7.21135563177877000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.3883675134382413 " "
y[1] (numeric) = 0.38836751343824083 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.14347671853012050000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.5717322061989694 " "
Order of pole (six term test) = -10.978683736892027 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6700000000000013 " "
y[1] (analytic) = 0.3918670199589902 " "
y[1] (numeric) = 0.39186701995898976 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.1332650803237730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.39538561658196614 " "
y[1] (numeric) = 0.39538561658196586 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 7.01987488962563000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.34275762440008545 " "
Order of pole (six term test) = -11.00859586841225 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6900000000000013 " "
y[1] (analytic) = 0.398923327009592 " "
y[1] (numeric) = 0.3989233270095916 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 9.74067025690532200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.4024801746384691 " "
y[1] (numeric) = 0.40248017463846886 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 5.51690788557435400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.4060561825590052 " "
y[1] (numeric) = 0.40605618255900483 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 9.56956390049151300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.4096513735550428 " "
y[1] (numeric) = 0.40965137355504244 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 8.13049653653350800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.4132657701034961 " "
y[1] (numeric) = 0.41326577010349574 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 8.05938772292066300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.4168993943739906 " "
y[1] (numeric) = 0.4168993943739904 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 5.32609564613184200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.17306699846763804 " "
Order of pole (six term test) = -11.003332359543752 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7500000000000013 " "
y[1] (analytic) = 0.420552268228509 " "
y[1] (numeric) = 0.4205522682285089 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.639916862894939300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.424224413221041 " "
y[1] (numeric) = 0.4242244132210409 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.617065378664753500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.42791585059723825 " "
y[1] (numeric) = 0.42791585059723813 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.59448913396320400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.43162660129407515 " "
y[1] (numeric) = 0.4316266012940747 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.02887358776920350000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.4353566859395124 " "
y[1] (numeric) = 0.435356685939512 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 8.92551030381541200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.8323016855016375 " "
Order of pole (six term test) = -10.991656982115238 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8000000000000014 " "
y[1] (analytic) = 0.4391061248521687 " "
y[1] (numeric) = 0.4391061248521685 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 5.056741237662895000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.4428749380409953 " "
y[1] (numeric) = 0.442874938040995 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 7.52056345434286300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.4466631452049544 " "
y[1] (numeric) = 0.44666314520495415 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 6.21398382955752400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.7729686167721075 " "
Order of pole (six term test) = -10.99101428984326 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8300000000000014 " "
y[1] (analytic) = 0.45047076573270584 " "
y[1] (numeric) = 0.45047076573270556 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 6.16145990528009900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.4967525919809779 " "
Order of pole (six term test) = -10.97288481559284 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8400000000000014 " "
y[1] (analytic) = 0.4542978187022958 " "
y[1] (numeric) = 0.4542978187022953 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 1.09971992053237590000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.4581443228808513 " "
y[1] (numeric) = 0.45814432288085083 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 9.69321647505290700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.46201029672428107 " "
y[1] (numeric) = 0.4620102967242807 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 8.41059304032569600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.4658957583769796 " "
y[1] (numeric) = 0.4658957583769792 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 8.34045066159170400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.4698007256715365 " "
y[1] (numeric) = 0.46980072567153613 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 8.27112512573003100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.47372521612845175 " "
y[1] (numeric) = 0.4737252161284514 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 7.03080385100790300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 0.8958543183500419 " "
Order of pole (six term test) = -10.986049497833513 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9000000000000015 " "
y[1] (analytic) = 0.47766924695585533 " "
y[1] (numeric) = 0.47766924695585483 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 1.04591276132016080000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.48163283504923093 " "
y[1] (numeric) = 0.48163283504923055 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 8.06793121941292900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.48561599699114766 " "
y[1] (numeric) = 0.485615996991147 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 1.37172955360289920000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.489618749050992 " "
y[1] (numeric) = 0.4896187490509914 " "
absolute error = 6.1062266354383610000000000000000E-16 " "
relative error = 1.24713905406478210000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.0544915673564597 " "
Order of pole (six term test) = -10.982289653859658 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9400000000000015 " "
y[1] (analytic) = 0.4936411071847101 " "
y[1] (numeric) = 0.49364110718470955 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 1.12452448597411330000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.497683087034551 " "
y[1] (numeric) = 0.49768308703455044 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 1.11539155493552140000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.7355753696242318 " "
Order of pole (six term test) = -10.964919186918364 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9600000000000015 " "
y[1] (analytic) = 0.5017447039288166 " "
y[1] (numeric) = 0.501744703928816 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 1.3276349696550050000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.5058259728816166 " "
y[1] (numeric) = 0.5058259728816159 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 1.31692291516828820000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.5099269085926278 " "
y[1] (numeric) = 0.5099269085926273 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 8.70887969171358600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"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) = 0.5140475254468604 " "
y[1] (numeric) = 0.5140475254468598 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 1.07988363883285120000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0000000000000013 " "
y[1] (analytic) = 0.5181878375144253 " "
y[1] (numeric) = 0.5181878375144249 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 8.57004309441554700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.010000000000001 " "
y[1] (analytic) = 0.5223478585503114 " "
y[1] (numeric) = 0.522347858550311 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 8.50179057080003200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.5247301809900002 " "
Order of pole (six term test) = -10.972378774872062 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.020000000000001 " "
y[1] (analytic) = 0.526527601994164 " "
y[1] (numeric) = 0.5265276019941637 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 6.32572549142900700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0300000000000007 " "
y[1] (analytic) = 0.5307270809700706 " "
y[1] (numeric) = 0.5307270809700705 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.091890661761361000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0400000000000005 " "
y[1] (analytic) = 0.5349463082863506 " "
y[1] (numeric) = 0.5349463082863506 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0500000000000003 " "
y[1] (analytic) = 0.5391852964353505 " "
y[1] (numeric) = 0.5391852964353503 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 4.118150223921303600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.06 " "
y[1] (analytic) = 0.5434440575932429 " "
y[1] (numeric) = 0.543444057593243 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.042938935687353700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.053262379092692 " "
Order of pole (six term test) = -10.867838340646022 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.07 " "
y[1] (analytic) = 0.5477226036198342 " "
y[1] (numeric) = 0.5477226036198344 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 4.05396095500833200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0799999999999996 " "
y[1] (analytic) = 0.5520209460583725 " "
y[1] (numeric) = 0.5520209460583726 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.011197278930350300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0899999999999994 " "
y[1] (analytic) = 0.5563390961353631 " "
y[1] (numeric) = 0.5563390961353637 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 9.97793461161884300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.8166072008598493 " "
Order of pole (six term test) = -10.9686964029688 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.099999999999999 " "
y[1] (analytic) = 0.5606770647603914 " "
y[1] (numeric) = 0.5606770647603919 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 9.90073515045257800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.109999999999999 " "
y[1] (analytic) = 0.5650348625259445 " "
y[1] (numeric) = 0.565034862525945 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 9.82437631956009500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.1993785506234795 " "
Order of pole (three term test) = -900.173585610999 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999999988 " "
y[1] (analytic) = 0.5694124997072447 " "
y[1] (numeric) = 0.5694124997072452 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 7.7990772959565300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999999986 " "
y[1] (analytic) = 0.5738099862620836 " "
y[1] (numeric) = 0.5738099862620841 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 9.67413474151415500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999999983 " "
y[1] (analytic) = 0.5782273318306634 " "
y[1] (numeric) = 0.5782273318306642 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 1.34403213832376130000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.39297738655065 " "
Order of pole (six term test) = -10.86747647960592 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.149999999999998 " "
y[1] (analytic) = 0.5826645457354431 " "
y[1] (numeric) = 0.5826645457354439 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 1.33379681829907450000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.8238425098298103 " "
Order of pole (six term test) = -10.973048981501481 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999998 " "
y[1] (analytic) = 0.5871216369809877 " "
y[1] (numeric) = 0.5871216369809886 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.5127673104796280000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.5043271654707098 " "
Order of pole (six term test) = -10.98069970665832 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1699999999999977 " "
y[1] (analytic) = 0.5915986142538261 " "
y[1] (numeric) = 0.591598614253827 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.5013193038330060000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.7137740070385516 " "
Order of pole (six term test) = -10.977235790926333 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1799999999999975 " "
y[1] (analytic) = 0.5960954859223102 " "
y[1] (numeric) = 0.5960954859223113 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.8624919175614310000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 5.183305355471323 " "
Order of pole (six term test) = -10.832895430116182 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1899999999999973 " "
y[1] (analytic) = 0.6006122600364832 " "
y[1] (numeric) = 0.6006122600364844 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 2.03333399656791840000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.2944849628752872 " "
Order of pole (six term test) = -10.986618118111876 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.199999999999997 " "
y[1] (analytic) = 0.6051489443279487 " "
y[1] (numeric) = 0.6051489443279499 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.83462771443503120000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.209999999999997 " "
y[1] (analytic) = 0.6097055462097478 " "
y[1] (numeric) = 0.6097055462097493 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 2.36719173867608270000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 5.868263477946317 " "
Order of pole (six term test) = -10.801082039868684 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999999966 " "
y[1] (analytic) = 0.6142820727762417 " "
y[1] (numeric) = 0.614282072776243 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 2.16882062588774180000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.007111050160732 " "
Order of pole (six term test) = -10.975674311683688 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999999964 " "
y[1] (analytic) = 0.6188785308029956 " "
y[1] (numeric) = 0.6188785308029972 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 2.511498068059490000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.239999999999996 " "
y[1] (analytic) = 0.6234949267466727 " "
y[1] (numeric) = 0.6234949267466745 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.84903174540502400000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999996 " "
y[1] (analytic) = 0.6281312667449301 " "
y[1] (numeric) = 0.6281312667449318 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 2.65125241347679900000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.391659204598538 " "
Order of pole (three term test) = -351.27374309867224 " "
Radius of convergence (six term test) for eq 1 = 9.66470732904689 " "
Order of pole (six term test) = -10.518353902289412 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999996 " "
y[1] (analytic) = 0.6327875566163195 " "
y[1] (numeric) = 0.6327875566163214 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.98264262962924850000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.7131033013573744 " "
Order of pole (six term test) = -10.929570638589302 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2699999999999956 " "
y[1] (analytic) = 0.6374638018601959 " "
y[1] (numeric) = 0.6374638018601978 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.96076284858084000000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2799999999999954 " "
y[1] (analytic) = 0.6421600076566285 " "
y[1] (numeric) = 0.6421600076566304 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.9391103764779647000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999995 " "
y[1] (analytic) = 0.646876178866318 " "
y[1] (numeric) = 0.64687617886632 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 3.08931061246926400000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.299999999999995 " "
y[1] (analytic) = 0.6516123200305188 " "
y[1] (numeric) = 0.651612320030521 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 3.40761827392446540000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999999947 " "
y[1] (analytic) = 0.6563684353709669 " "
y[1] (numeric) = 0.6563684353709693 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 3.72121894130222060000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.0035264299804005 " "
Order of pole (six term test) = -10.963503002245632 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999999945 " "
y[1] (analytic) = 0.6611445287898119 " "
y[1] (numeric) = 0.6611445287898142 " "
absolute error = 2.3314683517128287000000000000000E-15 " "
relative error = 3.52641253188686440000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 21.889113424200325 " "
Order of pole (three term test) = -3207.3812706107246 " "
Radius of convergence (six term test) for eq 1 = 4.55453017364349 " "
Order of pole (six term test) = -10.912061025112655 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999999943 " "
y[1] (analytic) = 0.6659406038695537 " "
y[1] (numeric) = 0.6659406038695562 " "
absolute error = 2.55351295663786000000000000000E-15 " "
relative error = 3.8344455073024040000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.339999999999994 " "
y[1] (analytic) = 0.6707566638729872 " "
y[1] (numeric) = 0.6707566638729898 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.97243203476384030000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.349999999999994 " "
y[1] (analytic) = 0.6755927117431482 " "
y[1] (numeric) = 0.6755927117431509 " "
absolute error = 2.7755575615628914000000000000000E-15 " "
relative error = 4.10832963902387900000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3599999999999937 " "
y[1] (analytic) = 0.6804487501032672 " "
y[1] (numeric) = 0.6804487501032701 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 4.24217086678067960000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3699999999999934 " "
y[1] (analytic) = 0.6853247812567276 " "
y[1] (numeric) = 0.6853247812567306 " "
absolute error = 2.9976021664879227000000000000000E-15 " "
relative error = 4.37398770403575940000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3799999999999932 " "
y[1] (analytic) = 0.6902208071870282 " "
y[1] (numeric) = 0.6902208071870312 " "
absolute error = 2.9976021664879227000000000000000E-15 " "
relative error = 4.34296117311292030000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999993 " "
y[1] (analytic) = 0.6951368295577516 " "
y[1] (numeric) = 0.6951368295577548 " "
absolute error = 3.219646771412954000000000000000E-15 " "
relative error = 4.6316734123572540000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.399999999999993 " "
y[1] (analytic) = 0.7000728497125386 " "
y[1] (numeric) = 0.7000728497125418 " "
absolute error = 3.219646771412954000000000000000E-15 " "
relative error = 4.5990167633768320000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999999926 " "
y[1] (analytic) = 0.705028868675065 " "
y[1] (numeric) = 0.7050288686750683 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 4.7241598491345110000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999999924 " "
y[1] (analytic) = 0.7100048871490265 " "
y[1] (numeric) = 0.71000488714903 " "
absolute error = 3.4416913763379850000000000000000E-15 " "
relative error = 4.8474192764473056000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.429999999999992 " "
y[1] (analytic) = 0.7150009055181272 " "
y[1] (numeric) = 0.7150009055181307 " "
absolute error = 3.4416913763379850000000000000000E-15 " "
relative error = 4.8135482763395310000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.439999999999992 " "
y[1] (analytic) = 0.720016923846073 " "
y[1] (numeric) = 0.7200169238460765 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.9342085736307070000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4499999999999917 " "
y[1] (analytic) = 0.7250529418765705 " "
y[1] (numeric) = 0.7250529418765745 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 5.5124290349144730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.26591160121256835 " "
Order of pole (three term test) = -53.65808962260314 " "
Radius of convergence (six term test) for eq 1 = 13.11279496542769 " "
Order of pole (six term test) = -10.447112981626788 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4599999999999915 " "
y[1] (analytic) = 0.7301089590333332 " "
y[1] (numeric) = 0.730108959033337 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 5.1701300703436450000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4699999999999913 " "
y[1] (analytic) = 0.7351849744200867 " "
y[1] (numeric) = 0.7351849744200906 " "
absolute error = 3.885780586188048000000000000000E-15 " "
relative error = 5.2854461412968190000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.15996278824960833 " "
Order of pole (three term test) = -40.13830100486610 " "
Radius of convergence (six term test) for eq 1 = 15.192579840034258 " "
Order of pole (six term test) = -10.277599927149039 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999991 " "
y[1] (analytic) = 0.7402809868205866 " "
y[1] (numeric) = 0.7402809868205907 " "
absolute error = 4.107825191113079000000000000000E-15 " "
relative error = 5.5490080986081650000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999991 " "
y[1] (analytic) = 0.7453969946986367 " "
y[1] (numeric) = 0.7453969946986411 " "
absolute error = 4.3298697960381105000000000000000E-15 " "
relative error = 5.8088103746496490000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4999999999999907 " "
y[1] (analytic) = 0.7505329961981138 " "
y[1] (numeric) = 0.7505329961981181 " "
absolute error = 4.3298697960381105000000000000000E-15 " "
relative error = 5.7690598787414020000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999999905 " "
y[1] (analytic) = 0.7556889891429961 " "
y[1] (numeric) = 0.7556889891430006 " "
absolute error = 4.551914400963142000000000000000E-15 " "
relative error = 6.0235288145793010000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999999902 " "
y[1] (analytic) = 0.7608649710374005 " "
y[1] (numeric) = 0.7608649710374049 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 5.8366362857337180000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.961335711054927 " "
Order of pole (three term test) = -151.53988332518188 " "
Radius of convergence (six term test) for eq 1 = 6.675221596637786 " "
Order of pole (six term test) = -10.910107507432853 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.52999999999999 " "
y[1] (analytic) = 0.7660609390656199 " "
y[1] (numeric) = 0.7660609390656244 " "
absolute error = 4.551914400963142000000000000000E-15 " "
relative error = 5.9419742853815320000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 37.36771265831955 " "
Order of pole (six term test) = -8.109150052716101 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.53999999999999 " "
y[1] (analytic) = 0.7712768900921703 " "
y[1] (numeric) = 0.7712768900921749 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 6.0457363150974490000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5499999999999896 " "
y[1] (analytic) = 0.7765128206618395 " "
y[1] (numeric) = 0.7765128206618445 " "
absolute error = 4.9960036108132044000000000000000E-15 " "
relative error = 6.4338971332823550000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5599999999999894 " "
y[1] (analytic) = 0.7817687269997438 " "
y[1] (numeric) = 0.7817687269997491 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.8166841856830860000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999989 " "
y[1] (analytic) = 0.7870446050113875 " "
y[1] (numeric) = 0.7870446050113927 " "
absolute error = 5.218048215738236000000000000000E-15 " "
relative error = 6.6299269222012360000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999989 " "
y[1] (analytic) = 0.792340450282728 " "
y[1] (numeric) = 0.7923404502827331 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 6.4454943723413320000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1711161609510222 " "
Order of pole (three term test) = -43.231151112881065 " "
Radius of convergence (six term test) for eq 1 = 11.056512369597582 " "
Order of pole (six term test) = -10.737721699873969 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5899999999999888 " "
y[1] (analytic) = 0.7976562580802471 " "
y[1] (numeric) = 0.7976562580802523 " "
absolute error = 5.218048215738236000000000000000E-15 " "
relative error = 6.5417254147754470000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5999999999999885 " "
y[1] (analytic) = 0.8029920233510268 " "
y[1] (numeric) = 0.8029920233510323 " "
absolute error = 5.440092820663267000000000000000E-15 " "
relative error = 6.7747781577714850000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 20.06056237975701 " "
Order of pole (six term test) = -10.550675485257173 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999999883 " "
y[1] (analytic) = 0.8083477407228301 " "
y[1] (numeric) = 0.8083477407228358 " "
absolute error = 5.662137425588298000000000000000E-15 " "
relative error = 7.0045812468346560000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.619999999999988 " "
y[1] (analytic) = 0.8137234045041868 " "
y[1] (numeric) = 0.8137234045041924 " "
absolute error = 5.662137425588298000000000000000E-15 " "
relative error = 6.9583072014971960000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3530518620313056 " "
Order of pole (three term test) = -67.42795600717768 " "
Radius of convergence (six term test) for eq 1 = 8.264902168115336 " "
Order of pole (six term test) = -10.90632253412107 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.629999999999988 " "
y[1] (analytic) = 0.8191190086844842 " "
y[1] (numeric) = 0.8191190086844898 " "
absolute error = 5.662137425588298000000000000000E-15 " "
relative error = 6.912472260510429000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999999877 " "
y[1] (analytic) = 0.8245345469340635 " "
y[1] (numeric) = 0.8245345469340695 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 7.2710165453567970000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.852368938696343 " "
Order of pole (three term test) = -272.10391340192024 " "
Radius of convergence (six term test) for eq 1 = 4.38386593814535 " "
Order of pole (six term test) = -11.01724539649919 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6499999999999875 " "
y[1] (analytic) = 0.8299700126043221 " "
y[1] (numeric) = 0.8299700126043282 " "
absolute error = 6.106226635438361000000000000000E-15 " "
relative error = 7.3571653706836130000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.5366757797007966 " "
Order of pole (three term test) = -92.16563110396804 " "
Radius of convergence (six term test) for eq 1 = 6.8869435382470305 " "
Order of pole (six term test) = -10.96772640894236 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6599999999999873 " "
y[1] (analytic) = 0.8354253987278186 " "
y[1] (numeric) = 0.8354253987278247 " "
absolute error = 6.106226635438361000000000000000E-15 " "
relative error = 7.3091225676606080000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999987 " "
y[1] (analytic) = 0.8409006980183844 " "
y[1] (numeric) = 0.8409006980183907 " "
absolute error = 6.328271240363392000000000000000E-15 " "
relative error = 7.5255868561843420000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.679999999999987 " "
y[1] (analytic) = 0.8463959028712413 " "
y[1] (numeric) = 0.8463959028712477 " "
absolute error = 6.328271240363392000000000000000E-15 " "
relative error = 7.4767271662066230000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6899999999999866 " "
y[1] (analytic) = 0.8519110053631218 " "
y[1] (numeric) = 0.8519110053631284 " "
absolute error = 6.5503158452884240000000000000000E-15 " "
relative error = 7.6889672795063750000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.35911091768108055 " "
Order of pole (three term test) = -68.29779817284481 " "
Radius of convergence (six term test) for eq 1 = 7.485283078283195 " "
Order of pole (six term test) = -10.970946079134798 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999999864 " "
y[1] (analytic) = 0.8574459972523973 " "
y[1] (numeric) = 0.8574459972524041 " "
absolute error = 6.772360450213455000000000000000E-15 " "
relative error = 7.8982938539742760000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.709999999999986 " "
y[1] (analytic) = 0.8630008699792093 " "
y[1] (numeric) = 0.863000869979216 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 7.718808148955190000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 13.090104973133776 " "
Order of pole (six term test) = -10.690334582394502 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.719999999999986 " "
y[1] (analytic) = 0.8685756146656054 " "
y[1] (numeric) = 0.8685756146656122 " "
absolute error = 6.772360450213455000000000000000E-15 " "
relative error = 7.7970879401452680000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3434155353548978 " "
Order of pole (three term test) = -66.20156324421974 " "
Radius of convergence (six term test) for eq 1 = 7.322234905956942 " "
Order of pole (six term test) = -10.99020748168093 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999999858 " "
y[1] (analytic) = 0.8741702221156831 " "
y[1] (numeric) = 0.8741702221156901 " "
absolute error = 6.994405055138486000000000000000E-15 " "
relative error = 8.0011934497270990000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.53651575592232870E-2 " "
Order of pole (three term test) = -28.318007526631003 " "
Radius of convergence (six term test) for eq 1 = 11.04412454148616 " "
Order of pole (six term test) = -10.843203340967449 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999999856 " "
y[1] (analytic) = 0.8797846828157361 " "
y[1] (numeric) = 0.8797846828157431 " "
absolute error = 6.994405055138486000000000000000E-15 " "
relative error = 7.9501327901652150000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 31.08953716325002 " "
Order of pole (six term test) = -10.743341581515034 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7499999999999853 " "
y[1] (analytic) = 0.885418986934406 " "
y[1] (numeric) = 0.8854189869344131 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 8.024932221300320000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 6.625305213415886 " "
Order of pole (six term test) = -11.292290648297097 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999985 " "
y[1] (analytic) = 0.8910731243228405 " "
y[1] (numeric) = 0.8910731243228478 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 8.2231993789448550000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 15.517195764530006 " "
Order of pole (six term test) = -11.099951343559578 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.769999999999985 " "
y[1] (analytic) = 0.8967470845148555 " "
y[1] (numeric) = 0.896747084514863 " "
absolute error = 7.438494264988549000000000000000E-15 " "
relative error = 8.2949745735864980000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 11.192667812120128 " "
Order of pole (six term test) = -11.178060349810531 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7799999999999847 " "
y[1] (analytic) = 0.9024408567271023 " "
y[1] (numeric) = 0.9024408567271098 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 8.3656635348171460000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 8.57290577020069 " "
Order of pole (six term test) = -11.245237095531838 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7899999999999845 " "
y[1] (analytic) = 0.9081544298592399 " "
y[1] (numeric) = 0.9081544298592478 " "
absolute error = 7.882583474838611000000000000000E-15 " "
relative error = 8.6797831025945440000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 27.317362240931843 " "
Order of pole (six term test) = -11.079903107215268 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999999843 " "
y[1] (analytic) = 0.913887792494114 " "
y[1] (numeric) = 0.913887792494122 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 8.7468131678240040000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 18.27180874427844 " "
Order of pole (six term test) = -11.149471582667076 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.809999999999984 " "
y[1] (analytic) = 0.919640932897938 " "
y[1] (numeric) = 0.9196409328979459 " "
absolute error = 7.882583474838611000000000000000E-15 " "
relative error = 8.5713708392680070000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3401268777181713 " "
Order of pole (three term test) = -65.56988840985923 " "
Radius of convergence (six term test) for eq 1 = 6.674597673213837 " "
Order of pole (six term test) = -11.044174013853201 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.819999999999984 " "
y[1] (analytic) = 0.9254138390204811 " "
y[1] (numeric) = 0.9254138390204891 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 8.6378714476131950000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 10.947175094458501 " "
Order of pole (six term test) = -11.216756036133209 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999999836 " "
y[1] (analytic) = 0.9312064984952619 " "
y[1] (numeric) = 0.9312064984952702 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 8.8225870368192670000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.11884571230940368 " "
Order of pole (three term test) = -37.846714152130566 " "
Radius of convergence (six term test) for eq 1 = 8.322524733845778 " "
Order of pole (six term test) = -11.015454096126636 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999999834 " "
y[1] (analytic) = 0.9370188986397459 " "
y[1] (numeric) = 0.9370188986397544 " "
absolute error = 8.548717289613705000000000000000E-15 " "
relative error = 9.1233136300919130000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.79749565900586300E-2 " "
Order of pole (three term test) = -0.6157782192890909 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.849999999999983 " "
y[1] (analytic) = 0.9428510264555481 " "
y[1] (numeric) = 0.9428510264555569 " "
absolute error = 8.770761894538737000000000000000E-15 " "
relative error = 9.3023835669040820000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 10.059206471449293 " "
Order of pole (six term test) = -11.245426761285618 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0);"
Iterations = 276
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 51 Seconds
"Expected Time Remaining "= 0 Years 0 Days 0 Hours 2 Minutes 19 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 2 Minutes 11 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 5 Minutes 13 Seconds
"Time to Timeout " Unknown
Percent Done = 56.530612244897604 "%"
(%o58) true
(%o58) diffeq.max