(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) display_poles() := block([rad_given],
if glob_type_given_pole = 4 then (rad_given :
sqrt(expt(array_given_rad_poles , 2.0)
1, 2
+ expt(array_x - array_given_rad_poles , 2.0)),
1 1, 1
omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " "), omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles , 4, " ")) elseif glob_type_given_pole = 3
1, 1
then omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"),
if array_poles # glob_large_float then (omniout_float(ALWAYS,
1, 1
"Radius of convergence (ratio test) for eq 1 ", 4, array_poles , 4,
1, 1
" "), omniout_str(ALWAYS,
"Order of pole (ratio test) Not computed"))
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"),
if (array_real_poles > 0.0) and (array_real_poles # glob_large_float)
1, 1 1, 1
then (omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4, array_real_poles ,
1, 1
4, " "), omniout_float(ALWAYS,
"Order of pole (three term test) ", 4, array_real_poles ,
1, 2
4, " ")) else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1"),
if (array_complex_poles > 0.0) and (array_complex_poles #
1, 1 1, 1
glob_large_float)
then (omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_complex_poles , 4, " "), omniout_float(ALWAYS,
1, 1
"Order of pole (six term test) ", 4,
array_complex_poles , 4, " ")) else omniout_str(ALWAYS,
1, 2
"NO COMPLEX POLE (six term test) for Equation 1"))
(%o3) display_poles() := block([rad_given],
if glob_type_given_pole = 4 then (rad_given :
sqrt(expt(array_given_rad_poles , 2.0)
1, 2
+ expt(array_x - array_given_rad_poles , 2.0)),
1 1, 1
omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " "), omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles , 4, " ")) elseif glob_type_given_pole = 3
1, 1
then omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"),
if array_poles # glob_large_float then (omniout_float(ALWAYS,
1, 1
"Radius of convergence (ratio test) for eq 1 ", 4, array_poles , 4,
1, 1
" "), omniout_str(ALWAYS,
"Order of pole (ratio test) Not computed"))
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"),
if (array_real_poles > 0.0) and (array_real_poles # glob_large_float)
1, 1 1, 1
then (omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4, array_real_poles ,
1, 1
4, " "), omniout_float(ALWAYS,
"Order of pole (three term test) ", 4, array_real_poles ,
1, 2
4, " ")) else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1"),
if (array_complex_poles > 0.0) and (array_complex_poles #
1, 1 1, 1
glob_large_float)
then (omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_complex_poles , 4, " "), omniout_float(ALWAYS,
1, 1
"Order of pole (six term test) ", 4,
array_complex_poles , 4, " ")) else omniout_str(ALWAYS,
1, 2
"NO COMPLEX POLE (six term test) for Equation 1"))
(%i4) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o4) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i5) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o5) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i6) test_suggested_h() := block([max_estimated_step_error, hn_div_ho,
hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp], max_estimated_step_error : 0.0,
no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25,
hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32,
""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
est_tmp : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if est_tmp >= max_estimated_step_error then max_estimated_step_error :
est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, ""), max_estimated_step_error)
(%o6) test_suggested_h() := block([max_estimated_step_error, hn_div_ho,
hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp], max_estimated_step_error : 0.0,
no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25,
hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32,
""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
est_tmp : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if est_tmp >= max_estimated_step_error then max_estimated_step_error :
est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, ""), max_estimated_step_error)
(%i7) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o7) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i8) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 3 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o8) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 3 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i9) adjust_for_pole(h_param) := (block([hnew, sz2, tmp], hnew : h_param,
glob_normmax : glob_small_float, if omniabs(array_y_higher ) >
1, 1
glob_small_float then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o9) adjust_for_pole(h_param) := (block([hnew, sz2, tmp], hnew : h_param,
glob_normmax : glob_small_float, if omniabs(array_y_higher ) >
1, 1
glob_small_float then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i10) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o10) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i11) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio,
term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad],
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
tmp_rad : glob_large_float, prev_tmp_rad : glob_large_float,
tmp_ratio : glob_large_float, rad_c : glob_large_float,
array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found_sing : 1, n : - 10 - 1 + glob_max_terms, cnt : 0,
while (cnt < 5) and (found_sing = 1) do (if (omniabs(array_y_higher ) =
1, n
0.0) or (omniabs(array_y_higher ) = 0.0) then found_sing : 0
1, 1 + n
array_y_higher glob_h
1, n tmp_rad
else (tmp_rad : omniabs(-------------------------), tmp_ratio : ------------,
array_y_higher prev_tmp_rad
1, 1 + n
if (cnt > 0) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)
then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt = 0
then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt > 0
then found_sing : 0), prev_tmp_rad : tmp_rad, cnt : 1 + cnt, n : 1 + n),
if found_sing = 1 then (if rad_c < array_pole
1
then (array_pole : rad_c, array_poles : rad_c)), n : glob_max_terms,
1 1, 1
m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) = 0.0)
1, m
or (omniabs(array_y_higher ) = 0.0)
1, m - 1
or (omniabs(array_y_higher ) = 0.0)) do m : m - 1,
1, m - 2
array_y_higher array_y_higher
1, m 1, m - 1
if m > 10 then (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1,
glob_h
if omniabs(hdrc) > 0.0 then (rcs : ------,
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
ord_no : -----------------------------------------------------,
hdrc
array_real_poles : rcs, array_real_poles : ord_no)
1, 1 1, 2
else (array_real_poles : glob_large_float,
1, 1
array_real_poles : glob_large_float))
1, 2
else (array_real_poles : glob_large_float,
1, 1
array_real_poles : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) #
1, n
0.0 then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) = 0.0)
rm4 rm3 rm2
or (omniabs(dr1) = 0.0) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) # 0.0
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) # 0.0 then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h)
else rad_c : glob_large_float) else (rad_c : glob_large_float,
ord_no : glob_large_float)) else (rad_c : glob_large_float,
ord_no : glob_large_float)), array_complex_poles : rad_c,
1, 1
array_complex_poles : ord_no), if array_pole glob_ratio_of_radius <
1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_poles())
(%o11) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio,
term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad],
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
tmp_rad : glob_large_float, prev_tmp_rad : glob_large_float,
tmp_ratio : glob_large_float, rad_c : glob_large_float,
array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found_sing : 1, n : - 10 - 1 + glob_max_terms, cnt : 0,
while (cnt < 5) and (found_sing = 1) do (if (omniabs(array_y_higher ) =
1, n
0.0) or (omniabs(array_y_higher ) = 0.0) then found_sing : 0
1, 1 + n
array_y_higher glob_h
1, n tmp_rad
else (tmp_rad : omniabs(-------------------------), tmp_ratio : ------------,
array_y_higher prev_tmp_rad
1, 1 + n
if (cnt > 0) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)
then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt = 0
then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt > 0
then found_sing : 0), prev_tmp_rad : tmp_rad, cnt : 1 + cnt, n : 1 + n),
if found_sing = 1 then (if rad_c < array_pole
1
then (array_pole : rad_c, array_poles : rad_c)), n : glob_max_terms,
1 1, 1
m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) = 0.0)
1, m
or (omniabs(array_y_higher ) = 0.0)
1, m - 1
or (omniabs(array_y_higher ) = 0.0)) do m : m - 1,
1, m - 2
array_y_higher array_y_higher
1, m 1, m - 1
if m > 10 then (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1,
glob_h
if omniabs(hdrc) > 0.0 then (rcs : ------,
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
ord_no : -----------------------------------------------------,
hdrc
array_real_poles : rcs, array_real_poles : ord_no)
1, 1 1, 2
else (array_real_poles : glob_large_float,
1, 1
array_real_poles : glob_large_float))
1, 2
else (array_real_poles : glob_large_float,
1, 1
array_real_poles : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) #
1, n
0.0 then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) = 0.0)
rm4 rm3 rm2
or (omniabs(dr1) = 0.0) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) # 0.0
dr1 dr2 - ds2 dr1 + ds1 dr2
then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) # 0.0 then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h)
else rad_c : glob_large_float) else (rad_c : glob_large_float,
ord_no : glob_large_float)) else (rad_c : glob_large_float,
ord_no : glob_large_float)), array_complex_poles : rad_c,
1, 1
array_complex_poles : ord_no), if array_pole glob_ratio_of_radius <
1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_poles())
(%i12) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o12) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i13) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_2D0 array_x ,
1 1 1
array_tmp2 : array_const_3D0 + array_tmp1 , array_tmp3 : sqrt(array_tmp2 ),
1 1 1 1 1
array_tmp4_a1 : sinh(array_tmp3 ), array_tmp4_a2 : cosh(array_tmp3 ),
1 1 1 1
array_tmp4_a1
1
array_tmp4 : --------------, array_tmp5 : array_tmp4 + array_const_0D0 ,
1 array_tmp4_a2 1 1 1
1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_2D0 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp2
2
-----------
array_tmp3
1
array_tmp3 : -----------, array_tmp4_a1 :
2 2.0 2
att(1, array_tmp4_a2, array_tmp3, 1), array_tmp4_a2 :
2
att(1, array_tmp4_a1, array_tmp3, 1), array_tmp4 :
2
array_tmp4_a1 - ats(2, array_tmp4_a2, array_tmp4, 2)
2
-----------------------------------------------------,
array_tmp4_a2
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, array_tmp3 : 0.0,
2, 2 3
- ats(3, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : -----------------------------------,
3 2.0
array_tmp4_a1 : att(2, array_tmp4_a2, array_tmp3, 1),
3
array_tmp4_a2 : att(2, array_tmp4_a1, array_tmp3, 1),
3
array_tmp4_a1 - ats(3, array_tmp4_a2, array_tmp4, 2)
3
array_tmp4 : -----------------------------------------------------,
3 array_tmp4_a2
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4, array_tmp3 : 0.0,
2, 3 4
- ats(4, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : -----------------------------------,
4 2.0
array_tmp4_a1 : att(3, array_tmp4_a2, array_tmp3, 1),
4
array_tmp4_a2 : att(3, array_tmp4_a1, array_tmp3, 1),
4
array_tmp4_a1 - ats(4, array_tmp4_a2, array_tmp4, 2)
4
array_tmp4 : -----------------------------------------------------,
4 array_tmp4_a2
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5, array_tmp3 : 0.0,
2, 4 5
- ats(5, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : -----------------------------------,
5 2.0
array_tmp4_a1 : att(4, array_tmp4_a2, array_tmp3, 1),
5
array_tmp4_a2 : att(4, array_tmp4_a1, array_tmp3, 1),
5
array_tmp4_a1 - ats(5, array_tmp4_a2, array_tmp4, 2)
5
array_tmp4 : -----------------------------------------------------,
5 array_tmp4_a2
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp3 : 0.0,
kkk
- ats(kkk, array_tmp3, array_tmp3, 2)
-------------------------------------
array_tmp3
1
array_tmp3 : -------------------------------------,
kkk 2.0
array_tmp4_a1 : att(kkk - 1, array_tmp4_a2, array_tmp3, 1),
kkk
array_tmp4_a2 : att(kkk - 1, array_tmp4_a1, array_tmp3, 1),
kkk
array_tmp4_a1 - ats(kkk, array_tmp4_a2, array_tmp4, 2)
kkk
array_tmp4 : ---------------------------------------------------------,
kkk array_tmp4_a2
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_2D0 array_x ,
1 1 1
array_tmp2 : array_const_3D0 + array_tmp1 , array_tmp3 : sqrt(array_tmp2 ),
1 1 1 1 1
array_tmp4_a1 : sinh(array_tmp3 ), array_tmp4_a2 : cosh(array_tmp3 ),
1 1 1 1
array_tmp4_a1
1
array_tmp4 : --------------, array_tmp5 : array_tmp4 + array_const_0D0 ,
1 array_tmp4_a2 1 1 1
1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_2D0 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp2
2
-----------
array_tmp3
1
array_tmp3 : -----------, array_tmp4_a1 :
2 2.0 2
att(1, array_tmp4_a2, array_tmp3, 1), array_tmp4_a2 :
2
att(1, array_tmp4_a1, array_tmp3, 1), array_tmp4 :
2
array_tmp4_a1 - ats(2, array_tmp4_a2, array_tmp4, 2)
2
-----------------------------------------------------,
array_tmp4_a2
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, array_tmp3 : 0.0,
2, 2 3
- ats(3, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : -----------------------------------,
3 2.0
array_tmp4_a1 : att(2, array_tmp4_a2, array_tmp3, 1),
3
array_tmp4_a2 : att(2, array_tmp4_a1, array_tmp3, 1),
3
array_tmp4_a1 - ats(3, array_tmp4_a2, array_tmp4, 2)
3
array_tmp4 : -----------------------------------------------------,
3 array_tmp4_a2
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4, array_tmp3 : 0.0,
2, 3 4
- ats(4, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : -----------------------------------,
4 2.0
array_tmp4_a1 : att(3, array_tmp4_a2, array_tmp3, 1),
4
array_tmp4_a2 : att(3, array_tmp4_a1, array_tmp3, 1),
4
array_tmp4_a1 - ats(4, array_tmp4_a2, array_tmp4, 2)
4
array_tmp4 : -----------------------------------------------------,
4 array_tmp4_a2
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5, array_tmp3 : 0.0,
2, 4 5
- ats(5, array_tmp3, array_tmp3, 2)
-----------------------------------
array_tmp3
1
array_tmp3 : -----------------------------------,
5 2.0
array_tmp4_a1 : att(4, array_tmp4_a2, array_tmp3, 1),
5
array_tmp4_a2 : att(4, array_tmp4_a1, array_tmp3, 1),
5
array_tmp4_a1 - ats(5, array_tmp4_a2, array_tmp4, 2)
5
array_tmp4 : -----------------------------------------------------,
5 array_tmp4_a2
1
array_tmp5 : array_tmp4 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp5 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp3 : 0.0,
kkk
- ats(kkk, array_tmp3, array_tmp3, 2)
-------------------------------------
array_tmp3
1
array_tmp3 : -------------------------------------,
kkk 2.0
array_tmp4_a1 : att(kkk - 1, array_tmp4_a2, array_tmp3, 1),
kkk
array_tmp4_a2 : att(kkk - 1, array_tmp4_a1, array_tmp3, 1),
kkk
array_tmp4_a1 - ats(kkk, array_tmp4_a2, array_tmp4, 2)
kkk
array_tmp4 : ---------------------------------------------------------,
kkk array_tmp4_a2
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(0.0)
(%o56) exact_soln_y(x) := block(0.0)
(%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/tanh_sqrtpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end: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, " (0.0) "), 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, 1 + max_terms), array(array_tmp4_g, 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 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4_g : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp4_a1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4_a2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
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, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_g : 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_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term),
term
array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 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 ) = tanh(sqrt(2.0*x + 3.0));"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-05-26T05:29:32-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "tanh_sqrt"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 189 | "), logitem_str(html_log_file, "tanh_sqrt diffeq.max"),
logitem_str(html_log_file,
"tanh_sqrt 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/tanh_sqrtpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end: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, " (0.0) "), 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, 1 + max_terms), array(array_tmp4_g, 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 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4_g : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp4_a1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4_a2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
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, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4_g : 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_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term),
term
array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1,
iiif, jjjf
x_end : 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 ) = tanh(sqrt(2.0*x + 3.0));"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-05-26T05:29:32-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "tanh_sqrt"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 189 | "), logitem_str(html_log_file, "tanh_sqrt diffeq.max"),
logitem_str(html_log_file,
"tanh_sqrt 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/tanh_sqrtpostode.ode#################"
"diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.1,"
"x_end: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("
" (0.0) "
"));"
"/* 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 = 1.3441454810443632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-165 ""
estimated_step_error = 1.3441454810443632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-165 ""
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 = 9.02040507999708300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-158 ""
estimated_step_error = 9.02040507999708300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-158 ""
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 = 6.053487957029646000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-150 ""
estimated_step_error = 6.053487957029646000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-150 ""
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 = 4.0624224096248670000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-142 ""
estimated_step_error = 4.0624224096248670000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-142 ""
best_h = 1.600000E-5 ""
opt_iter = 5
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.726239368448898000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-134 ""
estimated_step_error = 2.726239368448898000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-134 ""
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 = 1.829540000275164000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-126 ""
estimated_step_error = 1.829540000275164000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-126 ""
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 = 1.22777241120805220000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-118 ""
estimated_step_error = 1.22777241120805220000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-118 ""
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 = 8.239292207073277000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-111 ""
estimated_step_error = 8.239292207073277000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-111 ""
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 = 5.5290954690868370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 ""
estimated_step_error = 5.5290954690868370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 ""
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 = 3.71024484285542500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-95 ""
estimated_step_error = 3.71024484285542500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-95 ""
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 = 2.48954311658748000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-87 ""
estimated_step_error = 2.48954311658748000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-87 ""
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 = 1.67022106527925370000000000000000000000000000000000000000000000000000000000000000000000000000000E-79 ""
estimated_step_error = 1.67022106527925370000000000000000000000000000000000000000000000000000000000000000000000000000000E-79 ""
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 = 1.120218624562506600000000000000000000000000000000000000000000000000000000000000000000000E-71 ""
estimated_step_error = 1.120218624562506600000000000000000000000000000000000000000000000000000000000000000000000E-71 ""
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 = 7.5089810409001810000000000000000000000000000000000000000000000000000000000000000E-64 ""
estimated_step_error = 7.5089810409001810000000000000000000000000000000000000000000000000000000000000000E-64 ""
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 = 5.02758400512650400000000000000000000000000000000000000000000000000000000E-56 ""
estimated_step_error = 5.02758400512650400000000000000000000000000000000000000000000000000000000E-56 ""
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 = 3.358484059516463000000000000000000000000000000000000000000000000E-48 ""
estimated_step_error = 3.358484059516463000000000000000000000000000000000000000000000000E-48 ""
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 = 2.2333699855337730000000000000000000000000000000000000000E-40 ""
estimated_step_error = 2.2333699855337730000000000000000000000000000000000000000E-40 ""
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 = 1.472102229063346800000000000000000000000000000000E-32 ""
estimated_step_error = 1.472102229063346800000000000000000000000000000000E-32 ""
best_h = 0.1 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.0 " "
absolute error = 0.0 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.8057775114257972 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.2023205874288867 " "
Order of pole (six term test) = -0.43720317701807154 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.459338100498595000E-3 " "
absolute error = 9.459338100498595000E-3 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.817167850213272 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.216145260140069 " "
Order of pole (six term test) = -0.43261239053090783 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.89245085051277680E-2 " "
absolute error = 1.89245085051277680E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.8285600650347325 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.2304504839294976 " "
Order of pole (six term test) = -0.42734094309696147 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 2.839543226315865000E-2 " "
absolute error = 2.839543226315865000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.8399541616690624 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.2453498775470564 " "
Order of pole (six term test) = -0.42122726165676916 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 3.787203174874867500E-2 " "
absolute error = 3.787203174874867500E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.8513501454683716 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.2609956985302615 " "
Order of pole (six term test) = -0.4140540541454456 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000002 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 4.73542306338307300E-2 " "
absolute error = 4.73542306338307300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.8627480213494365 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.2775967979221883 " "
Order of pole (six term test) = -0.40552204054507257 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000003 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 5.684195386166700E-2 " "
absolute error = 5.684195386166700E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.8741477937854174 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.2954476346826342 " "
Order of pole (six term test) = -0.3952072477193358 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000004 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 6.63351276210484200E-2 " "
absolute error = 6.63351276210484200E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.885549466797848 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.314977155544129 " "
Order of pole (six term test) = -0.38248855018410666 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000005 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 7.58336793211210000E-2 " "
absolute error = 7.58336793211210000E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.8969530439489144 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.3368355730495467 " "
Order of pole (six term test) = -0.3664179349497889 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000006 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 8.53375375668212300E-2 " "
absolute error = 8.53375375668212300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.908358528334024 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.362058179964606 " "
Order of pole (six term test) = -0.3454730102379244 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20000000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 9.48466321349032300E-2 " "
absolute error = 9.48466321349032300E-2 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.9197659225746868 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.3924003030356626 " "
Order of pole (six term test) = -0.31704427258245005 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21000000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.10436089395054057 " "
absolute error = 0.10436089395054057 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.931175228811665 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.431095862098028 " "
Order of pole (six term test) = -0.27625388888520597 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22000000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.11388025506448704 " "
absolute error = 0.11388025506448704 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.9425864486984739 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.4848327896087143 " "
Order of pole (six term test) = -0.21280681161526083 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2300000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1234046486307802 " "
absolute error = 0.1234046486307802 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.9539995833951533 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.570062963576357 " "
Order of pole (six term test) = -0.10058002896201401 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2400000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.13293400888497278 " "
absolute error = 0.13293400888497278 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.9654146335623888 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.741254917819038 " "
Order of pole (six term test) = 0.1517866089029507 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.14246827112287727 " "
absolute error = 0.14246827112287727 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.976831599355922 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.3595167914873914 " "
Order of pole (six term test) = 1.2429673608182021 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.15200737167980924 " "
absolute error = 0.15200737167980924 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.9882504804213108 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.1615512479103159 " "
absolute error = 0.1615512479103159 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 1.9996712758889883 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.6889692029235586 " "
Order of pole (six term test) = -1.256960071643661 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.17109983816837643 " "
absolute error = 0.17109983816837643 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.0110939843696682 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 1.9929176489833247 " "
Order of pole (six term test) = -0.9433383288789816 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.18065308178806133 " "
absolute error = 0.18065308178806133 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.0225186039500582 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.1121496131762734 " "
Order of pole (six term test) = -0.8142915020371166 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.19021091906463797 " "
absolute error = 0.19021091906463797 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.0339451321889355 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.1795873193360054 " "
Order of pole (six term test) = -0.7439225163866148 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.19977329123611062 " "
absolute error = 0.19977329123611062 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.045373566113507 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.2251461805423833 " "
Order of pole (six term test) = -0.6996214313087457 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.20934014046518312 " "
absolute error = 0.20934014046518312 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.056803902216151 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.2594050655196116 " "
Order of pole (six term test) = -0.6691650256771826 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.2189114098216327 " "
absolute error = 0.2189114098216327 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.0682361364514477 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.2870652546939194 " "
Order of pole (six term test) = -0.6469387864731555 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.22848704326508412 " "
absolute error = 0.22848704326508412 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.079670264233568 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.3105363474167993 " "
Order of pole (six term test) = -0.630002352446434 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3500000000000002 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.2380669856281734 " "
absolute error = 0.2380669856281734 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.091106280433987 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.3311814259652515 " "
Order of pole (six term test) = -0.6166668397993522 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3600000000000002 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.2476511826000909 " "
absolute error = 0.2476511826000909 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.102544179379518 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.349829740025149 " "
Order of pole (six term test) = -0.6058930302460919 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.2572395807104934 " "
absolute error = 0.2572395807104934 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.1139839548506885 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.367014775989201 " "
Order of pole (six term test) = -0.5970064295283084 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000002 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.2668321273137762 " "
absolute error = 0.2668321273137762 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.1254256000804426 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.3830953581830574 " "
Order of pole (six term test) = -0.5895501647173571 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39000000000000024 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.27642877057369486 " "
absolute error = 0.27642877057369486 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.136869107753156 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.3983217466455815 " "
Order of pole (six term test) = -0.5832037572947577 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.28602945944832825 " "
absolute error = 0.28602945944832825 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.148314470003996 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.4128737962590905 " "
Order of pole (six term test) = -0.5777357897767352 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.29563414367537366 " "
absolute error = 0.29563414367537366 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.1597616784185822 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.426884108327162 " "
Order of pole (six term test) = -0.5729749623533991 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.30524277375776554 " "
absolute error = 0.30524277375776554 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.171210724032982 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.440452592531791 " "
Order of pole (six term test) = -0.5687917697994589 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000027 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.3148553009496094 " "
absolute error = 0.3148553009496094 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.1826615973340124 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.4536559646816847 " "
Order of pole (six term test) = -0.5650864837655352 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.32447167724242276 " "
absolute error = 0.32447167724242276 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.194114288259866 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.4665540970078785 " "
Order of pole (six term test) = -0.5617810793146809 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.33409185535167585 " "
absolute error = 0.33409185535167585 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.2055687862010265 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.479194415873925 " "
Order of pole (six term test) = -0.5588136198237592 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.34371578870362335 " "
absolute error = 0.34371578870362335 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.2170250800015103 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.491614967130014 " "
Order of pole (six term test) = -0.5561343289046512 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.35334343142242103 " "
absolute error = 0.35334343142242103 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.2284831579604 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.5038466397727106 " "
Order of pole (six term test) = -0.5537027316211613 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000003 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.36297473831751914 " "
absolute error = 0.36297473831751914 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.2399430078336797 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.5159147545198053 " "
Order of pole (six term test) = -0.5514856059092015 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000003 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.3726096648713261 " "
absolute error = 0.3726096648713261 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.2514046168363544 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.527840286104021 " "
Order of pole (six term test) = -0.5494554026786425 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000003 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.38224816722713545 " "
absolute error = 0.38224816722713545 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.2628679716448707 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.5396407421456133 " "
Order of pole (six term test) = -0.5475891064913085 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000003 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.3918902021773101 " "
absolute error = 0.3918902021773101 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.274333058399814 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.5513308702016237 " "
Order of pole (six term test) = -0.545867318010572 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000004 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.40153572715171615 " "
absolute error = 0.40153572715171615 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.2857998627088834 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.5629231550258957 " "
Order of pole (six term test) = -0.5442736057049178 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000004 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.411184700206402 " "
absolute error = 0.411184700206402 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.2972683696501472 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.574428261394759 " "
Order of pole (six term test) = -0.5427939298196325 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000004 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.42083708001251485 " "
absolute error = 0.42083708001251485 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.3087385637755595 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.5858553429227427 " "
Order of pole (six term test) = -0.5414162384939996 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000004 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.43049282584544996 " "
absolute error = 0.43049282584544996 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.320210429114743 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.597212305464671 " "
Order of pole (six term test) = -0.5401301236030829 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000004 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.4401518975742265 " "
absolute error = 0.4401518975742265 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.33168394917903 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.6085060088225838 " "
Order of pole (six term test) = -0.5389265561600087 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000004 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.44981425565108474 " "
absolute error = 0.44981425565108474 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.3431591069657522 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.619742437780292 " "
Order of pole (six term test) = -0.5377976623769243 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000004 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.4594798611012988 " "
absolute error = 0.4594798611012988 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.3546358849627844 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.6309268357129834 " "
Order of pole (six term test) = -0.5367365480206256 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000004 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.4691486755132001 " "
absolute error = 0.4691486755132001 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.3661142651533114 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.6420638185767564 " "
Order of pole (six term test) = -0.5357371488788427 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000004 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.4788206610284063 " "
absolute error = 0.4788206610284063 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.3775942290208456 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.6531574655960104 " "
Order of pole (six term test) = -0.5347941112974617 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000004 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.48849578033225083 " "
absolute error = 0.48849578033225083 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.389075757554466 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.6642113933199885 " "
Order of pole (six term test) = -0.5339026943030518 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000004 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.49817399664440815 " "
absolute error = 0.49817399664440815 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.4005588312542745 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.6752288220318396 " "
Order of pole (six term test) = -0.5330586825329107 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000004 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.5078552737097101 " "
absolute error = 0.5078552737097101 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.412043430137065 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.6862126291679154 " "
Order of pole (six term test) = -0.5322583156630838 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000005 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.5175395757891488 " "
absolute error = 0.5175395757891488 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.4235295337422187 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.6971653891878344 " "
Order of pole (six term test) = -0.5314982350496713 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.527226867651062 " "
absolute error = 0.527226867651062 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.4350171211377747 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.708089421605837 " "
Order of pole (six term test) = -0.5307754217703256 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000005 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.5369171145624957 " "
absolute error = 0.5369171145624957 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.446506170926719 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.71898681051228 " "
Order of pole (six term test) = -0.5300871686219573 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.5466102822807412 " "
absolute error = 0.5466102822807412 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.4579966612534445 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.7298594453978935 " "
Order of pole (six term test) = -0.5294310284911745 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000005 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.5563063370450408 " "
absolute error = 0.5563063370450408 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.469488569810409 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.740709034936403 " "
Order of pole (six term test) = -0.5288047942484706 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000005 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.5660052455684605 " "
absolute error = 0.5660052455684605 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.4809818738449505 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.751537131009323 " "
Order of pole (six term test) = -0.5282064674281752 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000005 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.575706975029923 " "
absolute error = 0.575706975029923 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.492476550166288 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.762345149637168 " "
Order of pole (six term test) = -0.5276342313622919 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000005 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.5854114930663996 " "
absolute error = 0.5854114930663996 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.503972575152674 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.7731343795353656 " "
Order of pole (six term test) = -0.5270864382304836 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000005 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.5951187677652571 " "
absolute error = 0.5951187677652571 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.5154699247587033 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.7839060006078835 " "
Order of pole (six term test) = -0.5265615856865882 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000005 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.6048287676567539 " "
absolute error = 0.6048287676567539 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.5269685745227752 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.794661096112759 " "
Order of pole (six term test) = -0.526058300824646 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000005 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.6145414617066852 " "
absolute error = 0.6145414617066852 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.5384684995746856 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.805400656172924 " "
Order of pole (six term test) = -0.5255753339101723 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000006 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.6242568193091714 " "
absolute error = 0.6242568193091714 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.5499696746433753 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.8161255965150866 " "
Order of pole (six term test) = -0.5251115358418836 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000006 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.6339748102795871 " "
absolute error = 0.6339748102795871 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.5614720740647763 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.826836757912988 " "
Order of pole (six term test) = -0.5246658568673173 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000006 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.6436954048476282 " "
absolute error = 0.6436954048476282 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.572975671789809 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.8375349170724564 " "
Order of pole (six term test) = -0.5242373328764547 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000006 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.653418573650513 " "
absolute error = 0.653418573650513 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.5844804413924716 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.848220793963449 " "
Order of pole (six term test) = -0.5238250762258776 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000006 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.6631442877263154 " "
absolute error = 0.6631442877263154 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.595986356078053 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.8588950532273767 " "
Order of pole (six term test) = -0.5234282725806594 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000006 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.6728725185074256 " "
absolute error = 0.6728725185074256 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.6074933886914446 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.8695583121207036 " "
Order of pole (six term test) = -0.5230461711891046 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000006 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.6826032378141373 " "
absolute error = 0.6826032378141373 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.6190015117255294 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.880211146083626 " "
Order of pole (six term test) = -0.5226780779609097 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000006 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.6923364178483573 " "
absolute error = 0.6923364178483573 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.6305106973296897 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.890854087297878 " "
Order of pole (six term test) = -0.5223233556243763 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000006 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.702072031187435 " "
absolute error = 0.702072031187435 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.6420209173183715 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.9014876339157962 " "
Order of pole (six term test) = -0.5219814132890672 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000006 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.7118100507781098 " "
absolute error = 0.7118100507781098 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.6535321431797367 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.9121122490016096 " "
Order of pole (six term test) = -0.5216517064699655 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000006 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.7215504499305728 " "
absolute error = 0.7215504499305728 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.6650443460843833 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.922728367378351 " "
Order of pole (six term test) = -0.5213337294331435 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.7312932023126414 " "
absolute error = 0.7312932023126414 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.6765574968941244 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.933336392438769 " "
Order of pole (six term test) = -0.5210270171579374 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.741038281944043 " "
absolute error = 0.741038281944043 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.6880715661708314 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.943936706644868 " "
Order of pole (six term test) = -0.5207311347688943 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.7507856631908068 " "
absolute error = 0.7507856631908068 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.699586524185324 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.95452966345756 " "
Order of pole (six term test) = -0.5204456840135308 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.7605353207597603 " "
absolute error = 0.7605353207597603 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.711102340926294 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.9651155981250037 " "
Order of pole (six term test) = -0.5201702926945835 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.7702872296931287 " "
absolute error = 0.7702872296931287 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.7226189861092966 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.9756948232802456 " "
Order of pole (six term test) = -0.5199046177098499 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.780041365363235 " "
absolute error = 0.780041365363235 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.7341364291857464 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.9862676359597753 " "
Order of pole (six term test) = -0.51964833856597 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.7897977034672982 " "
absolute error = 0.7897977034672982 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.7456546393519523 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 2.996834312748088 " "
Order of pole (six term test) = -0.5194011604829036 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.7995562200223282 " "
absolute error = 0.7995562200223282 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.757173585558177 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.007395116150113 " "
Order of pole (six term test) = -0.5191628085874953 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.8093168913601146 " "
absolute error = 0.8093168913601146 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.7686932365177124 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.0179502938498115 " "
Order of pole (six term test) = -0.518933027986856 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.8190796941223082 " "
absolute error = 0.8190796941223082 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.780213560715951 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.028500078249079 " "
Order of pole (six term test) = -0.5187115834020073 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.8288446052555914 " "
absolute error = 0.8288446052555914 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.791734526419489 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.0390446909079394 " "
Order of pole (six term test) = -0.5184982552904707 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.8386116020069394 " "
absolute error = 0.8386116020069394 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.8032561016852084 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.0495843397528666 " "
Order of pole (six term test) = -0.5182928414088792 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.8483806619189649 " "
absolute error = 0.8483806619189649 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.8147782543693602 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.0601192227490275 " "
Order of pole (six term test) = -0.5180951535809797 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.8581517628253498 " "
absolute error = 0.8581517628253498 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.8263009521366405 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.070649527116462 " "
Order of pole (six term test) = -0.517905017810218 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0000000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.8679248828463587 " "
absolute error = 0.8679248828463587 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.837824162469256 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.08117542995962 " "
Order of pole (six term test) = -0.5177222734883014 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0100000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.8777000003844336 " "
absolute error = 0.8777000003844336 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.8493478526759475 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.091697099815732 " "
Order of pole (six term test) = -0.5175467717409941 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0200000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.8874770941198681 " "
absolute error = 0.8874770941198681 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.860871989901028 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.1022146971455276 " "
Order of pole (six term test) = -0.5173783748725782 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0300000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.8972561430065592 " "
absolute error = 0.8972561430065592 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.872396541133355 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.112728373325224 " "
Order of pole (six term test) = -0.5172169565776699 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0400000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.9070371262678356 " "
absolute error = 0.9070371262678356 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.8839214732152856 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.1232382732754838 " "
Order of pole (six term test) = -0.5170623999106532 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0500000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.9168200233923605 " "
absolute error = 0.9168200233923605 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.8954467528515955 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.1337445349822697 " "
Order of pole (six term test) = -0.5169145972951572 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0600000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.9266048141301065 " "
absolute error = 0.9266048141301065 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.906972346618355 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.144247289236643 " "
Order of pole (six term test) = -0.5167734503772934 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0700000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.9363914784884041 " "
absolute error = 0.9363914784884041 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.918498220971751 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.1547466606004337 " "
Order of pole (six term test) = -0.5166388690494568 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0800000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.9461799967280577 " "
absolute error = 0.9461799967280577 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.9300243422568744 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.1652427683524484 " "
Order of pole (six term test) = -0.5165107707042527 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0900000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.9559703493595322 " "
absolute error = 0.9559703493595322 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.941550676716438 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.175735726526333 " "
Order of pole (six term test) = -0.5163890799963404 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1000000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.9657625171392057 " "
absolute error = 0.9657625171392057 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.9530771904994455 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.186225643251923 " "
Order of pole (six term test) = -0.5162737288937418 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1100000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.9755564810656887 " "
absolute error = 0.9755564810656887 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.9646038496698024 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.1967126213706827 " "
Order of pole (six term test) = -0.5161646560317106 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1200000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.9853522223762073 " "
absolute error = 0.9853522223762073 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.9761306202148488 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.207196760915607 " "
Order of pole (six term test) = -0.5160618053227299 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1300000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 0.9951497225430502 " "
absolute error = 0.9951497225430502 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.98765746805384 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.2176781566360884 " "
Order of pole (six term test) = -0.5159651270197951 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1400000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.0049489632700765 " "
absolute error = 1.0049489632700765 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 2.9991843590463514 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.2281568982314646 " "
Order of pole (six term test) = -0.5158745772267146 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1500000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.014749926489286 " "
absolute error = 1.014749926489286 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.0107112590005953 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.2386330727464805 " "
Order of pole (six term test) = -0.5157901166694945 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1600000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.024552594357447 " "
absolute error = 1.024552594357447 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.0222381336816793 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.249106763540141 " "
Order of pole (six term test) = -0.5157117110665261 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1700000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.0343569492527833 " "
absolute error = 1.0343569492527833 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.033764948819782 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.2595780496097375 " "
Order of pole (six term test) = -0.5156393311048486 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1800000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.044162973771719 " "
absolute error = 1.044162973771719 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.0452916701182273 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.2700470075848562 " "
Order of pole (six term test) = -0.5155729514976741 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1900000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.0539706507256783 " "
absolute error = 1.0539706507256783 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.056818263261497 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.280513709707829 " "
Order of pole (six term test) = -0.5155125516073849 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2000000000000008 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.0637799631379397 " "
absolute error = 1.0637799631379397 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.068344693923136 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.2909782276354527 " "
Order of pole (six term test) = -0.5154581139171341 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2100000000000009 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.0735908942405454 " "
absolute error = 1.0735908942405454 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.0798709277735745 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.30144062658083 " "
Order of pole (six term test) = -0.5154096258976697 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2200000000000009 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.0834034274712627 " "
absolute error = 1.0834034274712627 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.0913969304878663 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.3119009723657706 " "
Order of pole (six term test) = -0.5153670774767427 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2300000000000009 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.0932175464705969 " "
absolute error = 1.0932175464705969 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.1029226677533144 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.3223593262952806 " "
Order of pole (six term test) = -0.5153304626235293 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2400000000000009 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.1030332350788548 " "
absolute error = 1.1030332350788548 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.1144481052770043 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.332815748986244 " "
Order of pole (six term test) = -0.5152997780411503 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2500000000000009 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.1128504773332586 " "
absolute error = 1.1128504773332586 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.1259732087932472 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.3432702964369767 " "
Order of pole (six term test) = -0.5152750240651756 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.260000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.122669257465108 " "
absolute error = 1.122669257465108 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.137497944070914 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.353723023795666 " "
Order of pole (six term test) = -0.5152562036173922 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.270000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.1324895598969895 " "
absolute error = 1.1324895598969895 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.1490222769206673 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.364173984072214 " "
Order of pole (six term test) = -0.5152433223859063 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.280000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.142311369240034 " "
absolute error = 1.142311369240034 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.1605461732020785 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.3746232280453685 " "
Order of pole (six term test) = -0.5152363887971401 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.290000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.1521346702912187 " "
absolute error = 1.1521346702912187 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.172069598830661 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.385070804606583 " "
Order of pole (six term test) = -0.5152354137075079 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.300000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.1619594480307152 " "
absolute error = 1.1619594480307152 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.1835925197847876 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.395516760996377 " "
Order of pole (six term test) = -0.515240410485637 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.310000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.1717856876192811 " "
absolute error = 1.1717856876192811 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.195114902112468 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.405961142019466 " "
Order of pole (six term test) = -0.515251394723542 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.320000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.1816133743956956 " "
absolute error = 1.1816133743956956 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.20663671193807 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.4164039910928943 " "
Order of pole (six term test) = -0.515268384251609 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.330000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.1914424938742365 " "
absolute error = 1.1914424938742365 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.2181579154688844 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.4268453507313876 " "
Order of pole (six term test) = -0.5152913988468466 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.340000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.2012730317422005 " "
absolute error = 1.2012730317422005 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.229678479001587 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.4372852608653273 " "
Order of pole (six term test) = -0.5153204604764774 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.350000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.2111049738574624 " "
absolute error = 1.2111049738574624 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.2411983689286212 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.447723760226666 " "
Order of pole (six term test) = -0.5153555928529325 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.360000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.2209383062460764 " "
absolute error = 1.2209383062460764 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.2527175517444005 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.4581608864622484 " "
Order of pole (six term test) = -0.5153968215095244 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.370000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.230773015099915 " "
absolute error = 1.230773015099915 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.264235994051456 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.468596675464997 " "
Order of pole (six term test) = -0.5154441738073725 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.380000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.2406090867743482 " "
absolute error = 1.2406090867743482 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.2757536625664354 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.479031161882414 " "
Order of pole (six term test) = -0.5154976786718866 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.390000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.2504465077859592 " "
absolute error = 1.2504465077859592 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.2872705241260003 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.4894643795013325 " "
Order of pole (six term test) = -0.5155573666246145 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.400000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.2602852648102978 " "
absolute error = 1.2602852648102978 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.298786545692586 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.4998963599469715 " "
Order of pole (six term test) = -0.5156232696484544 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.410000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.2701253446796703 " "
absolute error = 1.2701253446796703 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.31030169436006 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.5103271342963396 " "
Order of pole (six term test) = -0.515695421256364 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.420000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.2799667343809653 " "
absolute error = 1.2799667343809653 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.3218159373592746 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.5207567332132146 " "
Order of pole (six term test) = -0.5157738563561463 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.430000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.2898094210535145 " "
absolute error = 1.2898094210535145 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.3333292420634617 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.53118518442743 " "
Order of pole (six term test) = -0.5158586109693886 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.440000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.299653391986988 " "
absolute error = 1.299653391986988 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.3448415759935446 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.5416125162465573 " "
Order of pole (six term test) = -0.5159497225872851 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.450000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.3094986346193231 " "
absolute error = 1.3094986346193231 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.356352906823311 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.5520387549706847 " "
Order of pole (six term test) = -0.5160472297259986 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.460000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.3193451365346873 " "
absolute error = 1.3193451365346873 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.3678632023844814 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.5624639268226823 " "
Order of pole (six term test) = -0.5161511722335934 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.470000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.3291928854614723 " "
absolute error = 1.3291928854614723 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.379372430671643 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.572888056148818 " "
Order of pole (six term test) = -0.5162615908625217 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.480000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.3390418692703216 " "
absolute error = 1.3390418692703216 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.390880559847071 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.5833111669863156 " "
Order of pole (six term test) = -0.5163785275231927 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.490000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.348892075972189 " "
absolute error = 1.348892075972189 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.4023875582454446 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.593733282298613 " "
Order of pole (six term test) = -0.5165020251049519 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.500000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.3587434937164269 " "
absolute error = 1.3587434937164269 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.4138933943784084 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.604154424360967 " "
Order of pole (six term test) = -0.5166321274952939 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5100000000000011 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.3685961107889066 " "
absolute error = 1.3685961107889066 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.4253980369390633 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.614574613854105 " "
Order of pole (six term test) = -0.516768879153009 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5200000000000011 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.3784499156101673 " "
absolute error = 1.3784499156101673 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.4369014548062955 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.62499387163777 " "
Order of pole (six term test) = -0.5169123258267305 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5300000000000011 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.3883048967335938 " "
absolute error = 1.3883048967335938 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.4484036170490153 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.635412217439819 " "
Order of pole (six term test) = -0.5170625139328919 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5400000000000011 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.3981610428436244 " "
absolute error = 1.3981610428436244 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.4599044929302605 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.64582966994144 " "
Order of pole (six term test) = -0.517219490513332 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5500000000000012 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.4080183427539859 " "
absolute error = 1.4080183427539859 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.471404051911208 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.6562462475553916 " "
Order of pole (six term test) = -0.5173833036091224 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5600000000000012 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.4178767854059555 " "
absolute error = 1.4178767854059555 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.4829022636550313 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.6666619676174323 " "
Order of pole (six term test) = -0.5175540017575564 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5700000000000012 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.427736359866652 " "
absolute error = 1.427736359866652 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.494399098030683 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.677076846967797 " "
Order of pole (six term test) = -0.5177316342345506 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5800000000000012 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.4375970553273512 " "
absolute error = 1.4375970553273512 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.505894525116523 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.6874909017009188 " "
Order of pole (six term test) = -0.517916250967156 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5900000000000012 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.4474588611018295 " "
absolute error = 1.4474588611018295 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.5173885152038786 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.697904147372098 " "
Order of pole (six term test) = -0.5181079024951583 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6000000000000012 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.457321766624732 " "
absolute error = 1.457321766624732 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.5288810388004315 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.7083165986343722 " "
Order of pole (six term test) = -0.5183066398105627 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6100000000000012 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.4671857614499657 " "
absolute error = 1.4671857614499657 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.5403720666335463 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.7187282698424546 " "
Order of pole (six term test) = -0.5185125145842182 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6200000000000012 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.4770508352491187 " "
absolute error = 1.4770508352491187 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.5518615696534632 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.729139174398887 " "
Order of pole (six term test) = -0.5187255787543865 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6300000000000012 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.4869169778099027 " "
absolute error = 1.4869169778099027 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.563349519036368 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.7395493255373227 " "
Order of pole (six term test) = -0.5189458850665094 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6400000000000012 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.4967841790346197 " "
absolute error = 1.4967841790346197 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.5748358861873895 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.7499587358244337 " "
Order of pole (six term test) = -0.5191734866112228 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6500000000000012 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.5066524289386525 " "
absolute error = 1.5066524289386525 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.5863206427434267 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.760367416467874 " "
Order of pole (six term test) = -0.5194084362699556 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6600000000000013 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.5165217176489776 " "
absolute error = 1.5165217176489776 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.597803760575935 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.7707753800052672 " "
Order of pole (six term test) = -0.5196507887740847 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6700000000000013 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.5263920354027016 " "
absolute error = 1.5263920354027016 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.609285211793571 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.7811826365528414 " "
Order of pole (six term test) = -0.5199005977563012 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6800000000000013 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.5362633725456194 " "
absolute error = 1.5362633725456194 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.6207649687447097 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.7915891961244204 " "
Order of pole (six term test) = -0.5201579174078788 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6900000000000013 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.5461357195307948 " "
absolute error = 1.5461357195307948 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.632243004019903 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.801995069406522 " "
Order of pole (six term test) = -0.5204228032647791 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7000000000000013 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.5560090669171611 " "
absolute error = 1.5560090669171611 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.6437192904542037 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.812400264612853 " "
Order of pole (six term test) = -0.5206953094285751 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7100000000000013 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.5658834053681456 " "
absolute error = 1.5658834053681456 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.6551938011293914 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.822804791664617 " "
Order of pole (six term test) = -0.5209754921680982 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7200000000000013 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.575758725650312 " "
absolute error = 1.575758725650312 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.666666509376103 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.833208658303111 " "
Order of pole (six term test) = -0.5212634064889947 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7300000000000013 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.5856350186320247 " "
absolute error = 1.5856350186320247 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.6781373887758626 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.8436118726232107 " "
Order of pole (six term test) = -0.5215591082615703 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7400000000000013 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.5955122752821336 " "
absolute error = 1.5955122752821336 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.6896064131629975 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.8540144420381446 " "
Order of pole (six term test) = -0.5218626533806265 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7500000000000013 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.605390486668677 " "
absolute error = 1.605390486668677 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.7010735566264694 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.8644163738688238 " "
Order of pole (six term test) = -0.5221740981713356 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7600000000000013 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.6152696439576057 " "
absolute error = 1.6152696439576057 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.7125387935116096 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.8748176743331944 " "
Order of pole (six term test) = -0.5224934984635077 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7700000000000014 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.625149738411525 " "
absolute error = 1.625149738411525 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.7240020984217534 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.885218349777151 " "
Order of pole (six term test) = -0.5228209106697612 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7800000000000014 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.6350307613884552 " "
absolute error = 1.6350307613884552 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.7354634462197835 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.8956184060562045 " "
Order of pole (six term test) = -0.5231563913829458 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7900000000000014 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.6449127043406118 " "
absolute error = 1.6449127043406118 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.7469228120295597 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.9060178484360772 " "
Order of pole (six term test) = -0.5234999968542695 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8000000000000014 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.6547955588132026 " "
absolute error = 1.6547955588132026 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.758380171237304 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.9164166817284434 " "
Order of pole (six term test) = -0.5238517833664318 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8100000000000014 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.664679316443243 " "
absolute error = 1.664679316443243 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.7698354994928445 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.9268149111287904 " "
Order of pole (six term test) = -0.5242118081946554 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8200000000000014 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.674563968958389 " "
absolute error = 1.674563968958389 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.781288772710799 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.9372125403922404 " "
Order of pole (six term test) = -0.5245801272882602 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8300000000000014 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.684449508175787 " "
absolute error = 1.684449508175787 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.7927399670716584 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.9476095731677145 " "
Order of pole (six term test) = -0.5249567967869258 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8400000000000014 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.6943359260009407 " "
absolute error = 1.6943359260009407 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.8041890590227974 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.9580060132423367 " "
Order of pole (six term test) = -0.5253418736287703 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8500000000000014 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.7042232144265943 " "
absolute error = 1.7042232144265943 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.815636025279383 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.968401863511687 " "
Order of pole (six term test) = -0.525735413754072 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8600000000000014 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.7141113655316327 " "
absolute error = 1.7141113655316327 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.827080842825219 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.9787971269187006 " "
Order of pole (six term test) = -0.5261374737352504 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8700000000000014 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.7240003714799974 " "
absolute error = 1.7240003714799974 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.8385234889134776 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.989191805562021 " "
Order of pole (six term test) = -0.5265481092014479 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8800000000000014 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.733890224519618 " "
absolute error = 1.733890224519618 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.8499639410673923 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 3.9995859021796782 " "
Order of pole (six term test) = -0.5269673771462884 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8900000000000015 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.7437809169813592 " "
absolute error = 1.7437809169813592 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.8614021770808282 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.009979418083545 " "
Order of pole (six term test) = -0.5273953327559298 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9000000000000015 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.7536724412779836 " "
absolute error = 1.7536724412779836 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.872838175018815 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.020372354576475 " "
Order of pole (six term test) = -0.5278320315333378 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9100000000000015 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.763564789903129 " "
absolute error = 1.763564789903129 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.8842719132179617 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.0307647127061195 " "
Order of pole (six term test) = -0.5282775288760853 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9200000000000015 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.7734579554303007 " "
absolute error = 1.7734579554303007 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.895703370286837 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.041156493396025 " "
Order of pole (six term test) = -0.5287318802513994 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9300000000000015 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.7833519305118781 " "
absolute error = 1.7833519305118781 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.9071325251062383 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.051547697110308 " "
Order of pole (six term test) = -0.5291951406793025 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9400000000000015 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.7932467078781362 " "
absolute error = 1.7932467078781362 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.9185593568294217 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.061938323676201 " "
Order of pole (six term test) = -0.5296673643607743 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9500000000000015 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.8031422803362804 " "
absolute error = 1.8031422803362804 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.929983844882241 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.072328373287881 " "
Order of pole (six term test) = -0.5301486062670513 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9600000000000015 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.8130386407694954 " "
absolute error = 1.8130386407694954 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.9414059689632115 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.082717845294507 " "
Order of pole (six term test) = -0.5306389202437245 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9700000000000015 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.8229357821360075 " "
absolute error = 1.8229357821360075 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.952825709043525 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.093106738997846 " "
Order of pole (six term test) = -0.5311383601776285 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9800000000000015 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.8328336974681612 " "
absolute error = 1.8328336974681612 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.9642430453669997 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.1034950533539085 " "
Order of pole (six term test) = -0.5316469795051084 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9900000000000015 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.8427323798715076 " "
absolute error = 1.8427323798715076 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.9756579584499256 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.113882786826125 " "
Order of pole (six term test) = -0.53216483096117 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0000000000000013 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.852631822523907 " "
absolute error = 1.852631822523907 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.9870704290809056 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.124269937867885 " "
Order of pole (six term test) = -0.5326919673058992 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.010000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.8625320186746424 " "
absolute error = 1.8625320186746424 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 3.9984804383205743 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.134656504985200 " "
Order of pole (six term test) = -0.533228441580647 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.020000000000001 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.8724329616435484 " "
absolute error = 1.8724329616435484 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 4.0098879675013075 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.145042485502144 " "
Order of pole (six term test) = -0.5337743046264798 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0300000000000007 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.8823346448201494 " "
absolute error = 1.8823346448201494 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 4.0212929982268335 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.1554278771318405 " "
Order of pole (six term test) = -0.5343296081727562 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0400000000000005 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.8922370616628121 " "
absolute error = 1.8922370616628121 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 4.032695512371810 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.165812676752875 " "
Order of pole (six term test) = -0.5348944022321902 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0500000000000003 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.9021402056979086 " "
absolute error = 1.9021402056979086 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 4.04409549208132 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.176196882545597 " "
Order of pole (six term test) = -0.5354687394898221 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.06 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.912044070518992 " "
absolute error = 1.912044070518992 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 4.05549291977035 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.186580489957436 " "
Order of pole (six term test) = -0.5360526672198755 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.07 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.9219486497859835 " "
absolute error = 1.9219486497859835 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 4.0668877781231645 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.196963496274212 " "
Order of pole (six term test) = -0.5366462362464475 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0799999999999996 " "
y[1] (analytic) = 0.0 " "
y[1] (numeric) = 1.9318539372243697 " "
absolute error = 1.9318539372243697 " "
relative error = -1. "%"
Correct digits = -1
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 4.0782800500926815 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
Radius of convergence (six term test) for eq 1 = 4.207345897348960 " "
Order of pole (six term test) = -0.537249494574354 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));"
Iterations = 199
"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 47 Seconds
"Expected Time Remaining "= 0 Years 0 Days 0 Hours 4 Minutes 23 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 4 Minutes 3 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 7 Minutes 4 Seconds
"Time to Timeout " Unknown
Percent Done = 40.81632653061222 "%"
(%o58) true
(%o58) diffeq.max