(%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 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : array_const_2D0 array_tmp1 ,
1 1 1
array_tmp3 : array_tmp2 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp3 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_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
array_tmp2 : array_const_2D0 array_tmp1 , array_tmp3 : array_tmp2 ,
2 1 2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
array_tmp2 : array_const_2D0 array_tmp1 , array_tmp3 : array_tmp2 ,
3 1 3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
array_tmp2 : array_const_2D0 array_tmp1 , array_tmp3 : array_tmp2 ,
4 1 4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
array_tmp2 : array_const_2D0 array_tmp1 , array_tmp3 : array_tmp2 ,
5 1 5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
array_tmp1_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------,
kkk kkk - 1
array_tmp2 : array_const_2D0 array_tmp1 , array_tmp3 : array_tmp2 ,
kkk 1 kkk kkk kkk
order_d : 1, if order_d + kkk < glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp3 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 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : array_const_2D0 array_tmp1 ,
1 1 1
array_tmp3 : array_tmp2 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp3 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_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
array_tmp2 : array_const_2D0 array_tmp1 , array_tmp3 : array_tmp2 ,
2 1 2 2 2
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
array_tmp2 : array_const_2D0 array_tmp1 , array_tmp3 : array_tmp2 ,
3 1 3 3 3
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
array_tmp2 : array_const_2D0 array_tmp1 , array_tmp3 : array_tmp2 ,
4 1 4 4 4
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
array_tmp2 : array_const_2D0 array_tmp1 , array_tmp3 : array_tmp2 ,
5 1 5 5 5
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
array_tmp1_g array_x
kkk - 1 2
while kkk <= glob_max_terms do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------,
kkk kkk - 1
array_tmp2 : array_const_2D0 array_tmp1 , array_tmp3 : array_tmp2 ,
kkk 1 kkk kkk kkk
order_d : 1, if order_d + kkk < glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp3 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(- cos(x) 2.0)
(%o56) exact_soln_y(x) := block(- cos(x) 2.0)
(%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/mult_c_sinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 2.0 * sin(x);"),
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, " (-cos(x) * 2.0) "), 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_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 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_g : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + term), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_real_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_complex_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 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_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_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 ) = 2.0 * sin(x);"),
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,
"2013-05-26T04:09:24-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mult_c_sin"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = 2.0 * sin(x);"),
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, "mult_c_sin diffeq.max"),
logitem_str(html_log_file,
"mult_c_sin 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/mult_c_sinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 2.0 * sin(x);"),
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, " (-cos(x) * 2.0) "), 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_g, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3, 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_g : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0,
term
term : 1 + term), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_real_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_complex_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_g : 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_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_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 ) = 2.0 * sin(x);"),
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,
"2013-05-26T04:09:24-05:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "mult_c_sin"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = 2.0 * sin(x);"),
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, "mult_c_sin diffeq.max"),
logitem_str(html_log_file,
"mult_c_sin 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/mult_c_sinpostode.ode#################"
"diff ( y , x , 1 ) = 2.0 * sin(x);"
"!"
"/* 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("
" (-cos(x) * 2.0) "
"));"
"/* 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 = 4.934417211064604500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-183 ""
estimated_step_error = 4.934417211064604500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-183 ""
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 = 3.3114313292131320000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-175 ""
estimated_step_error = 3.3114313292131320000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-175 ""
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 = 2.222263938916871400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-167 ""
estimated_step_error = 2.222263938916871400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-167 ""
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 = 1.4913360734048375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-159 ""
estimated_step_error = 1.4913360734048375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-159 ""
best_h = 1.600000E-5 ""
opt_iter = 5
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.00081868240756340000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-151 ""
estimated_step_error = 1.00081868240756340000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-151 ""
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 = 6.716380284963249000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 ""
estimated_step_error = 6.716380284963249000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 ""
best_h = 6.400000E-5 ""
opt_iter = 7
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 4.5072862431618405000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-136 ""
estimated_step_error = 4.5072862431618405000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-136 ""
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 = 3.02478823530861400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 ""
estimated_step_error = 3.02478823530861400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 ""
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 = 2.0299005403161113000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-120 ""
estimated_step_error = 2.0299005403161113000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-120 ""
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 = 1.36224254488162170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-112 ""
estimated_step_error = 1.36224254488162170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-112 ""
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 = 9.141846268720051000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
estimated_step_error = 9.141846268720051000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
best_h = 2.048000E-3 ""
opt_iter = 12
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 6.1349775004680440000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 ""
estimated_step_error = 6.1349775004680440000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 ""
best_h = 4.096000E-3 ""
opt_iter = 13
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 4.117098023236181500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 ""
estimated_step_error = 4.117098023236181500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 ""
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 = 2.7629166394804894000000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 ""
estimated_step_error = 2.7629166394804894000000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 ""
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 = 1.85413362368562120000000000000000000000000000000000000000000000000000000000000000000000000E-73 ""
estimated_step_error = 1.85413362368562120000000000000000000000000000000000000000000000000000000000000000000000000E-73 ""
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 = 1.244249800403223200000000000000000000000000000000000000000000000000000000000000000E-65 ""
estimated_step_error = 1.244249800403223200000000000000000000000000000000000000000000000000000000000000000E-65 ""
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 = 8.3495017501584830000000000000000000000000000000000000000000000000000000000E-58 ""
estimated_step_error = 8.3495017501584830000000000000000000000000000000000000000000000000000000000E-58 ""
best_h = 0.131072 ""
opt_iter = 18
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 5.60254950879920600000000000000000000000000000000000000000000000000E-50 ""
estimated_step_error = 5.60254950879920600000000000000000000000000000000000000000000000000E-50 ""
best_h = 0.1 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (analytic) = -1.9900083305560516 " "
y[1] (numeric) = -1.9900083305560516 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11 " "
y[1] (analytic) = -1.9879121959133936 " "
y[1] (numeric) = -1.9879121959133939 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.116973905494893400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12 " "
y[1] (analytic) = -1.9856172717077325 " "
y[1] (numeric) = -1.9856172717077327 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.118264874549875200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13 " "
y[1] (analytic) = -1.9831237874295762 " "
y[1] (numeric) = -1.9831237874295764 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.119670926910892500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14 " "
y[1] (analytic) = -1.9804319924252742 " "
y[1] (numeric) = -1.9804319924252747 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.24238555804293300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000002 " "
y[1] (analytic) = -1.9775421558720845 " "
y[1] (numeric) = -1.977542155872085 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.245662417518588200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000003 " "
y[1] (analytic) = -1.9744545667512539 " "
y[1] (numeric) = -1.9744545667512543 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.24917411283239720000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000004 " "
y[1] (analytic) = -1.9711695338191213 " "
y[1] (numeric) = -1.9711695338191217 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.252922451523711500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000005 " "
y[1] (analytic) = -1.967687385576243 " "
y[1] (numeric) = -1.9676873855762431 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.128454685193831800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000006 " "
y[1] (analytic) = -1.9640084702345406 " "
y[1] (numeric) = -1.9640084702345408 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.130568468976688700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20000000000000007 " "
y[1] (analytic) = -1.9601331556824833 " "
y[1] (numeric) = -1.9601331556824835 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.132803678573149500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21000000000000008 " "
y[1] (analytic) = -1.9560618294482965 " "
y[1] (numeric) = -1.9560618294482968 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.135161484070565100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22000000000000008 " "
y[1] (analytic) = -1.951794898661211 " "
y[1] (numeric) = -1.9517948986612113 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.13764312570617800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2300000000000001 " "
y[1] (analytic) = -1.9473327900107495 " "
y[1] (numeric) = -1.94733279001075 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.28049983098991100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2400000000000001 " "
y[1] (analytic) = -1.942675949704059 " "
y[1] (numeric) = -1.9426759497040595 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.285966477928105800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (analytic) = -1.9378248434212895 " "
y[1] (numeric) = -1.93782484342129 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.291689113996543700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (analytic) = -1.9327799562690264 " "
y[1] (numeric) = -1.9327799562690269 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.297670815602400600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (analytic) = -1.927541792731781 " "
y[1] (numeric) = -1.9275417927317815 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.303914817954133800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (analytic) = -1.9221108766215418 " "
y[1] (numeric) = -1.9221108766215425 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.465636779216112500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (analytic) = -1.9164877510253941 " "
y[1] (numeric) = -1.9164877510253948 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.475805229742204000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (analytic) = -1.910672978251212 " "
y[1] (numeric) = -1.9106729782512124 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.324255458181680200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (analytic) = -1.9046671397714268 " "
y[1] (numeric) = -1.9046671397714272 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.331584351811500400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (analytic) = -1.8984708361648817 " "
y[1] (numeric) = -1.898470836164882 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.339194268304754500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (analytic) = -1.8920846870567738 " "
y[1] (numeric) = -1.8920846870567742 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.34708949809674800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (analytic) = -1.8855093310566924 " "
y[1] (numeric) = -1.8855093310566928 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.355274527340485400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3500000000000002 " "
y[1] (analytic) = -1.8787454256947578 " "
y[1] (numeric) = -1.8787454256947582 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.363754044462085500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3600000000000002 " "
y[1] (analytic) = -1.8717936473558696 " "
y[1] (numeric) = -1.87179364735587 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.372532947087363200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (analytic) = -1.8646546912120687 " "
y[1] (numeric) = -1.8646546912120692 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.381616349359539400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000002 " "
y[1] (analytic) = -1.8573292711530203 " "
y[1] (numeric) = -1.8573292711530207 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.391009589669442000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39000000000000024 " "
y[1] (analytic) = -1.849818119714626 " "
y[1] (numeric) = -1.8498181197146264 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.400718238821084300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (analytic) = -1.84212198800577 " "
y[1] (numeric) = -1.8421219880057704 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.410748108657132200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (analytic) = -1.83424164563321 " "
y[1] (numeric) = -1.8342416456332105 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.42110526117051400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (analytic) = -1.8261778806246163 " "
y[1] (numeric) = -1.8261778806246167 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.431796018130329400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000027 " "
y[1] (analytic) = -1.81793149934977 " "
y[1] (numeric) = -1.8179314993497704 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.442826971252231300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (analytic) = -1.8095033264399265 " "
y[1] (numeric) = -1.809503326439927 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.45420499294564780000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (analytic) = -1.8008942047053536 " "
y[1] (numeric) = -1.800894204705354 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.465937247672583800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (analytic) = -1.7921049950510501 " "
y[1] (numeric) = -1.7921049950510506 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.478031203955280700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (analytic) = -1.7831365763906577 " "
y[1] (numeric) = -1.783136576390658 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.245247323536392700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000003 " "
y[1] (analytic) = -1.773989845558568 " "
y[1] (numeric) = -1.7739898455585685 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.503335692489459000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000003 " "
y[1] (analytic) = -1.7646657172202427 " "
y[1] (numeric) = -1.7646657172202431 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.516562800061679700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000003 " "
y[1] (analytic) = -1.755165123780745 " "
y[1] (numeric) = -1.7551651237807455 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.53018478907251930000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000003 " "
y[1] (analytic) = -1.7454890152915021 " "
y[1] (numeric) = -1.7454890152915026 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.544210854147932500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000004 " "
y[1] (analytic) = -1.7356383593552995 " "
y[1] (numeric) = -1.7356383593552998 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.279325291056078500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000004 " "
y[1] (analytic) = -1.7256141410295216 " "
y[1] (numeric) = -1.725614141029522 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.573513969844462600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000004 " "
y[1] (analytic) = -1.7154173627276479 " "
y[1] (numeric) = -1.7154173627276483 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.58881144320427100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000004 " "
y[1] (analytic) = -1.7050490441190111 " "
y[1] (numeric) = -1.7050490441190116 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.604553877096954000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000004 " "
y[1] (analytic) = -1.6945102220268318 " "
y[1] (numeric) = -1.6945102220268324 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.93112892513755530000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000004 " "
y[1] (analytic) = -1.683801950324537 " "
y[1] (numeric) = -1.6838019503245376 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.95612925051371360000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000004 " "
y[1] (analytic) = -1.6729252998303734 " "
y[1] (numeric) = -1.672925299830374 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.981850324354809000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000004 " "
y[1] (analytic) = -1.6618813582003265 " "
y[1] (numeric) = -1.6618813582003271 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.0083114928039100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000004 " "
y[1] (analytic) = -1.6506712298193562 " "
y[1] (numeric) = -1.6506712298193567 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.6903553041186900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000004 " "
y[1] (analytic) = -1.6392960356909585 " "
y[1] (numeric) = -1.6392960356909592 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.06353581215317450000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000004 " "
y[1] (analytic) = -1.6277569133250673 " "
y[1] (numeric) = -1.627756913325068 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.092342101710768600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000004 " "
y[1] (analytic) = -1.6160550166243033 " "
y[1] (numeric) = -1.616055016624304 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.121974858049991500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.582294584819396 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000005 " "
y[1] (analytic) = -1.6041915157685847 " "
y[1] (numeric) = -1.6041915157685853 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.152458158687757400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.890876444419295 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (analytic) = -1.592167597098111 " "
y[1] (numeric) = -1.5921675970981117 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.18381718098767500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.20408798267353 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000005 " "
y[1] (analytic) = -1.5799844629947295 " "
y[1] (numeric) = -1.5799844629947302 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.21607826138044760000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.522098256873289 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (analytic) = -1.567643331761698 " "
y[1] (numeric) = -1.5676433317616985 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.832845972374345400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.845083494565142 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000005 " "
y[1] (analytic) = -1.5551454375018552 " "
y[1] (numeric) = -1.5551454375018559 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.28341812097750700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.173227502851304 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000005 " "
y[1] (analytic) = -1.5424920299942126 " "
y[1] (numeric) = -1.542492029994213 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.87903730596085370000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.50672210538052 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000005 " "
y[1] (analytic) = -1.529684374568976 " "
y[1] (numeric) = -1.5296843745689768 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.354714121746798300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.84576760926161 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000005 " "
y[1] (analytic) = -1.5167237519810157 " "
y[1] (numeric) = -1.5167237519810162 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.927950520126232400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.190573304338834 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000005 " "
y[1] (analytic) = -1.5036114582817892 " "
y[1] (numeric) = -1.5036114582817899 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.43022571493502770000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.541357997496704 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000005 " "
y[1] (analytic) = -1.49034880468974 " "
y[1] (numeric) = -1.4903488046897406 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.46965041122550700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.89835058491631 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000005 " "
y[1] (analytic) = -1.476937117459175 " "
y[1] (numeric) = -1.4769371174591757 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.51023816045104550000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.261790665486036 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000006 " "
y[1] (analytic) = -1.463377737747641 " "
y[1] (numeric) = -1.4633777377476416 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.55202916917660900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.631929198881462 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000006 " "
y[1] (analytic) = -1.4496720214818095 " "
y[1] (numeric) = -1.4496720214818102 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.59506567626374400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 19.00902921217608 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000006 " "
y[1] (analytic) = -1.435821339221886 " "
y[1] (numeric) = -1.4358213392218866 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.63939207879506500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 19.393366559229815 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000006 " "
y[1] (analytic) = -1.421827076024554 " "
y[1] (numeric) = -1.4218270760245546 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.68505506757975300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 19.206245559681474 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000006 " "
y[1] (analytic) = -1.4076906313044713 " "
y[1] (numeric) = -1.4076906313044721 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.30947169746432700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.825930021943517 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000006 " "
y[1] (analytic) = -1.3934134186943299 " "
y[1] (numeric) = -1.3934134186943308 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.3741198971111890000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.453077412358997 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000006 " "
y[1] (analytic) = -1.3789968659034932 " "
y[1] (numeric) = -1.378996865903494 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.83056801103500240000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.087397774889016 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000006 " "
y[1] (analytic) = -1.3644424145752263 " "
y[1] (numeric) = -1.364442414575227 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.88209548207626300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.728615019669064 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000006 " "
y[1] (analytic) = -1.3497515201425332 " "
y[1] (numeric) = -1.349751520142534 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.58031057158086300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.37646608256649 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000006 " "
y[1] (analytic) = -1.3349256516826153 " "
y[1] (numeric) = -1.334925651682616 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.99004430647850200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.03070014462918 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000006 " "
y[1] (analytic) = -1.3199662917699633 " "
y[1] (numeric) = -1.3199662917699642 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.728796221827400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.69107790648819 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000007 " "
y[1] (analytic) = -1.3048749363281027 " "
y[1] (numeric) = -1.3048749363281036 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.80661720884489600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.357370913238025 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000007 " "
y[1] (analytic) = -1.2896530944800013 " "
y[1] (numeric) = -1.2896530944800022 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.88695606207377900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.029360925728202 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000007 " "
y[1] (analytic) = -1.2743022883971593 " "
y[1] (numeric) = -1.2743022883971602 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.96991936518682900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.70683933457039 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000007 " "
y[1] (analytic) = -1.2588240531473927 " "
y[1] (numeric) = -1.2588240531473935 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.05562002473216500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.38960661349667 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000007 " "
y[1] (analytic) = -1.243219936541328 " "
y[1] (numeric) = -1.2432199365413288 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.14417774035270200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.077471809004006 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000007 " "
y[1] (analytic) = -1.227491498977622 " "
y[1] (numeric) = -1.2274914989776229 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.23571951773099300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.77025206348853 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000007 " "
y[1] (analytic) = -1.2116403132869245 " "
y[1] (numeric) = -1.2116403132869256 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.16297528606782500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.467772169317152 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000007 " "
y[1] (analytic) = -1.1956679645745953 " "
y[1] (numeric) = -1.1956679645745965 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.28537903095999500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.169864151502582 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000007 " "
y[1] (analytic) = -1.1795760500621952 " "
y[1] (numeric) = -1.1795760500621963 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.41205125830265800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 13.876366876846797 " "
"Order of pole (ratio test) Not computed"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000007 " "
y[1] (analytic) = -1.1633661789277658 " "
y[1] (numeric) = -1.163366178927767 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.54319495215522300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000007 " "
y[1] (analytic) = -1.147039972144912 " "
y[1] (numeric) = -1.1470399721449134 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.16148317574226180000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000008 " "
y[1] (analytic) = -1.1305990623207074 " "
y[1] (numeric) = -1.1305990623207087 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.17837319519399620000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000008 " "
y[1] (analytic) = -1.1140450935324333 " "
y[1] (numeric) = -1.1140450935324346 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.19588303676811740000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000008 " "
y[1] (analytic) = -1.097379721163174 " "
y[1] (numeric) = -1.0973797211631753 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.21404433110723350000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0000000000000007 " "
y[1] (analytic) = -1.0806046117362784 " "
y[1] (numeric) = -1.0806046117362795 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.02740911205374940000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0100000000000007 " "
y[1] (analytic) = -1.0637214427487098 " "
y[1] (numeric) = -1.063721442748711 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.04371593916193360000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0200000000000007 " "
y[1] (analytic) = -1.046731902503298 " "
y[1] (numeric) = -1.046731902503299 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.06065652720626670000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0300000000000007 " "
y[1] (analytic) = -1.0296376899399096 " "
y[1] (numeric) = -1.0296376899399107 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.07826571955611890000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0400000000000007 " "
y[1] (analytic) = -1.0124405144655555 " "
y[1] (numeric) = -1.0124405144655568 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.31589719150409730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0500000000000007 " "
y[1] (analytic) = -0.9951420957834527 " "
y[1] (numeric) = -0.995142095783454 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.33877125206056520000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0600000000000007 " "
y[1] (analytic) = -0.9777441637210539 " "
y[1] (numeric) = -0.9777441637210552 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.36259328256167240000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0700000000000007 " "
y[1] (analytic) = -0.9602484580570669 " "
y[1] (numeric) = -0.9602484580570684 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.5030380105301140000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0800000000000007 " "
y[1] (analytic) = -0.9426567283474787 " "
y[1] (numeric) = -0.9426567283474802 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.53108749835463240000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0900000000000007 " "
y[1] (analytic) = -0.9249707337506005 " "
y[1] (numeric) = -0.9249707337506019 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.56036280862682650000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1000000000000008 " "
y[1] (analytic) = -0.9071922428511534 " "
y[1] (numeric) = -0.907192242851155 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.7133217867805790000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1100000000000008 " "
y[1] (analytic) = -0.8893230334834124 " "
y[1] (numeric) = -0.8893230334834139 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.74774764169448450000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1200000000000008 " "
y[1] (analytic) = -0.871364892553423 " "
y[1] (numeric) = -0.8713648925534245 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.78376733760813640000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1300000000000008 " "
y[1] (analytic) = -0.8533196158603132 " "
y[1] (numeric) = -0.8533196158603148 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.82148893050837480000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1400000000000008 " "
y[1] (analytic) = -0.8351890079167148 " "
y[1] (numeric) = -0.8351890079167164 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.86103052092636670000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1500000000000008 " "
y[1] (analytic) = -0.8169748817683131 " "
y[1] (numeric) = -0.8169748817683148 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 2.038415836400230000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1600000000000008 " "
y[1] (analytic) = -0.7986790588125449 " "
y[1] (numeric) = -0.7986790588125465 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 2.08511105751753470000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1700000000000008 " "
y[1] (analytic) = -0.7803033686164589 " "
y[1] (numeric) = -0.7803033686164607 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.2764951566848612000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1800000000000008 " "
y[1] (analytic) = -0.761849648733762 " "
y[1] (numeric) = -0.7618496487337638 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.33163701309393230000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1900000000000008 " "
y[1] (analytic) = -0.7433197445210643 " "
y[1] (numeric) = -0.7433197445210662 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.5391214961992460000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2000000000000008 " "
y[1] (analytic) = -0.7247155089533456 " "
y[1] (numeric) = -0.7247155089533475 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.6043035074391770000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2100000000000009 " "
y[1] (analytic) = -0.7060388024386591 " "
y[1] (numeric) = -0.706038802438661 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.67319463936508240000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2200000000000009 " "
y[1] (analytic) = -0.6872914926320924 " "
y[1] (numeric) = -0.6872914926320943 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.7461116019852750000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2300000000000009 " "
y[1] (analytic) = -0.6684754542490036 " "
y[1] (numeric) = -0.6684754542490055 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.8234082940010650000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2400000000000009 " "
y[1] (analytic) = -0.6495925688775508 " "
y[1] (numeric) = -0.6495925688775527 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.90548142372382970000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2500000000000009 " "
y[1] (analytic) = -0.6306447247905357 " "
y[1] (numeric) = -0.6306447247905376 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.99277718130385730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.260000000000001 " "
y[1] (analytic) = -0.6116338167565769 " "
y[1] (numeric) = -0.6116338167565789 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 3.26731679900004960000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.270000000000001 " "
y[1] (analytic) = -0.5925617458506357 " "
y[1] (numeric) = -0.5925617458506377 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 3.3724779878534540000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.280000000000001 " "
y[1] (analytic) = -0.5734304192639093 " "
y[1] (numeric) = -0.5734304192639113 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 3.48499377987403160000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.290000000000001 " "
y[1] (analytic) = -0.5542417501131135 " "
y[1] (numeric) = -0.5542417501131155 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 3.6056494190800930000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.300000000000001 " "
y[1] (analytic) = -0.534997657249173 " "
y[1] (numeric) = -0.534997657249175 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 3.7353461594590387000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.310000000000001 " "
y[1] (analytic) = -0.5157000650653375 " "
y[1] (numeric) = -0.5157000650653395 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 3.87512350628090600000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.320000000000001 " "
y[1] (analytic) = -0.4963509033047441 " "
y[1] (numeric) = -0.49635090330474607 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 4.02618677838554300000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.330000000000001 " "
y[1] (analytic) = -0.47695210686744455 " "
y[1] (numeric) = -0.47695210686744655 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 4.18994153826157960000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.340000000000001 " "
y[1] (analytic) = -0.45750561561691705 " "
y[1] (numeric) = -0.45750561561691905 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 4.368036972902649700000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.350000000000001 " "
y[1] (analytic) = -0.4380133741860813 " "
y[1] (numeric) = -0.43801337418608327 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 4.5624210631438405000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.360000000000001 " "
y[1] (analytic) = -0.4184773317828368 " "
y[1] (numeric) = -0.4184773317828388 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 4.7754114561271516000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.370000000000001 " "
y[1] (analytic) = -0.398899441995144 " "
y[1] (numeric) = -0.39889944199514604 " "
absolute error = 2.0539125955565396000000000000000E-15 " "
relative error = 5.1489482795053470000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.380000000000001 " "
y[1] (analytic) = -0.37928166259566676 " "
y[1] (numeric) = -0.3792816625956688 " "
absolute error = 2.0539125955565396000000000000000E-15 " "
relative error = 5.4152699645437730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.390000000000001 " "
y[1] (analytic) = -0.35962595534599695 " "
y[1] (numeric) = -0.35962595534599906 " "
absolute error = 2.1094237467877974000000000000000E-15 " "
relative error = 5.865604847009210000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.400000000000001 " "
y[1] (analytic) = -0.33993428580047985 " "
y[1] (numeric) = -0.33993428580048196 " "
absolute error = 2.1094237467877974000000000000000E-15 " "
relative error = 6.2053868494627140000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.410000000000001 " "
y[1] (analytic) = -0.32020862310966036 " "
y[1] (numeric) = -0.32020862310966247 " "
absolute error = 2.1094237467877974000000000000000E-15 " "
relative error = 6.5876544057509430000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.420000000000001 " "
y[1] (analytic) = -0.3004509398233695 " "
y[1] (numeric) = -0.3004509398233716 " "
absolute error = 2.1094237467877974000000000000000E-15 " "
relative error = 7.0208592059252510000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.430000000000001 " "
y[1] (analytic) = -0.28066321169347125 " "
y[1] (numeric) = -0.2806632116934734 " "
absolute error = 2.1649348980190553000000000000000E-15 " "
relative error = 7.7136397212738650000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.440000000000001 " "
y[1] (analytic) = -0.26084741747628887 " "
y[1] (numeric) = -0.2608474174762911 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 8.5124325582105960000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.450000000000001 " "
y[1] (analytic) = -0.24100553873473102 " "
y[1] (numeric) = -0.24100553873473324 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.2132573421655020000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.460000000000001 " "
y[1] (analytic) = -0.22113955964013696 " "
y[1] (numeric) = -0.2211395596401392 " "
absolute error = 2.248201624865942000000000000000E-15 " "
relative error = 1.0166438011021037000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.470000000000001 " "
y[1] (analytic) = -0.20125146677386124 " "
y[1] (numeric) = -0.2012514667738635 " "
absolute error = 2.248201624865942000000000000000E-15 " "
relative error = 1.117110677952058000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.480000000000001 " "
y[1] (analytic) = -0.18134324892861714 " "
y[1] (numeric) = -0.1813432489286194 " "
absolute error = 2.248201624865942000000000000000E-15 " "
relative error = 1.2397492810724432000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.490000000000001 " "
y[1] (analytic) = -0.16141689690959904 " "
y[1] (numeric) = -0.16141689690960132 " "
absolute error = 2.275957200481571000000000000000E-15 " "
relative error = 1.4099869617467697000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.500000000000001 " "
y[1] (analytic) = -0.1414744033354036 " "
y[1] (numeric) = -0.1414744033354059 " "
absolute error = 2.3037127760971998000000000000E-15 " "
relative error = 1.6283601286061772000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5100000000000011 " "
y[1] (analytic) = -0.12151776243876958 " "
y[1] (numeric) = -0.12151776243877188 " "
absolute error = 2.3037127760971998000000000000E-15 " "
relative error = 1.8957827480225334000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5200000000000011 " "
y[1] (analytic) = -0.10154896986715614 " "
y[1] (numeric) = -0.10154896986715846 " "
absolute error = 2.3175905639050143000000000000000E-15 " "
relative error = 2.2822393638624094000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5300000000000011 " "
y[1] (analytic) = -8.15700224831798500E-2 " "
y[1] (numeric) = -8.15700224831821800E-2 " "
absolute error = 2.3314683517128287000000000000000E-15 " "
relative error = 2.8582416440961380000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5400000000000011 " "
y[1] (analytic) = -6.15829181649300200E-2 " "
y[1] (numeric) = -6.15829181649323800E-2 " "
absolute error = 2.3522850334245504000000000000000E-15 " "
relative error = 3.819703748245109600000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5500000000000012 " "
y[1] (analytic) = -4.15896556061826400E-2 " "
y[1] (numeric) = -4.15896556061850050E-2 " "
absolute error = 2.366162821232365000000000000000E-15 " "
relative error = 5.689306118900911000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5600000000000012 " "
y[1] (analytic) = -2.159223411653256300E-2 " "
y[1] (numeric) = -2.15922341165349500E-2 " "
absolute error = 2.3869795029440866000000000000000E-15 " "
relative error = 1.105480558455247500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5700000000000012 " "
y[1] (analytic) = -1.5926534214643062000E-3 " "
y[1] (numeric) = -1.5926534214667082000E-3 " "
absolute error = 2.4019414929243865000000000000000E-15 " "
relative error = 1.50813821799096140000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5800000000000012 " "
y[1] (analytic) = 1.840708653761889400E-2 " "
y[1] (numeric) = 1.840708653761647000E-2 " "
absolute error = 2.4216739724636227000000000000000E-15 " "
relative error = 1.315620463626551700000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.874468381578253000E-3 " "
Order of pole (three term test) = -0.89490508967092 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5900000000000012 " "
y[1] (analytic) = 3.84049858033875200E-2 " "
y[1] (numeric) = 3.84049858033850830E-2 " "
absolute error = 2.435551760271437200000000000000E-15 " "
relative error = 6.3417593037011590000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.851326600938967300E-2 " "
Order of pole (three term test) = -0.901772189378976 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6000000000000012 " "
y[1] (analytic) = 5.83990446025798500E-2 " "
y[1] (numeric) = 5.8399044602577400E-2 " "
absolute error = 2.4494295480792516000000000000000E-15 " "
relative error = 4.194297295012674000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.814464333326631700E-2 " "
Order of pole (three term test) = -0.9134710156510109 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6100000000000012 " "
y[1] (analytic) = 7.83872635459776400E-2 " "
y[1] (numeric) = 7.83872635459751600E-2 " "
absolute error = 2.4702462297909733000000000000000E-15 " "
relative error = 3.151336222295939000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.776474002241432000E-2 " "
Order of pole (three term test) = -0.9299968698555369 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6200000000000012 " "
y[1] (analytic) = 9.83676438283433100E-2 " "
y[1] (numeric) = 9.83676438283408400E-2 " "
absolute error = 2.4702462297909733000000000000000E-15 " "
relative error = 2.511238587865012300000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.7369700295246100E-2 " "
Order of pole (three term test) = -0.9513431147005369 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6300000000000012 " "
y[1] (analytic) = 0.11833818742829894 " "
y[1] (numeric) = 0.11833818742829644 " "
absolute error = 2.4980018054066022000000000000000E-15 " "
relative error = 2.1109008509363392000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.6955674474254890E-2 " "
Order of pole (three term test) = -0.9775011769318743 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6400000000000012 " "
y[1] (analytic) = 0.13829689730812655 " "
y[1] (numeric) = 0.13829689730812403 " "
absolute error = 2.525757381022231000000000000000E-15 " "
relative error = 1.826329751559663800000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.65188205383684800E-2 " "
Order of pole (three term test) = -1.0084605508186815 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6500000000000012 " "
y[1] (analytic) = 0.15824177761347039 " "
y[1] (numeric) = 0.15824177761346783 " "
absolute error = 2.55351295663786000000000000000E-15 " "
relative error = 1.6136781292202138000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.60553056721396700E-2 " "
Order of pole (three term test) = -1.0442088024242429 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6600000000000013 " "
y[1] (analytic) = 0.17817083387292057 " "
y[1] (numeric) = 0.17817083387291802 " "
absolute error = 2.55351295663786000000000000000E-15 " "
relative error = 1.4331823571410907000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.55613078111358900E-2 " "
Order of pole (three term test) = -1.0847315746605615 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6700000000000013 " "
y[1] (analytic) = 0.19808207319745869 " "
y[1] (numeric) = 0.1980820731974561 " "
absolute error = 2.581268532253489000000000000000E-15 " "
relative error = 1.3031308137008157000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.50330171828872700E-2 " "
Order of pole (three term test) = -1.1300125931244465 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6800000000000013 " "
y[1] (analytic) = 0.21797350447974487 " "
y[1] (numeric) = 0.21797350447974229 " "
absolute error = 2.581268532253489000000000000000E-15 " "
relative error = 1.1842120621102152000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.10446663784276027 " "
Order of pole (three term test) = -1.1800336727126428 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6900000000000013 " "
y[1] (analytic) = 0.2378431385932271 " "
y[1] (numeric) = 0.23784313859322448 " "
absolute error = 2.609024107869118000000000000000E-15 " "
relative error = 1.0969515973009504000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.11385838920412136 " "
Order of pole (three term test) = -1.2347747250131897 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7000000000000013 " "
y[1] (analytic) = 0.25768898859105194 " "
y[1] (numeric) = 0.2576889885910493 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.0340120754360009000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.12320450756215931 " "
Order of pole (three term test) = -1.2942137664698514 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7100000000000013 " "
y[1] (analytic) = 0.27750906990475777 " "
y[1] (numeric) = 0.2775090699047551 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 9.6016150391583780000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1325012476107403 " "
Order of pole (three term test) = -1.3583269273161624 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7200000000000013 " "
y[1] (analytic) = 0.2973014005427299 " "
y[1] (numeric) = 0.29730140054272725 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 8.9624039921648900000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.14174488395166787 " "
Order of pole (three term test) = -1.4270884612752714 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7300000000000013 " "
y[1] (analytic) = 0.3170640012883981 " "
y[1] (numeric) = 0.31706400128839546 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 8.403777307650710000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.15093171259572807 " "
Order of pole (three term test) = -1.5004707560214685 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7400000000000013 " "
y[1] (analytic) = 0.33679489589815664 " "
y[1] (numeric) = 0.3367948958981539 " "
absolute error = 2.7200464103316335000000000000000E-15 " "
relative error = 8.0762696925019550000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.16005805245490146 " "
Order of pole (three term test) = -1.57844434439895 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7500000000000013 " "
y[1] (analytic) = 0.3564921112989868 " "
y[1] (numeric) = 0.35649211129898406 " "
absolute error = 2.7200464103316335000000000000000E-15 " "
relative error = 7.6300325424322070000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.16912024682512736 " "
Order of pole (three term test) = -1.660977916393046 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7600000000000013 " "
y[1] (analytic) = 0.37615367778576286 " "
y[1] (numeric) = 0.3761536777857601 " "
absolute error = 2.7755575615628914000000000000000E-15 " "
relative error = 7.3787861862770390000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.17811466485901056 " "
Order of pole (three term test) = -1.7480383318488222 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7700000000000014 " "
y[1] (analytic) = 0.39577762921822063 " "
y[1] (numeric) = 0.3957776292182179 " "
absolute error = 2.7200464103316335000000000000000E-15 " "
relative error = 6.8726633582209800000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.18703770302786682 " "
Order of pole (three term test) = -1.839590633931674 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7800000000000014 " "
y[1] (analytic) = 0.4153620032175702 " "
y[1] (numeric) = 0.41536200321756744 " "
absolute error = 2.7755575615628914000000000000000E-15 " "
relative error = 6.6822615936514310000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.19588578657250533 " "
Order of pole (three term test) = -1.9355980633241856 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7900000000000014 " "
y[1] (analytic) = 0.4349048413627319 " "
y[1] (numeric) = 0.4349048413627291 " "
absolute error = 2.7755575615628914000000000000000E-15 " "
relative error = 6.3819881904877220000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.20465537094215186 " "
Order of pole (three term test) = -2.0360220731532155 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8000000000000014 " "
y[1] (analytic) = 0.45440418938617677 " "
y[1] (numeric) = 0.454404189386174 " "
absolute error = 2.7755575615628914000000000000000E-15 " "
relative error = 6.1081249389716240000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2133429432209245 " "
Order of pole (three term test) = -2.1408223446409056 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8100000000000014 " "
y[1] (analytic) = 0.47385809736935197 " "
y[1] (numeric) = 0.47385809736934914 " "
absolute error = 2.831068712794149000000000000000E-15 " "
relative error = 5.9745074074094650000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.22194502354127857 " "
Order of pole (three term test) = -2.249956803472989 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8200000000000014 " "
y[1] (analytic) = 0.4932646199376706 " "
y[1] (numeric) = 0.4932646199376678 " "
absolute error = 2.831068712794149000000000000000E-15 " "
relative error = 5.739452209550090000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2304581664838357 " "
Order of pole (three term test) = -2.3633816368773917 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8300000000000014 " "
y[1] (analytic) = 0.512621816455048 " "
y[1] (numeric) = 0.5126218164550451 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 5.6310125152048260000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.23887896246303275 " "
Order of pole (three term test) = -2.4810513114059862 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8400000000000014 " "
y[1] (analytic) = 0.5319277512179633 " "
y[1] (numeric) = 0.5319277512179604 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 5.4266389700780980000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.24720403909801902 " "
Order of pole (three term test) = -2.6029185914119175 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8500000000000014 " "
y[1] (analytic) = 0.5511804936490284 " "
y[1] (numeric) = 0.5511804936490255 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 5.2370863941775770000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2554300625682416 " "
Order of pole (three term test) = -2.728934558214675 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8600000000000014 " "
y[1] (analytic) = 0.5703781184900443 " "
y[1] (numeric) = 0.5703781184900413 " "
absolute error = 2.9976021664879227000000000000000E-15 " "
relative error = 5.2554648737638140000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.26355373895317225 " "
Order of pole (three term test) = -2.8590486299448874 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8700000000000014 " "
y[1] (analytic) = 0.5895187059945245 " "
y[1] (numeric) = 0.5895187059945216 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 4.8965025785835160000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2715718155556204 " "
Order of pole (three term test) = -2.9932085820603325 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8800000000000014 " "
y[1] (analytic) = 0.6086003421196694 " "
y[1] (numeric) = 0.6086003421196664 " "
absolute error = 2.9976021664879227000000000000000E-15 " "
relative error = 4.9254033542730130000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.27948108220810114 " "
Order of pole (three term test) = -3.131360568524606 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8900000000000015 " "
y[1] (analytic) = 0.6276211187177675 " "
y[1] (numeric) = 0.6276211187177645 " "
absolute error = 2.9976021664879227000000000000000E-15 " "
relative error = 4.7761333662768335000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2872783725617256 " "
Order of pole (three term test) = -3.273449143639473 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9000000000000015 " "
y[1] (analytic) = 0.6465791337270096 " "
y[1] (numeric) = 0.6465791337270066 " "
absolute error = 2.9976021664879227000000000000000E-15 " "
relative error = 4.6360948105596184000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.29496056535708703 " "
Order of pole (three term test) = -3.419417284521679 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9100000000000015 " "
y[1] (analytic) = 0.6654724913616933 " "
y[1] (numeric) = 0.6654724913616902 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 4.6713042376696207000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3025245856766332 " "
Order of pole (three term test) = -3.569206414214798 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9200000000000015 " "
y[1] (analytic) = 0.6842993023017993 " "
y[1] (numeric) = 0.6842993023017961 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 4.54278479971243540000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3099674061780097 " "
Order of pole (three term test) = -3.7227564254262995 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9300000000000015 " "
y[1] (analytic) = 0.7030576838819226 " "
y[1] (numeric) = 0.7030576838819195 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 4.42157811544881260000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3172860483078862 " "
Order of pole (three term test) = -3.8800057048799794 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9400000000000015 " "
y[1] (analytic) = 0.7217457602795372 " "
y[1] (numeric) = 0.7217457602795341 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 4.30709072367317600000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3244775834957641 " "
Order of pole (three term test) = -4.040891158273372 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9500000000000015 " "
y[1] (analytic) = 0.7403616627025766 " "
y[1] (numeric) = 0.7403616627025735 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 4.19879178725014200000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.33153913432729304 " "
Order of pole (three term test) = -4.205348235829767 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9600000000000015 " "
y[1] (analytic) = 0.7589035295763118 " "
y[1] (numeric) = 0.7589035295763087 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 4.09620504820415340000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.33846787569661835 " "
Order of pole (three term test) = -4.373310958434025 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9700000000000015 " "
y[1] (analytic) = 0.7773695067295069 " "
y[1] (numeric) = 0.7773695067295038 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.99890199196109400000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3452610359373005 " "
Order of pole (three term test) = -4.544711944341315 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9800000000000015 " "
y[1] (analytic) = 0.7957577475798348 " "
y[1] (numeric) = 0.7957577475798316 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.9064960138997130000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3519158979313488 " "
Order of pole (three term test) = -4.7194824364474925 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9900000000000015 " "
y[1] (analytic) = 0.8140664133185339 " "
y[1] (numeric) = 0.8140664133185308 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.8186374208440320000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3584298001959296 " "
Order of pole (three term test) = -4.897552330109791 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0000000000000013 " "
y[1] (analytic) = 0.8322936730942871 " "
y[1] (numeric) = 0.8322936730942845 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.20143639827780050000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.364800137947307 " "
Order of pole (three term test) = -5.078850201506022 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.010000000000001 " "
y[1] (analytic) = 0.8504377041963068 " "
y[1] (numeric) = 0.8504377041963045 " "
absolute error = 2.3314683517128287000000000000000E-15 " "
relative error = 2.74149222242697670000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.37102436414160417 " "
Order of pole (three term test) = -5.263303336520732 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.020000000000001 " "
y[1] (analytic) = 0.8684966922366025 " "
y[1] (numeric) = 0.8684966922366005 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 2.3009891254494980000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.37709999049195575 " "
Order of pole (three term test) = -5.4508377601458635 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0300000000000007 " "
y[1] (analytic) = 0.8864688313314194 " "
y[1] (numeric) = 0.8864688313314179 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.75337494059519460000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.38302458846165965 " "
Order of pole (three term test) = -5.64137826638401 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0400000000000005 " "
y[1] (analytic) = 0.9043523242818248 " "
y[1] (numeric) = 0.9043523242818235 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.35040878902755350000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.38879579023292743 " "
Order of pole (three term test) = -5.834848448641554 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0500000000000003 " "
y[1] (analytic) = 0.9221453827534263 " "
y[1] (numeric) = 0.9221453827534255 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 8.42769623719315900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.39441128965085176 " "
Order of pole (three term test) = -6.03117073059917 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.06 " "
y[1] (analytic) = 0.9398462274552044 " "
y[1] (numeric) = 0.939846227455204 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.72512626935270740000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3998688431422204 " "
Order of pole (three term test) = -6.230266397546773 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.07 " "
y[1] (analytic) = 0.9574530883174396 " "
y[1] (numeric) = 0.9574530883174396 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4051662706088129 " "
Order of pole (three term test) = -6.43205562816998 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0799999999999996 " "
y[1] (analytic) = 0.974964204668718 " "
y[1] (numeric) = 0.9749642046687184 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.416196264361514600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4103014562948282 " "
Order of pole (three term test) = -6.636457526774711 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0899999999999994 " "
y[1] (analytic) = 0.9923778254119969 " "
y[1] (numeric) = 0.9923778254119977 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 7.83125234499233700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.41527234962810705 " "
Order of pole (three term test) = -6.843390155936788 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.099999999999999 " "
y[1] (analytic) = 1.0096922091997136 " "
y[1] (numeric) = 1.0096922091997147 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.09956580283522650000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4200769660348202 " "
Order of pole (three term test) = -7.0527705695629015 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.109999999999999 " "
y[1] (analytic) = 1.0269056246079176 " "
y[1] (numeric) = 1.026905624607919 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.29736131307963220000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.424713387727301 " "
Order of pole (three term test) = -7.2645148463491385 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999999988 " "
y[1] (analytic) = 1.0440163503094124 " "
y[1] (numeric) = 1.0440163503094142 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.70146457847503650000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4291797644647234 " "
Order of pole (three term test) = -7.478538123623476 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999999986 " "
y[1] (analytic) = 1.0610226752458873 " "
y[1] (numeric) = 1.0610226752458893 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.8834672349129210000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.43347431428632704 " "
Order of pole (three term test) = -7.694754631558117 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999999983 " "
y[1] (analytic) = 1.0779228987990201 " "
y[1] (numeric) = 1.0779228987990226 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.26592333913369200000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.43759532421690805 " "
Order of pole (three term test) = -7.913077727737536 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.149999999999998 " "
y[1] (analytic) = 1.094715330960539 " "
y[1] (numeric) = 1.094715330960542 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.6368314961777570000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.44154115094430624 " "
Order of pole (three term test) = -8.133419932068065 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999998 " "
y[1] (analytic) = 1.1113982925012218 " "
y[1] (numeric) = 1.111398292501225 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.7970390902386790000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.44531022146862903 " "
Order of pole (three term test) = -8.355692962014661 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1699999999999977 " "
y[1] (analytic) = 1.1279701151388164 " "
y[1] (numeric) = 1.12797011513882 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.1496523100377330000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.44890103372296525 " "
Order of pole (three term test) = -8.579807768150248 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1799999999999975 " "
y[1] (analytic) = 1.1444291417048693 " "
y[1] (numeric) = 1.144429141704873 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.2983765845932855000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4523121571653567 " "
Order of pole (three term test) = -8.805674570003243 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1899999999999973 " "
y[1] (analytic) = 1.1607737263104394 " "
y[1] (numeric) = 1.1607737263104436 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.63451325434919300000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45554223334179816 " "
Order of pole (three term test) = -9.033202892188202 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.199999999999997 " "
y[1] (analytic) = 1.1770022345106868 " "
y[1] (numeric) = 1.1770022345106912 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 3.7730532434773423000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 13.830019744091002 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4585899764200656 " "
Order of pole (three term test) = -9.26230160080532 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.209999999999997 " "
y[1] (analytic) = 1.1931130434683148 " "
y[1] (numeric) = 1.1931130434683197 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.094315568079210000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.122828980062188 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4614541736941657 " "
Order of pole (three term test) = -9.49287894009336 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999999966 " "
y[1] (analytic) = 1.2091045421158537 " "
y[1] (numeric) = 1.2091045421158588 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.22380839322525350000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.420023903190474 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.46413368605922356 " "
Order of pole (three term test) = -9.724842569321325 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999999964 " "
y[1] (analytic) = 1.2249751313167647 " "
y[1] (numeric) = 1.2249751313167703 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.53161454564282640000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.721764591441373 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.46662744845663817 " "
Order of pole (three term test) = -9.958099599903806 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.239999999999996 " "
y[1] (analytic) = 1.2407232240253534 " "
y[1] (numeric) = 1.2407232240253592 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.653060099351249400000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.028217904630887 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.468934470289338 " "
Order of pole (three term test) = -10.192556632724667 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999996 " "
y[1] (analytic) = 1.256347245445472 " "
y[1] (numeric) = 1.256347245445478 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.7719325645913147000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.339557871251518 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.47105383580699445 " "
Order of pole (three term test) = -10.428119795654194 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999996 " "
y[1] (analytic) = 1.2718456331879986 " "
y[1] (numeric) = 1.271845633188005 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 5.0629521183991680000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.65596610144359 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4729847044610517 " "
Order of pole (three term test) = -10.664694781244089 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2699999999999956 " "
y[1] (analytic) = 1.2872168374270743 " "
y[1] (numeric) = 1.287216837427081 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 5.174993019098330000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.977632228217344 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.474726311229453 " "
Order of pole (three term test) = -10.902186884585332 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2799999999999954 " "
y[1] (analytic) = 1.3024593210550843 " "
y[1] (numeric) = 1.3024593210550914 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.4553929191777770000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.30475437922631 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.47627796691094826 " "
Order of pole (three term test) = -11.14050104131329 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999995 " "
y[1] (analytic) = 1.3175715598363682 " "
y[1] (numeric) = 1.3175715598363755 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 5.561346484616020000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.637539681608544 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4776390583888867 " "
Order of pole (three term test) = -11.37954186574483 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.299999999999995 " "
y[1] (analytic) = 1.3325520425596409 " "
y[1] (numeric) = 1.3325520425596487 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 5.8320882968653480000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.97620480265129 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.47880904886440695 " "
Order of pole (three term test) = -11.619213689131941 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999999947 " "
y[1] (analytic) = 1.347399271189114 " "
y[1] (numeric) = 1.347399271189122 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 5.9326184511340630000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.32097652929946 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.47978747805895033 " "
Order of pole (three term test) = -11.859420598016396 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999999945 " "
y[1] (analytic) = 1.3621117610142972 " "
y[1] (numeric) = 1.3621117610143056 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 6.1945687781654980000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.67209238982252 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4805739623860378 " "
Order of pole (three term test) = -12.10006647267006 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999999943 " "
y[1] (analytic) = 1.3766880407984683 " "
y[1] (numeric) = 1.3766880407984772 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.4515590560733620000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.02980132128031 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.48116819509225783 " "
Order of pole (three term test) = -12.341055025605204 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.339999999999994 " "
y[1] (analytic) = 1.3911266529257957 " "
y[1] (numeric) = 1.391126652925805 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 6.7038277120471270000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.39436438679251 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.48156994636743294 " "
Order of pole (three term test) = -12.582289840139438 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.349999999999994 " "
y[1] (analytic) = 1.405426153547099 " "
y[1] (numeric) = 1.4054261535471086 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 6.7936105982365110000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.766055547019743 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4817790634239389 " "
Order of pole (three term test) = -12.823674408999718 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3599999999999937 " "
y[1] (analytic) = 1.4195851127242323 " "
y[1] (numeric) = 1.419585112724242 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 6.8822661840630940000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 19.145162490716583 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4817954705451636 " "
Order of pole (three term test) = -13.065112172949947 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3699999999999934 " "
y[1] (analytic) = 1.4336021145730766 " "
y[1] (numeric) = 1.4336021145730866 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 6.9698608282270880000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 19.45526533957687 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.48161916910310976 " "
Order of pole (three term test) = -13.306506559426598 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3799999999999932 " "
y[1] (analytic) = 1.447475757405128 " "
y[1] (numeric) = 1.4474757574051385 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 7.2098592173903720000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 19.069748975804067 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4812502375451523 " "
Order of pole (three term test) = -13.547761021167009 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999993 " "
y[1] (analytic) = 1.4612046538676648 " "
y[1] (numeric) = 1.4612046538676755 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 7.2940782170317150000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.691515117292617 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4806888313499766 " "
Order of pole (three term test) = -13.788779074814867 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.399999999999993 " "
y[1] (analytic) = 1.4747874310824813 " "
y[1] (numeric) = 1.4747874310824922 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 7.3774602441116350000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.320285793468468 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4799351829527357 " "
Order of pole (three term test) = -14.02946433948729 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999999926 " "
y[1] (analytic) = 1.488222730783175 " "
y[1] (numeric) = 1.4882227307831861 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 7.4600595842324170000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.9557959866648 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4789896016394763 " "
Order of pole (three term test) = -14.26972057528845 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999999924 " "
y[1] (analytic) = 1.5015092094509719 " "
y[1] (numeric) = 1.5015092094509832 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 7.5419283344371410000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.59779286390787 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.47785247341089676 " "
Order of pole (three term test) = -14.509451721754068 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.429999999999992 " "
y[1] (analytic) = 1.5146455384490771 " "
y[1] (numeric) = 1.5146455384490887 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 7.623116539810690000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.24603506219555 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.47652426081551097 " "
Order of pole (three term test) = -14.748561936211733 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.439999999999992 " "
y[1] (analytic) = 1.5276304041555377 " "
y[1] (numeric) = 1.5276304041555497 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 7.8490246288204080000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.900292022956116 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.47500550275230335 " "
Order of pole (three term test) = -14.986955632041594 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4499999999999917 " "
y[1] (analytic) = 1.5404625080946042 " "
y[1] (numeric) = 1.5404625080946164 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 7.9277835109289920000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.560343371767242 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4732968142429781 " "
Order of pole (three term test) = -15.22453751682241 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4599999999999915 " "
y[1] (analytic) = 1.5531405670665754 " "
y[1] (numeric) = 1.5531405670665879 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 8.0060350875303290000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.22597833976715 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4713988861739059 " "
Order of pole (three term test) = -15.461212630347855 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4699999999999913 " "
y[1] (analytic) = 1.5656633132761197 " "
y[1] (numeric) = 1.5656633132761324 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 8.0838213256994680000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.896995223508176 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4693124850078996 " "
Order of pole (three term test) = -15.696886382497713 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999991 " "
y[1] (analytic) = 1.5780294944590514 " "
y[1] (numeric) = 1.5780294944590643 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 8.1611827477702480000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.573200880287127 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.46703845246594455 " "
Order of pole (three term test) = -15.931464590949561 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999991 " "
y[1] (analytic) = 1.5902378740075573 " "
y[1] (numeric) = 1.5902378740075704 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 8.2381585199967310000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.254410256246732 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4645777051790352 " "
Order of pole (three term test) = -16.164853518715468 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4999999999999907 " "
y[1] (analytic) = 1.6022872310938563 " "
y[1] (numeric) = 1.6022872310938696 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 8.3147865357490850000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.940445944773503 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4619312343102737 " "
Order of pole (three term test) = -16.39695991148932 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999999905 " "
y[1] (analytic) = 1.6141763607922808 " "
y[1] (numeric) = 1.6141763607922943 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 8.391103493659640000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.63113777292888 " "
"Order of pole (ratio test) Not computed"
Radius of convergence (three term test) for eq 1 = 0.4591001051473992 " "
Order of pole (three term test) = -16.627691034789876 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999999902 " "
y[1] (analytic) = 1.6259040741997686 " "
y[1] (numeric) = 1.6259040741997823 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 8.4671449711002270000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45608545666592903 " "
Order of pole (three term test) = -16.856954710884995 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.52999999999999 " "
y[1] (analytic) = 1.637469198554752 " "
y[1] (numeric) = 1.637469198554766 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 8.5429454933403610000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45288850106310335 " "
Order of pole (three term test) = -17.084659355482597 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.53999999999999 " "
y[1] (analytic) = 1.648870577354433 " "
y[1] (numeric) = 1.6488705773544472 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.6185385987073190000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4495105232628372 " "
Order of pole (three term test) = -17.310714014173815 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5499999999999896 " "
y[1] (analytic) = 1.6601070704704328 " "
y[1] (numeric) = 1.6601070704704473 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 8.6939569000432680000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.445952880391892 " "
Order of pole (three term test) = -17.5350283986143 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5599999999999894 " "
y[1] (analytic) = 1.6711775542628036 " "
y[1] (numeric) = 1.6711775542628182 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 8.7692321427310660000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.44221700122749547 " "
Order of pole (three term test) = -17.757512922429243 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999989 " "
y[1] (analytic) = 1.6820809216923913 " "
y[1] (numeric) = 1.6820809216924062 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 8.8443952595389520000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.43830438561664137 " "
Order of pole (three term test) = -17.97807873682837 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999989 " "
y[1] (analytic) = 1.6928160824315392 " "
y[1] (numeric) = 1.6928160824315543 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 8.9194764225148850000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.43421660386732147 " "
Order of pole (three term test) = -18.196637765916748 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5899999999999888 " "
y[1] (analytic) = 1.7033819629731195 " "
y[1] (numeric) = 1.7033819629731348 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 8.9945050921435280000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4299552961119409 " "
Order of pole (three term test) = -18.413102741687933 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5999999999999885 " "
y[1] (analytic) = 1.7137775067378826 " "
y[1] (numeric) = 1.7137775067378982 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 9.0695100639627360000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.425522171643193 " "
Order of pole (three term test) = -18.627387238685515 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999999883 " "
y[1] (analytic) = 1.7240016741801152 " "
y[1] (numeric) = 1.724001674180131 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 9.144519512821630000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.42091900822266254 " "
Order of pole (three term test) = -18.839405708319887 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.619999999999988 " "
y[1] (analytic) = 1.734053442891593 " "
y[1] (numeric) = 1.734053442891609 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 9.2195610349488630000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.41614765136245496 " "
Order of pole (three term test) = -19.049073512826734 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.629999999999988 " "
y[1] (analytic) = 1.7439318077038213 " "
y[1] (numeric) = 1.7439318077038375 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 9.2946616879873810000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4112100135801464 " "
Order of pole (three term test) = -19.256306958854136 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999999877 " "
y[1] (analytic) = 1.753635780788551 " "
y[1] (numeric) = 1.7536357807885674 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 9.3698480291407580000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4061080736273622 " "
Order of pole (three term test) = -19.46102333066521 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6499999999999875 " "
y[1] (analytic) = 1.76316439175656 " "
y[1] (numeric) = 1.7631643917565767 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 9.4451461515658120000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.40084387569230595 " "
Order of pole (three term test) = -19.66314092294364 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6599999999999873 " "
y[1] (analytic) = 1.772516687754692 " "
y[1] (numeric) = 1.7725166877547092 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 9.6458525312307890000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.395419528576566 " "
Order of pole (three term test) = -19.8625790731891 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999987 " "
y[1] (analytic) = 1.7816917335611413 " "
y[1] (numeric) = 1.7816917335611584 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 9.596179999698410000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3898372048465346 " "
Order of pole (three term test) = -20.0592581936905 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.679999999999987 " "
y[1] (analytic) = 1.7906886116789722 " "
y[1] (numeric) = 1.7906886116789897 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 9.7959654596955970000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.38409913995979594 " "
Order of pole (three term test) = -20.25309980306419 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6899999999999866 " "
y[1] (analytic) = 1.799506422427871 " "
y[1] (numeric) = 1.7995064224278887 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 9.8713559299422370000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.378207631366827 " "
Order of pole (three term test) = -20.444026557345563 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999999864 " "
y[1] (analytic) = 1.8081442840341106 " "
y[1] (numeric) = 1.8081442840341286 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 9.947000998615130000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3721650375883891 " "
Order of pole (three term test) = -20.631962280621593 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.709999999999986 " "
y[1] (analytic) = 1.8166013327187287 " "
y[1] (numeric) = 1.816601332718747 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 1.0022924279485668000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3659737772689778 " "
Order of pole (three term test) = -20.816831995192885 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.719999999999986 " "
y[1] (analytic) = 1.8248767227839044 " "
y[1] (numeric) = 1.8248767227839227 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 9.9774726569344570000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3596363282067169 " "
Order of pole (three term test) = -20.99856195125352 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999999858 " "
y[1] (analytic) = 1.8329696266975273 " "
y[1] (numeric) = 1.8329696266975457 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.0054559519342667000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3531552263600885 " "
Order of pole (three term test) = -21.17707965607731 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999999856 " "
y[1] (analytic) = 1.84087923517595 " "
y[1] (numeric) = 1.8408792351759686 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.0131977403677926000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.346533064831901 " "
Order of pole (three term test) = -21.352313902699322 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7499999999999853 " "
y[1] (analytic) = 1.8486047572649158 " "
y[1] (numeric) = 1.8486047572649347 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.0209749458046502000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3397724928309025 " "
Order of pole (three term test) = -21.524194798081705 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999985 " "
y[1] (analytic) = 1.8561454204186543 " "
y[1] (numeric) = 1.8561454204186731 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.0168271952728074000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.33287621461145683 " "
Order of pole (three term test) = -21.69265379075306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.769999999999985 " "
y[1] (analytic) = 1.8635004705771334 " "
y[1] (numeric) = 1.8635004705771525 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.0247293373442850000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.32584698839170956 " "
Order of pole (three term test) = -21.857623697910793 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7799999999999847 " "
y[1] (analytic) = 1.8706691722414668 " "
y[1] (numeric) = 1.870669172241486 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.0326722070974592000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.31868762525067273 " "
Order of pole (three term test) = -22.019038731976075 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7899999999999845 " "
y[1] (analytic) = 1.8776508085474617 " "
y[1] (numeric) = 1.8776508085474812 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.0406581002416905000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.31140098800467386 " "
Order of pole (three term test) = -22.17683452659138 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999999843 " "
y[1] (analytic) = 1.8844446813373057 " "
y[1] (numeric) = 1.8844446813373255 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.0486893053450423000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3039899900636132 " "
Order of pole (three term test) = -22.330948162050657 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.809999999999984 " "
y[1] (analytic) = 1.8910501112293814 " "
y[1] (numeric) = 1.8910501112294011 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.0450262381191174000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2964575942674875 " "
Order of pole (three term test) = -22.48131819015242 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.819999999999984 " "
y[1] (analytic) = 1.897466437686204 " "
y[1] (numeric) = 1.8974664376862238 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.0414924578284397000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.28880681170363853 " "
Order of pole (three term test) = -22.627884658466485 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999999836 " "
y[1] (analytic) = 1.9036930190804746 " "
y[1] (numeric) = 1.9036930190804946 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.049749841122259000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2810407005052025 " "
Order of pole (three term test) = -22.77058913400488 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999999834 " "
y[1] (analytic) = 1.909729232759243 " "
y[1] (numeric) = 1.909729232759263 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.0464318239701038000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2731623646312278 " "
Order of pole (three term test) = -22.9093747262882 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.849999999999983 " "
y[1] (analytic) = 1.915574475106171 " "
y[1] (numeric) = 1.9155744751061912 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.0548302512257021000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2651749526289518 " "
Order of pole (three term test) = -23.04418610979856 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.859999999999983 " "
y[1] (analytic) = 1.9212281616018951 " "
y[1] (numeric) = 1.9212281616019156 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 1.063283583979437000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.25708165637871977 " "
Order of pole (three term test) = -23.174969545810626 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.869999999999983 " "
y[1] (analytic) = 1.9266897268824772 " "
y[1] (numeric) = 1.9266897268824978 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 1.0717941747393515000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.24888570982204408 " "
Order of pole (three term test) = -23.3016729035925 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8799999999999826 " "
y[1] (analytic) = 1.9319586247959406 " "
y[1] (numeric) = 1.9319586247959613 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 1.0688711441845211000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.24059038767330337 " "
Order of pole (three term test) = -23.42424568096847 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8899999999999824 " "
y[1] (analytic) = 1.9370343284568845 " "
y[1] (numeric) = 1.9370343284569052 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 1.0660703300224218000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.23219900411558989 " "
Order of pole (three term test) = -23.542639024235836 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.899999999999982 " "
y[1] (analytic) = 1.9419163302991724 " "
y[1] (numeric) = 1.9419163302991933 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 1.0748245193312404000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2237149114812163 " "
Order of pole (three term test) = -23.656805747428255 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.909999999999982 " "
y[1] (analytic) = 1.9466041421266889 " "
y[1] (numeric) = 1.9466041421267097 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 1.0722361270715174000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2151414989174014 " "
Order of pole (three term test) = -23.766700350918423 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999999817 " "
y[1] (analytic) = 1.9510972951621572 " "
y[1] (numeric) = 1.9510972951621783 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.0811473892246268000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.206482191037655 " "
Order of pole (three term test) = -23.872279039353025 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9299999999999815 " "
y[1] (analytic) = 1.9553953400940185 " "
y[1] (numeric) = 1.9553953400940396 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.0787709797274923000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.19774044655939355 " "
Order of pole (three term test) = -23.973499738913258 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9399999999999813 " "
y[1] (analytic) = 1.959497847121361 " "
y[1] (numeric) = 1.9594978471213822 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.0765124084656118000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1889197569283196 " "
Order of pole (three term test) = -24.07032211389434 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.949999999999981 " "
y[1] (analytic) = 1.963404405996901 " "
y[1] (numeric) = 1.963404405996922 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.0743704864595925000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.18002364493009892 " "
Order of pole (three term test) = -24.16270758259783 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.959999999999981 " "
y[1] (analytic) = 1.967114626068006 " "
y[1] (numeric) = 1.967114626068027 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.0723440916121131000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1710556632898801 " "
Order of pole (three term test) = -24.250619332530842 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9699999999999807 " "
y[1] (analytic) = 1.970628136315761 " "
y[1] (numeric) = 1.970628136315782 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.0704321672436513000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1620193932602058 " "
Order of pole (three term test) = -24.33402233490634 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9799999999999804 " "
y[1] (analytic) = 1.973944585392069 " "
y[1] (numeric) = 1.97394458539209 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.0686337207226206000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.15291844319786113 " "
Order of pole (three term test) = -24.41288335843907 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9899999999999802 " "
y[1] (analytic) = 1.977063641654786 " "
y[1] (numeric) = 1.9770636416548073 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.0781788518937839000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.14375644713021565 " "
Order of pole (three term test) = -24.487170982432144 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.99999999999998 " "
y[1] (analytic) = 1.9799849932008853 " "
y[1] (numeric) = 1.9799849932009066 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.0765880623338796000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.13453706331161822 " "
Order of pole (three term test) = -24.55685560914899 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.00999999999998 " "
y[1] (analytic) = 1.9827083478976464 " "
y[1] (numeric) = 1.9827083478976677 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.0751093117354152000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1252639727704056 " "
Order of pole (three term test) = -24.621909475466534 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0199999999999796 " "
y[1] (analytic) = 1.9852334334118693 " "
y[1] (numeric) = 1.9852334334118906 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.0737418438580464000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.11594087784708727 " "
Order of pole (three term test) = -24.682306663804752 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0299999999999794 " "
y[1] (analytic) = 1.9875599972371065 " "
y[1] (numeric) = 1.987559997237128 " "
absolute error = 2.153832667772803700000000000000E-14 " "
relative error = 1.0836566799325965000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1065715007242784 " "
Order of pole (three term test) = -24.73802311232888 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.039999999999979 " "
y[1] (analytic) = 1.9896878067189148 " "
y[1] (numeric) = 1.9896878067189363 " "
absolute error = 2.153832667772803700000000000000E-14 " "
relative error = 1.0824977971416387000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.7159581948949200E-2 " "
Order of pole (three term test) = -24.789036624420184 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.049999999999979 " "
y[1] (analytic) = 1.9916166490781186 " "
y[1] (numeric) = 1.9916166490781402 " "
absolute error = 2.153832667772803700000000000000E-14 " "
relative error = 1.0814494188777603000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.77088789475633500E-2 " "
Order of pole (three term test) = -24.835326877411994 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0599999999999787 " "
y[1] (analytic) = 1.9933463314320896 " "
y[1] (numeric) = 1.9933463314321114 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.09165030378939000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.82231645346839300E-2 " "
Order of pole (three term test) = -24.8768754305875 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0699999999999785 " "
y[1] (analytic) = 1.994876680814034 " "
y[1] (numeric) = 1.9948766808140557 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.090812855347704000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.87062254156232600E-2 " "
Order of pole (three term test) = -24.913665732436517 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0799999999999783 " "
y[1] (analytic) = 1.9962075441902887 " "
y[1] (numeric) = 1.9962075441903102 " "
absolute error = 2.153832667772803700000000000000E-14 " "
relative error = 1.0789622922933355000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.91618606837165400E-2 " "
Order of pole (three term test) = -24.945683127168348 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.089999999999978 " "
y[1] (analytic) = 1.9973387884756248 " "
y[1] (numeric) = 1.9973387884756466 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.0894682168196738000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.959388031280357300E-2 " "
Order of pole (three term test) = -24.972914860478436 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.099999999999978 " "
y[1] (analytic) = 1.9982703005465572 " "
y[1] (numeric) = 1.9982703005465787 " "
absolute error = 2.153832667772803700000000000000E-14 " "
relative error = 1.0778485108764804000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.000610364549956300E-2 " "
Order of pole (three term test) = -24.995350084566578 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1099999999999777 " "
y[1] (analytic) = 1.9990019872526543 " "
y[1] (numeric) = 1.999001987252676 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.088561763390722000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.040235787784215700E-2 " "
Order of pole (three term test) = -25.012979862404837 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1199999999999775 " "
y[1] (analytic) = 1.9995337754258558 " "
y[1] (numeric) = 1.9995337754258775 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.0882722537666861000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.078647654090022300E-2 " "
Order of pole (three term test) = -25.025797171253558 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1299999999999772 " "
y[1] (analytic) = 1.999865611887787 " "
y[1] (numeric) = 1.9998656118878089 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.0880916774258755000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.116229797993256600E-2 " "
Order of pole (three term test) = -25.03379690542423 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.139999999999977 " "
y[1] (analytic) = 1.999997463455079 " "
y[1] (numeric) = 1.9999974634551008 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.088019944038384900000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.5336638316842946000E-3 " "
Order of pole (three term test) = -25.03697587828805 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.149999999999977 " "
y[1] (analytic) = 1.9999293169426844 " "
y[1] (numeric) = 1.9999293169427061 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.0880570177309268000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1599999999999766 " "
y[1] (analytic) = 1.9996611791651975 " "
y[1] (numeric) = 1.9996611791652195 " "
absolute error = 2.1982415887578100000000000000E-14 " "
relative error = 1.0993070284414454000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1699999999999764 " "
y[1] (analytic) = 1.999193076936173 " "
y[1] (numeric) = 1.999193076936195 " "
absolute error = 2.1982415887578100000000000000E-14 " "
relative error = 1.0995644263267884000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.179999999999976 " "
y[1] (analytic) = 1.9985250570654436 " "
y[1] (numeric) = 1.9985250570654656 " "
absolute error = 2.1982415887578100000000000000E-14 " "
relative error = 1.0999319628174302000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.189999999999976 " "
y[1] (analytic) = 1.9976571863544397 " "
y[1] (numeric) = 1.9976571863544617 " "
absolute error = 2.1982415887578100000000000000E-14 " "
relative error = 1.1004098219521940000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999999758 " "
y[1] (analytic) = 1.996589551589509 " "
y[1] (numeric) = 1.9965895515895309 " "
absolute error = 2.1982415887578100000000000000E-14 " "
relative error = 1.100998243233199000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999999755 " "
y[1] (analytic) = 1.9953222595332385 " "
y[1] (numeric) = 1.9953222595332603 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.0905692641219482000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999999753 " "
y[1] (analytic) = 1.9938554369137778 " "
y[1] (numeric) = 1.9938554369137995 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.0913715648480123000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.229999999999975 " "
y[1] (analytic) = 1.9921892304121662 " "
y[1] (numeric) = 1.992189230412188 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.0922843548426893000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.239999999999975 " "
y[1] (analytic) = 1.9903238066476656 " "
y[1] (numeric) = 1.9903238066476874 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.0933080943901492000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2499999999999747 " "
y[1] (analytic) = 1.9882593521610978 " "
y[1] (numeric) = 1.9882593521611196 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.0944433008199397000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2599999999999745 " "
y[1] (analytic) = 1.9859960733961914 " "
y[1] (numeric) = 1.985996073396213 " "
absolute error = 2.153832667772803700000000000000E-14 " "
relative error = 1.0845100333403983000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2699999999999743 " "
y[1] (analytic) = 1.9835341966789364 " "
y[1] (numeric) = 1.983534196678958 " "
absolute error = 2.153832667772803700000000000000E-14 " "
relative error = 1.08585608021228000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.279999999999974 " "
y[1] (analytic) = 1.9808739681949534 " "
y[1] (numeric) = 1.9808739681949747 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.0761049120266446000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.289999999999974 " "
y[1] (analytic) = 1.9780156539648734 " "
y[1] (numeric) = 1.9780156539648948 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.0776599280230748000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999999736 " "
y[1] (analytic) = 1.9749595398177382 " "
y[1] (numeric) = 1.9749595398177593 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.0680845375609407000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999999734 " "
y[1] (analytic) = 1.971705931362415 " "
y[1] (numeric) = 1.971705931362436 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.0698470361298866000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.319999999999973 " "
y[1] (analytic) = 1.9682551539570385 " "
y[1] (numeric) = 1.9682551539570596 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.0717227096024362000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.329999999999973 " "
y[1] (analytic) = 1.9646075526764735 " "
y[1] (numeric) = 1.9646075526764946 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.0737125304817415000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3399999999999728 " "
y[1] (analytic) = 1.9607634922778083 " "
y[1] (numeric) = 1.9607634922778294 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.075817534901821000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3499999999999726 " "
y[1] (analytic) = 1.9567233571638796 " "
y[1] (numeric) = 1.9567233571639004 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 1.0666910468736666000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3599999999999723 " "
y[1] (analytic) = 1.9524875513448317 " "
y[1] (numeric) = 1.9524875513448525 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 1.069005169768003000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.369999999999972 " "
y[1] (analytic) = 1.9480564983977169 " "
y[1] (numeric) = 1.9480564983977378 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 1.0714367309223523000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.379999999999972 " "
y[1] (analytic) = 1.9434306414241374 " "
y[1] (numeric) = 1.9434306414241582 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 1.0739870216133823000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3899999999999717 " "
y[1] (analytic) = 1.9386104430059357 " "
y[1] (numeric) = 1.9386104430059563 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 1.0652036015037956000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999999715 " "
y[1] (analytic) = 1.9335963851589366 " "
y[1] (numeric) = 1.933596385158957 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 1.0564823046782715000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999999713 " "
y[1] (analytic) = 1.9283889692847467 " "
y[1] (numeric) = 1.9283889692847669 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.047820713041748000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.419999999999971 " "
y[1] (analytic) = 1.9229887161206136 " "
y[1] (numeric) = 1.9229887161206338 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.0507632665126095000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.429999999999971 " "
y[1] (analytic) = 1.9173961656873537 " "
y[1] (numeric) = 1.917396165687374 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.0538280721414878000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4399999999999706 " "
y[1] (analytic) = 1.91161187723535 " "
y[1] (numeric) = 1.91161187723537 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.0454012491361218000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4499999999999704 " "
y[1] (analytic) = 1.9056364291886274 " "
y[1] (numeric) = 1.9056364291886472 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.0370272910211913000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.45999999999997 " "
y[1] (analytic) = 1.8994704190870109 " "
y[1] (numeric) = 1.8994704190870306 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.0403936612935762000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.46999999999997 " "
y[1] (analytic) = 1.8931144635263726 " "
y[1] (numeric) = 1.8931144635263921 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.0321576222604643000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.47999999999997 " "
y[1] (analytic) = 1.8865691980969717 " "
y[1] (numeric) = 1.886569198096991 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.0239688344304647000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999999696 " "
y[1] (analytic) = 1.8798352773198967 " "
y[1] (numeric) = 1.879835277319916 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.027636881887835100000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999999694 " "
y[1] (analytic) = 1.8729133745816142 " "
y[1] (numeric) = 1.8729133745816333 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.0195792439048852000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.509999999999969 " "
y[1] (analytic) = 1.8658041820666293 " "
y[1] (numeric) = 1.8658041820666482 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.0115633569714909000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.519999999999969 " "
y[1] (analytic) = 1.8585084106882694 " "
y[1] (numeric) = 1.858508410688288 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.0035868929318026000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999999687 " "
y[1] (analytic) = 1.8510267900175925 " "
y[1] (numeric) = 1.8510267900176112 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.007643266660952000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5399999999999685 " "
y[1] (analytic) = 1.8433600682104312 " "
y[1] (numeric) = 1.8433600682104496 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 9.9978851265176330000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5499999999999683 " "
y[1] (analytic) = 1.835509011932577 " "
y[1] (numeric) = 1.8355090119325952 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 9.9196775856099050000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999968 " "
y[1] (analytic) = 1.8274744062831154 " "
y[1] (numeric) = 1.8274744062831334 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 9.8417865317787520000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999968 " "
y[1] (analytic) = 1.8192570547159157 " "
y[1] (numeric) = 1.8192570547159335 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 9.7641882701267610000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5799999999999677 " "
y[1] (analytic) = 1.8108577789592868 " "
y[1] (numeric) = 1.8108577789593046 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 9.8094773650371140000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999999674 " "
y[1] (analytic) = 1.802277418933805 " "
y[1] (numeric) = 1.8022774189338227 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 9.732976513379790000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999999672 " "
y[1] (analytic) = 1.793516832668323 " "
y[1] (numeric) = 1.7935168326683404 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 9.6567140428702910000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.609999999999967 " "
y[1] (analytic) = 1.7845768962141664 " "
y[1] (numeric) = 1.7845768962141837 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 9.7050898848316920000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.619999999999967 " "
y[1] (analytic) = 1.7754585035575308 " "
y[1] (numeric) = 1.7754585035575479 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 9.6298699997599780000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999999666 " "
y[1] (analytic) = 1.7661625665300833 " "
y[1] (numeric) = 1.7661625665301002 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 9.5548339060638430000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6399999999999664 " "
y[1] (analytic) = 1.7566900147177802 " "
y[1] (numeric) = 1.7566900147177966 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 9.3535573304275180000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999966 " "
y[1] (analytic) = 1.7470417953679087 " "
y[1] (numeric) = 1.747041795367925 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 9.2781158427373420000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999966 " "
y[1] (analytic) = 1.7372188732943636 " "
y[1] (numeric) = 1.7372188732943796 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 9.202761839839451000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6699999999999657 " "
y[1] (analytic) = 1.7272222307811667 " "
y[1] (numeric) = 1.7272222307811826 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 9.2560246560581580000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6799999999999655 " "
y[1] (analytic) = 1.7170528674842387 " "
y[1] (numeric) = 1.7170528674842545 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 9.1815268173866730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999999653 " "
y[1] (analytic) = 1.706711800331435 " "
y[1] (numeric) = 1.7067118003314505 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 9.107057408130531000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.699999999999965 " "
y[1] (analytic) = 1.6962000634208534 " "
y[1] (numeric) = 1.6962000634208685 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 8.9016817417461840000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.709999999999965 " "
y[1] (analytic) = 1.6855187079174248 " "
y[1] (numeric) = 1.6855187079174399 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 8.9580928790508840000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999999647 " "
y[1] (analytic) = 1.6746688019477989 " "
y[1] (numeric) = 1.6746688019478135 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 8.7509505807996040000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999999645 " "
y[1] (analytic) = 1.6636514304935308 " "
y[1] (numeric) = 1.6636514304935452 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 8.6754346827601030000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7399999999999642 " "
y[1] (analytic) = 1.6524676952825847 " "
y[1] (numeric) = 1.6524676952825992 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 8.7341491524037920000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999964 " "
y[1] (analytic) = 1.6411187146791626 " "
y[1] (numeric) = 1.6411187146791766 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 8.5239477102738260000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999964 " "
y[1] (analytic) = 1.6296056235718668 " "
y[1] (numeric) = 1.6296056235718805 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 8.4479123698512550000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7699999999999636 " "
y[1] (analytic) = 1.617929573260214 " "
y[1] (numeric) = 1.6179295732602275 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 8.3716381258385540000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.533564701308725 " "
"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] = 3.7799999999999634 " "
y[1] (analytic) = 1.6060917313395051 " "
y[1] (numeric) = 1.6060917313395184 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 8.2950905203842640000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.841424363992722 " "
"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] = 3.789999999999963 " "
y[1] (analytic) = 1.5940932815840678 " "
y[1] (numeric) = 1.594093281584081 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 8.2182340531280630000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.153887416453099 " "
"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] = 3.799999999999963 " "
y[1] (analytic) = 1.5819354238288788 " "
y[1] (numeric) = 1.5819354238288916 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 8.1410321127273270000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.471121810061335 " "
"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] = 3.8099999999999627 " "
y[1] (analytic) = 1.5696193738495818 " "
y[1] (numeric) = 1.5696193738495945 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 8.0634469041280280000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.793302603675023 " "
"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] = 3.8199999999999625 " "
y[1] (analytic) = 1.557146363240912 " "
y[1] (numeric) = 1.5571463632409241 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 7.8428422396073040000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.120612368721133 " "
"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] = 3.8299999999999623 " "
y[1] (analytic) = 1.5445176392935354 " "
y[1] (numeric) = 1.5445176392935474 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 7.7632060398067850000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.453241621632433 " "
"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] = 3.839999999999962 " "
y[1] (analytic) = 1.5317344648693234 " "
y[1] (numeric) = 1.531734464869335 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 7.5380685888573240000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.791389285837763 " "
"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] = 3.849999999999962 " "
y[1] (analytic) = 1.5187981182750654 " "
y[1] (numeric) = 1.5187981182750767 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 7.4560764297218380000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.135263185710787 " "
"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] = 3.8599999999999617 " "
y[1] (analytic) = 1.5057098931346409 " "
y[1] (numeric) = 1.505709893134652 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 7.373419207028350000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.485080575107062 " "
"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] = 3.8699999999999615 " "
y[1] (analytic) = 1.4924710982596572 " "
y[1] (numeric) = 1.4924710982596678 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 7.1412713109351090000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.841068703369324 " "
"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] = 3.8799999999999613 " "
y[1] (analytic) = 1.479083057518569 " "
y[1] (numeric) = 1.4790830575185794 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 7.0557879616205740000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.20346542195674 " "
"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] = 3.889999999999961 " "
y[1] (analytic) = 1.4655471097042942 " "
y[1] (numeric) = 1.4655471097043042 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 6.8179365613450060000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.572519835161494 " "
"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] = 3.899999999999961 " "
y[1] (analytic) = 1.4518646084003342 " "
y[1] (numeric) = 1.451864608400344 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 6.7292518601069360000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.94849299871636 " "
"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] = 3.9099999999999606 " "
y[1] (analytic) = 1.4380369218454172 " "
y[1] (numeric) = 1.4380369218454268 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 6.6395499772868180000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 19.331658670476116 " "
"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] = 3.9199999999999604 " "
y[1] (analytic) = 1.4240654327966757 " "
y[1] (numeric) = 1.424065432796685 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 6.5487674878369430000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 19.267525626352306 " "
"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] = 3.92999999999996 " "
y[1] (analytic) = 1.409951538391372 " "
y[1] (numeric) = 1.409951538391381 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.2993542367665830000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.88599376702037 " "
"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] = 3.93999999999996 " "
y[1] (analytic) = 1.3956966500071848 " "
y[1] (numeric) = 1.3956966500071935 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 6.2046001128050590000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.511972355076207 " "
"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] = 3.9499999999999598 " "
y[1] (analytic) = 1.3813021931210736 " "
y[1] (numeric) = 1.3813021931210818 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 5.9477574300108580000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 18.14516914423352 " "
"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] = 3.9599999999999596 " "
y[1] (analytic) = 1.3667696071667315 " "
y[1] (numeric) = 1.3667696071667395 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 5.8485393115168920000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.785305894116792 " "
"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] = 3.9699999999999593 " "
y[1] (analytic) = 1.3521003453906437 " "
y[1] (numeric) = 1.3521003453906513 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 5.5835475474787230000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.432117519791618 " "
"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] = 3.979999999999959 " "
y[1] (analytic) = 1.3372958747067634 " "
y[1] (numeric) = 1.3372958747067707 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 5.4793199479006630000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 17.08535130201765 " "
"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] = 3.989999999999959 " "
y[1] (analytic) = 1.3223576755498219 " "
y[1] (numeric) = 1.3223576755498287 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 5.2053864699003880000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.744766153210122 " "
"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] = 3.9999999999999587 " "
y[1] (analytic) = 1.3072872417272863 " "
y[1] (numeric) = 1.307287241727293 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 5.0955428425580570000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.410131934563086 " "
"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] = 4.009999999999959 " "
y[1] (analytic) = 1.2920860802699798 " "
y[1] (numeric) = 1.292086080269987 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.499190391491820000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 16.081228820205748 " "
"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] = 4.019999999999959 " "
y[1] (analytic) = 1.2767557112813819 " "
y[1] (numeric) = 1.2767557112813888 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 5.3913075867643050000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.75784670464002 " "
"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] = 4.0299999999999585 " "
y[1] (analytic) = 1.2612976677856154 " "
y[1] (numeric) = 1.2612976677856218 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 5.1052925152323390000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.439784650043997 " "
"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] = 4.039999999999958 " "
y[1] (analytic) = 1.2457134955741482 " "
y[1] (numeric) = 1.2457134955741542 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.8126670813762530000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 15.126850370331084 " "
"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] = 4.049999999999958 " "
y[1] (analytic) = 1.2300047530512148 " "
y[1] (numeric) = 1.2300047530512204 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.5130842863455550000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.818859749127565 " "
"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] = 4.059999999999958 " "
y[1] (analytic) = 1.2141730110779767 " "
y[1] (numeric) = 1.214173011077982 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.38905367651802270000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.515636389078503 " "
"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] = 4.069999999999958 " "
y[1] (analytic) = 1.1982198528154382 " "
y[1] (numeric) = 1.1982198528154433 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.2621776807284760000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 14.217011190115072 " "
"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] = 4.079999999999957 " "
y[1] (analytic) = 1.1821468735661316 " "
y[1] (numeric) = 1.1821468735661362 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.9444647764953070000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
Radius of convergence (ratio test) for eq 1 = 13.922821954517971 " "
"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] = 4.089999999999957 " "
y[1] (analytic) = 1.1659556806145874 " "
y[1] (numeric) = 1.1659556806145916 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.6183600832510170000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999957 " "
y[1] (analytic) = 1.149647893066608 " "
y[1] (numeric) = 1.149647893066612 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.47654522115407150000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999957 " "
y[1] (analytic) = 1.133225141687359 " "
y[1] (numeric) = 1.1332251416873627 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.1350466452858180000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.119999999999957 " "
y[1] (analytic) = 1.1166890687382924 " "
y[1] (numeric) = 1.1166890687382955 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.7837869609154170000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999956 " "
y[1] (analytic) = 1.1000413278129229 " "
y[1] (numeric) = 1.1000413278129257 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.6240649246919107000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999956 " "
y[1] (analytic) = 1.0832835836714703 " "
y[1] (numeric) = 1.0832835836714727 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.254710300231120000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.149999999999956 " "
y[1] (analytic) = 1.066417512074384 " "
y[1] (numeric) = 1.066417512074386 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.87393907329786100000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999956 " "
y[1] (analytic) = 1.0494447996147682 " "
y[1] (numeric) = 1.04944479961477 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.69266343503947800000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.1699999999999555 " "
y[1] (analytic) = 1.0323671435497255 " "
y[1] (numeric) = 1.032367143549727 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.50558088194362730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.179999999999955 " "
y[1] (analytic) = 1.0151862516306311 " "
y[1] (numeric) = 1.015186251630632 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.74892088297589700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999955 " "
y[1] (analytic) = 0.9979038419323591 " "
y[1] (numeric) = 0.9979038419323598 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.67533069604362100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999955 " "
y[1] (analytic) = 0.9805216426814778 " "
y[1] (numeric) = 0.9805216426814781 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.396833816708967000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.209999999999955 " "
y[1] (analytic) = 0.963041392083427 " "
y[1] (numeric) = 0.9630413920834269 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.152830017226278700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.2199999999999545 " "
y[1] (analytic) = 0.9454648381486996 " "
y[1] (numeric) = 0.9454648381486991 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.87130784683155200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999954 " "
y[1] (analytic) = 0.9277937385180421 " "
y[1] (numeric) = 0.9277937385180413 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 9.57301588517730200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.239999999999954 " "
y[1] (analytic) = 0.9100298602866916 " "
y[1] (numeric) = 0.9100298602866904 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.34198379677666490000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999954 " "
y[1] (analytic) = 0.8921749798276682 " "
y[1] (numeric) = 0.8921749798276666 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 1.86660080655860730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999954 " "
y[1] (analytic) = 0.8742308826141387 " "
y[1] (numeric) = 0.8742308826141367 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 2.28589664820536970000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.269999999999953 " "
y[1] (analytic) = 0.8561993630408712 " "
y[1] (numeric) = 0.8561993630408687 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.8527125335629927000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999953 " "
y[1] (analytic) = 0.8380822242447966 " "
y[1] (numeric) = 0.8380822242447937 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 3.44426809270000900000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.289999999999953 " "
y[1] (analytic) = 0.819881277924697 " "
y[1] (numeric) = 0.8198812779246938 " "
absolute error = 3.219646771412954000000000000000E-15 " "
relative error = 3.92696705986822940000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.299999999999953 " "
y[1] (analytic) = 0.8015983441600372 " "
y[1] (numeric) = 0.8015983441600335 " "
absolute error = 3.6637359812630166000000000000000E-15 " "
relative error = 4.5705383599589380000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3099999999999525 " "
y[1] (analytic) = 0.7832352512289577 " "
y[1] (numeric) = 0.7832352512289537 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 5.1029405052687120000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.319999999999952 " "
y[1] (analytic) = 0.7647938354254492 " "
y[1] (numeric) = 0.7647938354254448 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 5.8066525811236310000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.329999999999952 " "
y[1] (analytic) = 0.7462759408757241 " "
y[1] (numeric) = 0.7462759408757194 " "
absolute error = 4.773959005888173000000000000000E-15 " "
relative error = 6.3970426278061820000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999952 " "
y[1] (analytic) = 0.7276834193538062 " "
y[1] (numeric) = 0.727683419353801 " "
absolute error = 5.218048215738236000000000000000E-15 " "
relative error = 7.170766952986151000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.349999999999952 " "
y[1] (analytic) = 0.7090181300963536 " "
y[1] (numeric) = 0.7090181300963481 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 7.8292992625892390000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3599999999999515 " "
y[1] (analytic) = 0.6902819396167379 " "
y[1] (numeric) = 0.6902819396167319 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 8.6851531075904090000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999951 " "
y[1] (analytic) = 0.6714767215183935 " "
y[1] (numeric) = 0.6714767215183871 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 9.5897494826997040000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.379999999999951 " "
y[1] (analytic) = 0.6526043563074594 " "
y[1] (numeric) = 0.6526043563074526 " "
absolute error = 6.772360450213455000000000000000E-15 " "
relative error = 1.0377436780429358000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.389999999999950 " "
y[1] (analytic) = 0.6336667312047297 " "
y[1] (numeric) = 0.6336667312047225 " "
absolute error = 7.216449660063518000000000000000E-15 " "
relative error = 1.1388399145310303000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999950 " "
y[1] (analytic) = 0.6146657399569333 " "
y[1] (numeric) = 0.6146657399569257 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 1.2282312282412265000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.40999999999995 " "
y[1] (analytic) = 0.5956032826473611 " "
y[1] (numeric) = 0.5956032826473531 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 1.3421023708551152000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.41999999999995 " "
y[1] (analytic) = 0.5764812655058584 " "
y[1] (numeric) = 0.5764812655058501 " "
absolute error = 8.326672684688674000000000000000E-15 " "
relative error = 1.4443960598410904000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.42999999999995 " "
y[1] (analytic) = 0.5573016007182047 " "
y[1] (numeric) = 0.557301600718196 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 1.5538694991933020000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.43999999999995 " "
y[1] (analytic) = 0.5380662062348956 " "
y[1] (numeric) = 0.5380662062348865 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 1.6919532757186312000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4499999999999496 " "
y[1] (analytic) = 0.51877700557935 " "
y[1] (numeric) = 0.5187770055793406 " "
absolute error = 9.43689570931383100000000000000E-15 " "
relative error = 1.819065920004506000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999950 " "
y[1] (analytic) = 0.4994359276555593 " "
y[1] (numeric) = 0.4994359276555494 " "
absolute error = 9.880984919163893000000000000000E-15 " "
relative error = 1.9784289379314354000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.469999999999950 " "
y[1] (analytic) = 0.48004490655519816 " "
y[1] (numeric) = 0.4800449065551879 " "
absolute error = 1.026956297778269800000000000000E-14 " "
relative error = 2.1392921448697527000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.479999999999949 " "
y[1] (analytic) = 0.4606058813642176 " "
y[1] (numeric) = 0.46060588136420694 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 2.31393941493633000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999949 " "
y[1] (analytic) = 0.4411207959689376 " "
y[1] (numeric) = 0.4411207959689265 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 2.5168231350020850000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4999999999999485 " "
y[1] (analytic) = 0.42159159886166014 " "
y[1] (numeric) = 0.4215915988616486 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 2.73874514750243000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.509999999999948 " "
y[1] (analytic) = 0.40202024294582167 " "
y[1] (numeric) = 0.40202024294580974 " "
absolute error = 1.193489751472043300000000000000E-14 " "
relative error = 2.9687304866210040000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999948 " "
y[1] (analytic) = 0.3824086853407044 " "
y[1] (numeric) = 0.382408685340692 " "
absolute error = 1.237898672457049500000000000000E-14 " "
relative error = 3.2371091973346583000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.529999999999948 " "
y[1] (analytic) = 0.36275888718572585 " "
y[1] (numeric) = 0.3627588871857131 " "
absolute error = 1.2767564783189300000000000000E-14 " "
relative error = 3.5195732576642685000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.539999999999948 " "
y[1] (analytic) = 0.34307281344432683 " "
y[1] (numeric) = 0.3430728134443136 " "
absolute error = 1.321165399303936300000000000000E-14 " "
relative error = 3.850976665973366000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999947 " "
y[1] (analytic) = 0.32335243270747643 " "
y[1] (numeric) = 0.3233524327074628 " "
absolute error = 1.365574320288942500000000000000E-14 " "
relative error = 4.2231762688617874000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.559999999999947 " "
y[1] (analytic) = 0.3035997169968147 " "
y[1] (numeric) = 0.30359971699680066 " "
absolute error = 1.40443212615082300000000000000E-14 " "
relative error = 4.625933581372732000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.569999999999947 " "
y[1] (analytic) = 0.2838166415674523 " "
y[1] (numeric) = 0.2838166415674378 " "
absolute error = 1.448841047135829300000000000000E-14 " "
relative error = 5.104848817652913000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999947 " "
y[1] (analytic) = 0.2640051847104462 " "
y[1] (numeric) = 0.2640051847104313 " "
absolute error = 1.493249968120835500000000000000E-14 " "
relative error = 5.656138798026228000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.589999999999947 " "
y[1] (analytic) = 0.2441673275549726 " "
y[1] (numeric) = 0.2441673275549573 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 6.274827141390457000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.599999999999946 " "
y[1] (analytic) = 0.22430505387021565 " "
y[1] (numeric) = 0.2243050538701999 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 7.0284492826448090000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999946 " "
y[1] (analytic) = 0.20442034986699192 " "
y[1] (numeric) = 0.20442034986697574 " "
absolute error = 1.618150058391165700000000000000E-14 " "
relative error = 7.915797323720611000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.619999999999946 " "
y[1] (analytic) = 0.1845152039991312 " "
y[1] (numeric) = 0.1845152039991146 " "
absolute error = 1.65978342181460900000000000000E-14 " "
relative error = 8.995374830046114000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.629999999999946 " "
y[1] (analytic) = 0.16459160676463275 " "
y[1] (numeric) = 0.16459160676461573 " "
absolute error = 1.701416785238052400000000000000E-14 " "
relative error = 1.033720259910392200000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6399999999999455 " "
y[1] (analytic) = 0.14465155050661704 " "
y[1] (numeric) = 0.1446515505065996 " "
absolute error = 1.743050148661495800000000000000E-14 " "
relative error = 1.204999284526687800000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999945 " "
y[1] (analytic) = 0.12469702921409323 " "
y[1] (numeric) = 0.12469702921407537 " "
absolute error = 1.786071290865720600000000000000E-14 " "
relative error = 1.432328662617296200000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.659999999999945 " "
y[1] (analytic) = 0.10473003832256185 " "
y[1] (numeric) = 0.10473003832254357 " "
absolute error = 1.82770465428916400000000000000E-14 " "
relative error = 1.745158011553428200000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999945 " "
y[1] (analytic) = 8.47525745144729600E-2 " "
y[1] (numeric) = 8.47525745144542600E-2 " "
absolute error = 1.870725796493388800000000000000E-14 " "
relative error = 2.207279020384130300000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999945 " "
y[1] (analytic) = 6.47666355195595300E-2 " "
y[1] (numeric) = 6.4766635519540400E-2 " "
absolute error = 1.913746938697613600000000000000E-14 " "
relative error = 2.95483457392141600000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.689999999999944 " "
y[1] (analytic) = 4.47742199150661700E-2 " "
y[1] (numeric) = 4.477421991504660400E-2 " "
absolute error = 1.956768080901838400000000000000E-14 " "
relative error = 4.370300777129567700000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999944 " "
y[1] (analytic) = 2.47773269258930200E-2 " "
y[1] (numeric) = 2.477732692587303300E-2 " "
absolute error = 1.99874838902047700000000000000E-14 " "
relative error = 8.06684431697806600000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999944 " "
y[1] (analytic) = 4.777956224674987000E-3 " "
y[1] (numeric) = 4.777956224654572600E-3 " "
absolute error = 2.041422586529506600000000000000E-14 " "
relative error = 4.2725853702612590000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
"NO REAL POLE (three term test) for Equation 1"
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.719999999999944 " "
y[1] (analytic) = -1.522189226818389800E-2 " "
y[1] (numeric) = -1.52218922682047400E-2 " "
absolute error = 2.084270256386133700000000000000E-14 " "
relative error = 1.36925831536896400000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.338913477308628000E-3 " "
Order of pole (three term test) = -0.894257651745016 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999944 " "
y[1] (analytic) = -3.522021858450083400E-2 " "
y[1] (numeric) = -3.5220218584522100E-2 " "
absolute error = 2.126770981547565500000000000000E-14 " "
relative error = 6.03849455517996700000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.697853631389673600E-2 " "
Order of pole (three term test) = -0.9003549199517773 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999943 " "
y[1] (analytic) = -5.5215022908309400E-2 " "
y[1] (numeric) = -5.52150229083310900E-2 " "
absolute error = 2.169098234361399600000000000000E-14 " "
relative error = 3.928456641163447500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.661135398006439500E-2 " "
Order of pole (three term test) = -0.9112844839455716 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.749999999999943 " "
y[1] (analytic) = -7.5204305775839500E-2 " "
y[1] (numeric) = -7.52043057758616200E-2 " "
absolute error = 2.212119376565624400000000000000E-14 " "
relative error = 2.941479684898973000000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.623350556415961000E-2 " "
Order of pole (three term test) = -0.9270419540531252 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999943 " "
y[1] (analytic) = -9.51860682754620700E-2 " "
y[1] (numeric) = -9.51860682754846100E-2 " "
absolute error = 2.255140518769849200000000000000E-14 " "
relative error = 2.369191794164272300000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.58411344559086440E-2 " "
Order of pole (three term test) = -0.9476210015836062 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999943 " "
y[1] (analytic) = -0.11515831224757855 " "
y[1] (numeric) = -0.11515831224760152 " "
absolute error = 2.296773882193292600000000000000E-14 " "
relative error = 1.994449065261971500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.54303899016334400E-2 " "
Order of pole (three term test) = -0.9730133614015779 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.7799999999999425 " "
y[1] (analytic) = -0.1351190404844352 " "
y[1] (numeric) = -0.1351190404844586 " "
absolute error = 2.339795024397517400000000000000E-14 " "
relative error = 1.73165455883106700000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.49974285570490400E-2 " "
Order of pole (three term test) = -1.0032088352871376 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999942 " "
y[1] (analytic) = -0.15506625692984224 " "
y[1] (numeric) = -0.1550662569298661 " "
absolute error = 2.384203945382523700000000000000E-14 " "
relative error = 1.537538851190060300000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.45384160370016000E-2 " "
Order of pole (three term test) = -1.038195296081815 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999942 " "
y[1] (analytic) = -0.17499796687877778 " "
y[1] (numeric) = -0.17499796687880204 " "
absolute error = 2.42583730880596700000000000000E-14 " "
relative error = 1.386208852635619500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.40495284615051700E-2 " "
Order of pole (three term test) = -1.0779586926184568 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.809999999999942 " "
y[1] (analytic) = -0.19491217717685655 " "
y[1] (numeric) = -0.19491217717688125 " "
absolute error = 2.470246229790973300000000000000E-14 " "
relative error = 1.267363725330284000000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.35269539974408400E-2 " "
Order of pole (three term test) = -1.1224830554330052 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999942 " "
y[1] (analytic) = -0.21480689641964393 " "
y[1] (numeric) = -0.21480689641966905 " "
absolute error = 2.511879593214416700000000000000E-14 " "
relative error = 1.169366363502241400000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.10296689439528019 " "
Order of pole (three term test) = -1.1717505032557325 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.8299999999999415 " "
y[1] (analytic) = -0.23468013515179448 " "
y[1] (numeric) = -0.23468013515182004 " "
absolute error = 2.55628851419942300000000000000E-14 " "
relative error = 1.089264974449575300000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.11236556652020069 " "
Order of pole (three term test) = -1.2257412502791736 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.839999999999941 " "
y[1] (analytic) = -0.254529906065996 " "
y[1] (numeric) = -0.254529906066022 " "
absolute error = 2.597921877622866300000000000000E-14 " "
relative error = 1.020674512388835700000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.12171920387696034 " "
Order of pole (three term test) = -1.2844336141996577 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.849999999999941 " "
y[1] (analytic) = -0.27435422420169847 " "
y[1] (numeric) = -0.2743542242017249 " "
absolute error = 2.642330798607872600000000000000E-14 " "
relative error = 9.631092090148742000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.13102405812790505 " "
Order of pole (three term test) = -1.347804025029032 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999940 " "
y[1] (analytic) = -0.2941511071436085 " "
y[1] (numeric) = -0.29415110714363535 " "
absolute error = 2.686739719592879000000000000000E-14 " "
relative error = 9.133875937720597000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.14027640060347835 " "
Order of pole (three term test) = -1.415827034672798 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.869999999999940 " "
y[1] (analytic) = -0.3139185752199293 " "
y[1] (numeric) = -0.3139185752199566 " "
absolute error = 2.73114864057788500000000000000E-14 " "
relative error = 8.700181690951102000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1494725238046181 " "
Order of pole (three term test) = -1.4884753272706304 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.87999999999994 " "
y[1] (analytic) = -0.33365465170032604 " "
y[1] (numeric) = -0.33365465170035374 " "
absolute error = 2.770006446439765600000000000000E-14 " "
relative error = 8.302016568100071000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.15860874289641474 " "
Order of pole (three term test) = -1.565719730294838 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.88999999999994 " "
y[1] (analytic) = -0.3533573629935974 " "
y[1] (numeric) = -0.35335736299362547 " "
absolute error = 2.80886425230164600000000000000E-14 " "
relative error = 7.949075203938911000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.16768139719242278 " "
Order of pole (three term test) = -1.6475292264020929 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.89999999999994 " "
y[1] (analytic) = -0.37302473884503284 " "
y[1] (numeric) = -0.3730247388450613 " "
absolute error = 2.847722058163526500000000000000E-14 " "
relative error = 7.634137261192661000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.17668685162900896 " "
Order of pole (three term test) = -1.7338709660333504 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.90999999999994 " "
y[1] (analytic) = -0.3926548125334367 " "
y[1] (numeric) = -0.3926548125334656 " "
absolute error = 2.89213097914853300000000000000E-14 " "
relative error = 7.365581388111097000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.18562149822913657 " "
Order of pole (three term test) = -1.824710280756647 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9199999999999395 " "
y[1] (analytic) = -0.4122456210677985 " "
y[1] (numeric) = -0.4122456210678278 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 7.109811809325147000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.19448175755498098 " "
Order of pole (three term test) = -1.9200106973470839 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.929999999999940 " "
y[1] (analytic) = -0.43179520538359034 " "
y[1] (numeric) = -0.4317952053836201 " "
absolute error = 2.975397705995419500000000000000E-14 " "
relative error = 6.890761335231108000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.20326408014878247 " "
Order of pole (three term test) = -2.019733952598044 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.939999999999939 " "
y[1] (analytic) = -0.451301610538672 " "
y[1] (numeric) = -0.45130161053870216 " "
absolute error = 3.014255511857300000000000000E-14 " "
relative error = 6.679026711780388000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.21196494796134271 " "
Order of pole (three term test) = -2.12384000885733 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.949999999999939 " "
y[1] (analytic) = -0.47076288590878324 " "
y[1] (numeric) = -0.47076288590881377 " "
absolute error = 3.053113317719180500000000000000E-14 " "
relative error = 6.485458835237838000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.22058087576758392 " "
Order of pole (three term test) = -2.2322870702816906 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.959999999999939 " "
y[1] (analytic) = -0.4901770853826047 " "
y[1] (numeric) = -0.4901770853826356 " "
absolute error = 3.09197112358106100000000000000E-14 " "
relative error = 6.3078654955231980000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.22910841256858552 " "
Order of pole (three term test) = -2.3450315998027733 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9699999999999385 " "
y[1] (analytic) = -0.5095422675563673 " "
y[1] (numeric) = -0.5095422675563988 " "
absolute error = 3.14193115968919300000000000000E-14 " "
relative error = 6.1661835724778650000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.23754414297952903 " "
Order of pole (three term test) = -2.462028336797388 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.979999999999938 " "
y[1] (analytic) = -0.5288564959279916 " "
y[1] (numeric) = -0.5288564959280234 " "
absolute error = 3.18634008067419900000000000000E-14 " "
relative error = 6.024961601507959000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2458846886029823 " "
Order of pole (three term test) = -2.5832303154545624 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.989999999999938 " "
y[1] (analytic) = -0.5481178390907353 " "
y[1] (numeric) = -0.5481178390907675 " "
absolute error = 3.21964677141295400000000000000E-14 " "
relative error = 5.874004715398388000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2541267093869622 " "
Order of pole (three term test) = -2.7085888838316365 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.999999999999938 " "
y[1] (analytic) = -0.5673243709263333 " "
y[1] (numeric) = -0.5673243709263659 " "
absolute error = 3.2640556923979600000000000000E-14 " "
relative error = 5.753420546817644000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2622669049672212 " "
Order of pole (three term test) = -2.8380537235913152 " "
"NO COMPLEX POLE (six term test) for Equation 1"
"Finished!"
"diff ( y , x , 1 ) = 2.0 * sin(x);"
Iterations = 491
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 2 Minutes 13 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 10 Seconds
"Time to Timeout "= 0 Years 0 Days 0 Hours 0 Minutes 46 Seconds
Percent Done = 100.40816326530485 "%"
(%o58) true
(%o58) diffeq.max