##############ECHO OF PROBLEM#################
##############temp/expt_lin_cpostode.ode#################
diff  (  y  ,  x  ,  1  )   =   expt (  ( 0.2  *  x  +  0.3 )   ,  2.0 )  ; 
!
#BEGIN FIRST INPUT BLOCK
# Digits:=32; ELIMINATED in preodein.rb
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 
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
$glob_type_given_pole=3 
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
$glob_desired_digits_correct=16 
$glob_max_minutes=3.0 
$glob_subiter_method=3 
$glob_max_iter=100000000 
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
def exact_soln_y (x)
return(5.0/3.0 * expt((0.2 * x + 0.3),3.0))  
end
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   1.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               4900000.000000001
step_error                    1.5058465048420852e-21
est_needed_step_err           1.5058465048420852e-21
opt_iter                        1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   1.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               4900000.000000001
step_error                    1.5058465048420852e-21
est_needed_step_err           1.5058465048420852e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   2.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               2450000.0000000005
step_error                    2.1295885499997994e-21
est_needed_step_err           2.1295885499997994e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   4.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               1225000.0000000002
step_error                    3.0116930096841704e-21
est_needed_step_err           3.0116930096841704e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   8.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               612500.0000000001
step_error                    4.259177099999599e-21
est_needed_step_err           4.259177099999599e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   1.6e-05
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               306250.00000000006
step_error                    6.023386019368341e-21
est_needed_step_err           6.023386019368341e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        6
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   3.2e-05
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               153125.00000000003
step_error                    8.518354199999198e-21
est_needed_step_err           8.518354199999198e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        7
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   6.4e-05
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               76562.50000000001
step_error                    1.2046772038736681e-20
est_needed_step_err           1.2046772038736681e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        8
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.000128
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               38281.25000000001
step_error                    1.7036708399998395e-20
est_needed_step_err           1.7036708399998395e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        9
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.000256
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               19140.625000000004
step_error                    2.4093544077473363e-20
est_needed_step_err           2.4093544077473363e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        10
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.000512
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               9570.312500000002
step_error                    3.407341679999679e-20
est_needed_step_err           3.407341679999679e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        11
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.001024
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               4785.156250000001
step_error                    4.8187088154946726e-20
est_needed_step_err           4.8187088154946726e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        12
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.002048
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               2392.5781250000005
step_error                    6.814683359999358e-20
est_needed_step_err           6.814683359999358e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        13
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.004096
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               1196.2890625000002
step_error                    9.637417630989345e-20
est_needed_step_err           9.637417630989345e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.008192
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               598.1445312500001
step_error                    1.3629366719998716e-19
est_needed_step_err           1.3629366719998716e-19
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        15
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.016384
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               299.07226562500006
step_error                    1.927483526197869e-19
est_needed_step_err           1.927483526197869e-19
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.032768
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               149.53613281250003
step_error                    2.7258733439997433e-19
est_needed_step_err           2.7258733439997433e-19
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        17
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.05461333333333335
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.065536
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               74.76806640625001
step_error                    3.854967052395738e-19
est_needed_step_err           3.854967052395738e-19
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      0.0
estimated_step_error          0.0
Double H and LOOP
opt_iter                        18
SETTING H FOR MAX H
SETTING H FOR DISPLAY INTERVAL
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                             0.1 
y[1] (closed_form)               0.05461333333333335 
y[1] (numeric)                   0.05461333333333335 
absolute error                   0.0 
relative error                   0.0%
Desired digits                   16 
Estimated correct digits         14 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.2 
y[1] (closed_form)               0.06550666666666666 
y[1] (numeric)                   0.06550666666666669 
absolute error                   2.7755575615628914e-17 
relative error                   4.237061207352267e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.30000000000000004 
y[1] (closed_form)               0.07776 
y[1] (numeric)                   0.07776000000000002 
absolute error                   2.7755575615628914e-17 
relative error                   3.5693898682650354e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.4 
y[1] (closed_form)               0.09145333333333334 
y[1] (numeric)                   0.09145333333333336 
absolute error                   1.3877787807814457e-17 
relative error                   1.5174720594636013e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5 
y[1] (closed_form)               0.1066666666666667 
y[1] (numeric)                   0.10666666666666669 
absolute error                   1.3877787807814457e-17 
relative error                   1.3010426069826048e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.6 
y[1] (closed_form)               0.12347999999999998 
y[1] (numeric)                   0.12348000000000002 
absolute error                   4.163336342344337e-17 
relative error                   3.371668563608955e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.7 
y[1] (closed_form)               0.14197333333333328 
y[1] (numeric)                   0.14197333333333334 
absolute error                   5.551115123125783e-17 
relative error                   3.909970268918424e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.7999999999999999 
y[1] (closed_form)               0.16222666666666663 
y[1] (numeric)                   0.16222666666666669 
absolute error                   5.551115123125783e-17 
relative error                   3.421826532706779e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.8999999999999999 
y[1] (closed_form)               0.18431999999999998 
y[1] (numeric)                   0.18432 
absolute error                   2.7755575615628914e-17 
relative error                   1.505836350674312e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.9999999999999999 
y[1] (closed_form)               0.20833333333333334 
y[1] (numeric)                   0.20833333333333334 
absolute error                   0.0 
relative error                   0.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.0999999999999999 
y[1] (closed_form)               0.2343466666666667 
y[1] (numeric)                   0.23434666666666668 
absolute error                   2.7755575615628914e-17 
relative error                   1.1843810714452481e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.2 
y[1] (closed_form)               0.26244000000000006 
y[1] (numeric)                   0.26244 
absolute error                   5.551115123125783e-17 
relative error                   2.1151939960089092e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.3 
y[1] (closed_form)               0.2926933333333334 
y[1] (numeric)                   0.29269333333333336 
absolute error                   5.551115123125783e-17 
relative error                   1.8965635670300362e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.4000000000000001 
y[1] (closed_form)               0.3251866666666668 
y[1] (numeric)                   0.3251866666666667 
absolute error                   1.1102230246251565e-16 
relative error                   3.4141099203282915e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.5000000000000002 
y[1] (closed_form)               0.3600000000000002 
y[1] (numeric)                   0.36000000000000004 
absolute error                   1.6653345369377348e-16 
relative error                   4.6259292692714826e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.6000000000000003 
y[1] (closed_form)               0.39721333333333353 
y[1] (numeric)                   0.3972133333333334 
absolute error                   1.1102230246251565e-16 
relative error                   2.7950296011173407e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.7000000000000004 
y[1] (closed_form)               0.43690666666666694 
y[1] (numeric)                   0.4369066666666668 
absolute error                   1.6653345369377348e-16 
relative error                   3.811648262644349e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.8000000000000005 
y[1] (closed_form)               0.47916000000000036 
y[1] (numeric)                   0.47916000000000014 
absolute error                   2.220446049250313e-16 
relative error                   4.634038837236646e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.9000000000000006 
y[1] (closed_form)               0.5240533333333337 
y[1] (numeric)                   0.5240533333333335 
absolute error                   2.220446049250313e-16 
relative error                   4.2370612073522635e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.0000000000000004 
y[1] (closed_form)               0.5716666666666671 
y[1] (numeric)                   0.5716666666666669 
absolute error                   2.220446049250313e-16 
relative error                   3.884162185277513e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.1000000000000005 
y[1] (closed_form)               0.6220800000000005 
y[1] (numeric)                   0.6220800000000002 
absolute error                   3.3306690738754696e-16 
relative error                   5.354084802397548e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.2000000000000006 
y[1] (closed_form)               0.6753733333333339 
y[1] (numeric)                   0.6753733333333336 
absolute error                   3.3306690738754696e-16 
relative error                   4.931596954586303e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.3000000000000007 
y[1] (closed_form)               0.7316266666666674 
y[1] (numeric)                   0.731626666666667 
absolute error                   4.440892098500626e-16 
relative error                   6.0698882378544e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.400000000000001 
y[1] (closed_form)               0.7909200000000008 
y[1] (numeric)                   0.7909200000000003 
absolute error                   5.551115123125783e-16 
relative error                   7.018554497453316e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.500000000000001 
y[1] (closed_form)               0.8533333333333343 
y[1] (numeric)                   0.8533333333333337 
absolute error                   5.551115123125783e-16 
relative error                   6.505213034913019e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.600000000000001 
y[1] (closed_form)               0.9189466666666676 
y[1] (numeric)                   0.9189466666666671 
absolute error                   4.440892098500626e-16 
relative error                   4.8325895937021607e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.700000000000001 
y[1] (closed_form)               0.9878400000000012 
y[1] (numeric)                   0.9878400000000005 
absolute error                   6.661338147750939e-16 
relative error                   6.743337127217901e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.800000000000001 
y[1] (closed_form)               1.0600933333333347 
y[1] (numeric)                   1.060093333333334 
absolute error                   6.661338147750939e-16 
relative error                   6.283727987237851e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.9000000000000012 
y[1] (closed_form)               1.135786666666668 
y[1] (numeric)                   1.1357866666666674 
absolute error                   6.661338147750939e-16 
relative error                   5.864955403377627e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.0000000000000013 
y[1] (closed_form)               1.2150000000000014 
y[1] (numeric)                   1.2150000000000007 
absolute error                   6.661338147750939e-16 
relative error                   5.4825828376550875e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.1000000000000014 
y[1] (closed_form)               1.297813333333335 
y[1] (numeric)                   1.2978133333333342 
absolute error                   8.881784197001252e-16 
relative error                   6.843653065413547e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.2000000000000015 
y[1] (closed_form)               1.3843066666666684 
y[1] (numeric)                   1.3843066666666675 
absolute error                   8.881784197001252e-16 
relative error                   6.416052462123933e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.3000000000000016 
y[1] (closed_form)               1.4745600000000019 
y[1] (numeric)                   1.4745600000000008 
absolute error                   1.1102230246251565e-15 
relative error                   7.529181753371549e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.4000000000000017 
y[1] (closed_form)               1.5686533333333355 
y[1] (numeric)                   1.5686533333333341 
absolute error                   1.3322676295501878e-15 
relative error                   8.49306600279339e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.5000000000000018 
y[1] (closed_form)               1.666666666666669 
y[1] (numeric)                   1.6666666666666676 
absolute error                   1.3322676295501878e-15 
relative error                   7.993605777301116e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.600000000000002 
y[1] (closed_form)               1.7686800000000025 
y[1] (numeric)                   1.7686800000000011 
absolute error                   1.3322676295501878e-15 
relative error                   7.53255325751513e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.700000000000002 
y[1] (closed_form)               1.874773333333336 
y[1] (numeric)                   1.8747733333333345 
absolute error                   1.5543122344752192e-15 
relative error                   8.290667500116726e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.800000000000002 
y[1] (closed_form)               1.9850266666666694 
y[1] (numeric)                   1.985026666666668 
absolute error                   1.3322676295501878e-15 
relative error                   6.711585551580429e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.900000000000002 
y[1] (closed_form)               2.099520000000003 
y[1] (numeric)                   2.0995200000000014 
absolute error                   1.7763568394002505e-15 
relative error                   8.460775984035627e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.000000000000002 
y[1] (closed_form)               2.218333333333335 
y[1] (numeric)                   2.218333333333335 
absolute error                   0.0 
relative error                   0.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.100000000000001 
y[1] (closed_form)               2.341546666666669 
y[1] (numeric)                   2.3415466666666687 
absolute error                   4.440892098500626e-16 
relative error                   1.896563567030035e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.200000000000001 
y[1] (closed_form)               2.4692400000000023 
y[1] (numeric)                   2.469240000000002 
absolute error                   4.440892098500626e-16 
relative error                   1.7984854038087113e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.300000000000001 
y[1] (closed_form)               2.6014933333333343 
y[1] (numeric)                   2.601493333333335 
absolute error                   8.881784197001252e-16 
relative error                   3.4141099203282915e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.4 
y[1] (closed_form)               2.738386666666668 
y[1] (numeric)                   2.7383866666666687 
absolute error                   8.881784197001252e-16 
relative error                   3.243436840062001e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.5 
y[1] (closed_form)               2.88 
y[1] (numeric)                   2.880000000000002 
absolute error                   2.220446049250313e-15 
relative error                   7.709882115452476e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.6 
y[1] (closed_form)               3.026413333333333 
y[1] (numeric)                   3.0264133333333354 
absolute error                   2.220446049250313e-15 
relative error                   7.336889594008903e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.699999999999999 
y[1] (closed_form)               3.1777066666666665 
y[1] (numeric)                   3.1777066666666687 
absolute error                   2.220446049250313e-15 
relative error                   6.987574002793356e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.799999999999999 
y[1] (closed_form)               3.333959999999998 
y[1] (numeric)                   3.333960000000002 
absolute error                   3.9968028886505635e-15 
relative error                   1.1988154892831845e-13%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   15 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.899999999999999 
y[1] (closed_form)               3.495253333333332 
y[1] (numeric)                   3.495253333333335 
absolute error                   3.1086244689504383e-15 
relative error                   8.893845946170157e-14%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.999999999999998 
y[1] (closed_form)               3.661666666666663 
y[1] (numeric)                   3.6616666666666684 
absolute error                   5.329070518200751e-15 
relative error                   1.4553674605919226e-13%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   15 
h                                0.1 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff  (  y  ,  x  ,  1  )   =   expt (  ( 0.2  *  x  +  0.3 )   ,  2.0 )  ; 
Iterations                      50 
Total Elapsed Time              0 Seconds
Elapsed Time(since restart)     0 Seconds
Time to Timeout                 3 Minutes 0.0 Seconds
Percent Done                    104.08163265306118%