##############ECHO OF PROBLEM#################
##############temp/h2sinpostode.ode#################
diff  (  y  ,  x  ,  2  )   =  sin ( x )  ; 
!
#BEGIN FIRST INPUT BLOCK
# Digits:=32; ELIMINATED in preodein.rb
max_terms=40 
!
#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)
$array_y_init[1 + 1] = exact_soln_yp(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(2.0 - sin(x)) 
end
def exact_soln_yp (x)
return(- cos(x)) 
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                    1.129384878631564e-21
est_needed_step_err           1.129384878631564e-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                      1.9001665833531718
$glob_desired_digits_correct  16
estimated_h                   1.0e-06
estimated_answer              1.9001665833531718
desired_abs_gbl_error         1.9001665833531718e-16
range                         4.9
estimated_steps               4900000.000000001
step_error                    2.1460194061200752e-21
est_needed_step_err           2.1460194061200752e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.683742500284564e-259
estimated_step_error          2.683742500284564e-259
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                      1.9001665833531718
$glob_desired_digits_correct  16
estimated_h                   2.0e-06
estimated_answer              1.9001665833531718
desired_abs_gbl_error         1.9001665833531718e-16
range                         4.9
estimated_steps               2450000.0000000005
step_error                    3.0349297492508657e-21
est_needed_step_err           3.0349297492508657e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.844254051529349e-248
estimated_step_error          1.844254051529349e-248
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                      1.9001665833531718
$glob_desired_digits_correct  16
estimated_h                   4.0e-06
estimated_answer              1.9001665833531718
desired_abs_gbl_error         1.9001665833531718e-16
range                         4.9
estimated_steps               1225000.0000000002
step_error                    4.2920388122401504e-21
est_needed_step_err           4.2920388122401504e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.2673620752810228e-237
estimated_step_error          1.2673620752810228e-237
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                      1.9001665833531718
$glob_desired_digits_correct  16
estimated_h                   8.0e-06
estimated_answer              1.9001665833531718
desired_abs_gbl_error         1.9001665833531718e-16
range                         4.9
estimated_steps               612500.0000000001
step_error                    6.0698594985017314e-21
est_needed_step_err           6.0698594985017314e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      8.709250556831352e-227
estimated_step_error          8.709250556831352e-227
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                      1.9001665833531718
$glob_desired_digits_correct  16
estimated_h                   1.6e-05
estimated_answer              1.9001665833531718
desired_abs_gbl_error         1.9001665833531718e-16
range                         4.9
estimated_steps               306250.00000000006
step_error                    8.584077624480301e-21
est_needed_step_err           8.584077624480301e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      5.984957858910476e-216
estimated_step_error          5.984957858910476e-216
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                      1.9001665833531718
$glob_desired_digits_correct  16
estimated_h                   3.2e-05
estimated_answer              1.9001665833531718
desired_abs_gbl_error         1.9001665833531718e-16
range                         4.9
estimated_steps               153125.00000000003
step_error                    1.2139718997003463e-20
est_needed_step_err           1.2139718997003463e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      4.112840586441048e-205
estimated_step_error          4.112840586441048e-205
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                      1.9001665833531718
$glob_desired_digits_correct  16
estimated_h                   6.4e-05
estimated_answer              1.9001665833531718
desired_abs_gbl_error         1.9001665833531718e-16
range                         4.9
estimated_steps               76562.50000000001
step_error                    1.7168155248960602e-20
est_needed_step_err           1.7168155248960602e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.8263347111023736e-194
estimated_step_error          2.8263347111023736e-194
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                      1.9001665833531718
$glob_desired_digits_correct  16
estimated_h                   0.000128
estimated_answer              1.9001665833531718
desired_abs_gbl_error         1.9001665833531718e-16
range                         4.9
estimated_steps               38281.25000000001
step_error                    2.4279437994006926e-20
est_needed_step_err           2.4279437994006926e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.9422591658713157e-183
estimated_step_error          1.9422591658713157e-183
Double H and LOOP
opt_iter                        9
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.09933466539752886 
Order of pole (three term test)                   32.99003328892069 
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE ACCURACY
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                             0.1 
y[1] (closed_form)               1.9001665833531718 
y[1] (numeric)                   1.9001665833531718 
absolute error                   0.0 
relative error                   0.0%
Desired digits                   16 
Estimated correct digits         14 
Correct digits                   16 
h                                0.000128 
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]                             0.2000959999999943 
y[1] (closed_form)               1.8012365837290845 
y[1] (numeric)                   1.8012365837290778 
absolute error                   6.661338147750939e-15 
relative error                   3.6982027835344255e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
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]                             0.3000639999999968 
y[1] (closed_form)               1.7044186524086267 
y[1] (numeric)                   1.7044186524086236 
absolute error                   3.1086244689504383e-15 
relative error                   1.8238620332847424e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
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]                             0.40003200000001005 
y[1] (closed_form)               1.6105521839389194 
y[1] (numeric)                   1.610552183938928 
absolute error                   8.659739592076221e-15 
relative error                   5.376876128842432e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
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]                             0.5000000000000233 
y[1] (closed_form)               1.5205744613957766 
y[1] (numeric)                   1.520574461395795 
absolute error                   1.84297022087776e-14 
relative error                   1.2120223426520313e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
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]                             0.6000960000000366 
y[1] (closed_form)               1.4352782969878972 
y[1] (numeric)                   1.4352782969879265 
absolute error                   2.930988785010413e-14 
relative error                   2.0421048594975924e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
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]                             0.7000640000000499 
y[1] (closed_form)               1.3557333641816758 
y[1] (numeric)                   1.3557333641817122 
absolute error                   3.6415315207705135e-14 
relative error                   2.686023385556017e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
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]                             0.8000320000000631 
y[1] (closed_form)               1.2826216148530243 
y[1] (numeric)                   1.2826216148530687 
absolute error                   4.440892098500626e-14 
relative error                   3.4623555747651333e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
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]                             0.9000000000000764 
y[1] (closed_form)               1.2166730903724692 
y[1] (numeric)                   1.2166730903725205 
absolute error                   5.129230373768223e-14 
relative error                   4.215783528341186e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
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]                             1.0000960000000896 
y[1] (closed_form)               1.1584771500482698 
y[1] (numeric)                   1.158477150048324 
absolute error                   5.417888360170764e-14 
relative error                   4.6767330369399334e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
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]                             1.1000640000000161 
y[1] (closed_form)               1.1087636116119985 
y[1] (numeric)                   1.108763611612014 
absolute error                   1.554312234475219e-14 
relative error                   1.4018427536735723e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
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]                             1.2000319999999427 
y[1] (closed_form)               1.0679493190618572 
y[1] (numeric)                   1.0679493190618479 
absolute error                   9.325873406851315e-15 
relative error                   8.732505597778416e-13%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   15 
h                                0.000128 
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]                             1.2999999999998693 
y[1] (closed_form)               1.036441814582842 
y[1] (numeric)                   1.0364418145828163 
absolute error                   2.5757174171303632e-14 
relative error                   2.4851538995144316e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
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]                             1.4000959999997957 
y[1] (closed_form)               1.0145339577068335 
y[1] (numeric)                   1.014533957706809 
absolute error                   2.4424906541753444e-14 
relative error                   2.40750014883301e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
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]                             1.5000639999997223 
y[1] (closed_form)               1.0025004882579314 
y[1] (numeric)                   1.0025004882579271 
absolute error                   4.218847493575595e-15 
relative error                   4.2083246272595687e-13%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   15 
h                                0.000128 
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]                             1.6000319999996488 
y[1] (closed_form)               1.0004273318549797 
y[1] (numeric)                   1.0004273318550063 
absolute error                   2.6645352591003757e-14 
relative error                   2.6633971046750876e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
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]                             1.6999999999995754 
y[1] (closed_form)               1.0083351895474766 
y[1] (numeric)                   1.0083351895475494 
absolute error                   7.283063041541027e-14 
relative error                   7.222859141521719e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
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]                             1.8000959999995019 
y[1] (closed_form)               1.0261741850102384 
y[1] (numeric)                   1.02617418501037 
absolute error                   1.3167245072054357e-13 
relative error                   1.2831393796875707e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             1.9000639999994284 
y[1] (closed_form)               1.0537206047826884 
y[1] (numeric)                   1.053720604782894 
absolute error                   2.05613304160579e-13 
relative error                   1.951307616338993e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             2.000031999999355 
y[1] (closed_form)               1.0907158903383776 
y[1] (numeric)                   1.090715890338675 
absolute error                   2.9753977059954195e-13 
relative error                   2.7279310151723828e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             2.099999999999455 
y[1] (closed_form)               1.1367906333508513 
y[1] (numeric)                   1.1367906333511617 
absolute error                   3.1041835768519377e-13 
relative error                   2.7306554837647784e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             2.2000959999995553 
y[1] (closed_form)               1.1915600960128692 
y[1] (numeric)                   1.1915600960131751 
absolute error                   3.0597746558669314e-13 
relative error                   2.567872712509739e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             2.3000639999996553 
y[1] (closed_form)               1.2543374310155873 
y[1] (numeric)                   1.2543374310158726 
absolute error                   2.8532731732866523e-13 
relative error                   2.2747253671418147e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             2.4000319999997553 
y[1] (closed_form)               1.324560416393399 
y[1] (numeric)                   1.3245604163936513 
absolute error                   2.5224267119483557e-13 
relative error                   1.9043500626544363e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             2.4999999999998552 
y[1] (closed_form)               1.4015278558959277 
y[1] (numeric)                   1.401527855896131 
absolute error                   2.0339285811132868e-13 
relative error                   1.4512223731815138e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             2.6000959999999553 
y[1] (closed_form)               1.484580891874125 
y[1] (numeric)                   1.4845808918742698 
absolute error                   1.4477308241112041e-13 
relative error                   9.751781341356201e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
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]                             2.7000640000000553 
y[1] (closed_form)               1.5726779812585436 
y[1] (numeric)                   1.572677981258618 
absolute error                   7.438494264988549e-14 
relative error                   4.729826673758003e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
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]                             2.8000320000001553 
y[1] (closed_form)               1.6650420011306517 
y[1] (numeric)                   1.6650420011306493 
absolute error                   2.4424906541753444e-15 
relative error                   1.4669243493658202e-13%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   15 
h                                0.000128 
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]                             2.9000000000002553 
y[1] (closed_form)               1.7607506707862655 
y[1] (numeric)                   1.7607506707861793 
absolute error                   8.615330671091215e-14 
relative error                   4.8929873002655324e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
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]                             3.0000960000003554 
y[1] (closed_form)               1.8589750318702933 
y[1] (numeric)                   1.8589750318701161 
absolute error                   1.7719159473017498e-13 
relative error                   9.531682335286911e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
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]                             3.1000640000004553 
y[1] (closed_form)               1.9584832823018954 
y[1] (numeric)                   1.958483282301623 
absolute error                   2.724487302430134e-13 
relative error                   1.3911210409863285e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             3.2000320000005553 
y[1] (closed_form)               2.0584060888310667 
y[1] (numeric)                   2.058406088830691 
absolute error                   3.7569947153315297e-13 
relative error                   1.8251960756028768e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             3.3000000000006553 
y[1] (closed_form)               2.1577456941438955 
y[1] (numeric)                   2.1577456941434248 
absolute error                   4.707345624410664e-13 
relative error                   2.1816035305672776e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             3.4000960000007554 
y[1] (closed_form)               2.255633913476373 
y[1] (numeric)                   2.255633913475803 
absolute error                   5.702105454474804e-13 
relative error                   2.5279392282618874e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             3.5000640000008554 
y[1] (closed_form)               2.3508431601999624 
y[1] (numeric)                   2.350843160199309 
absolute error                   6.532552276894421e-13 
relative error                   2.7788124650301055e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             3.6000320000009554 
y[1] (closed_form)               2.4425491393384564 
y[1] (numeric)                   2.442549139337722 
absolute error                   7.345235530920036e-13 
relative error                   3.007200720190804e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             3.7000000000010553 
y[1] (closed_form)               2.529836140909388 
y[1] (numeric)                   2.5298361409085826 
absolute error                   8.055778266680136e-13 
relative error                   3.184308318002115e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             3.8000960000011554 
y[1] (closed_form)               2.6119338210244187 
y[1] (numeric)                   2.611933821023558 
absolute error                   8.606448886894214e-13 
relative error                   3.2950486025402836e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             3.9000640000012554 
y[1] (closed_form)               2.687812617443777 
y[1] (numeric)                   2.687812617442867 
absolute error                   9.099387909827783e-13 
relative error                   3.385424955137566e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             4.000032000001355 
y[1] (closed_form)               2.7568234115171952 
y[1] (numeric)                   2.756823411516252 
absolute error                   9.43245481721533e-13 
relative error                   3.421494020186174e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             4.100000000001455 
y[1] (closed_form)               2.818277111065247 
y[1] (numeric)                   2.8182771110642904 
absolute error                   9.565681580170349e-13 
relative error                   3.3941593403335454e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             4.2000960000015555 
y[1] (closed_form)               2.8716228334369056 
y[1] (numeric)                   2.87162283343595 
absolute error                   9.556799795973347e-13 
relative error                   3.328013583362993e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             4.3000640000016555 
y[1] (closed_form)               2.916191586020806 
y[1] (numeric)                   2.9161915860198677 
absolute error                   9.383605004131823e-13 
relative error                   3.217760125608179e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             4.400032000001755 
y[1] (closed_form)               2.951611908054673 
y[1] (numeric)                   2.9516119080537737 
absolute error                   8.992806499463768e-13 
relative error                   3.046744212856453e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             4.500000000001855 
y[1] (closed_form)               2.9775301176654883 
y[1] (numeric)                   2.9775301176646365 
absolute error                   8.517631044924201e-13 
relative error                   2.8606364027653866e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             4.6000960000019555 
y[1] (closed_form)               2.993701765697325 
y[1] (numeric)                   2.993701765696547 
absolute error                   7.780442956573097e-13 
relative error                   2.5989372240493682e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             4.7000640000020555 
y[1] (closed_form)               2.9999240483907443 
y[1] (numeric)                   2.999924048390061 
absolute error                   6.834532939592464e-13 
relative error                   2.2782353250772222e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             4.8000320000021555 
y[1] (closed_form)               2.996161808358146 
y[1] (numeric)                   2.9961618083575803 
absolute error                   5.657696533489798e-13 
relative error                   1.8883147491256938e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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]                             4.900000000002255 
y[1] (closed_form)               2.982452612623912 
y[1] (numeric)                   2.9824526126234856 
absolute error                   4.263256414560601e-13 
relative error                   1.4294464886098759e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
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  ,  2  )   =  sin ( x )  ; 
Iterations                      38282 
Total Elapsed Time              10 Seconds
Elapsed Time(since restart)     10 Seconds
Time to Timeout                 2 Minutes 50.0 Seconds
Percent Done                    100.00457142861951%