##############ECHO OF PROBLEM#################
##############temp/mtest4postode.ode#################
diff  (  y2  ,  x  ,  3  )   =  m1  *  cos  (  x  )   ; 
diff  (  y1  ,  x  ,  1  )   =  m1  *  y2  ; 
!
#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_y1_init[0 + 1] = exact_soln_y1(x_start)
$array_y2_init[0 + 1] = exact_soln_y2(x_start)
$array_y2_init[1 + 1] = exact_soln_y2p(x_start)
$array_y2_init[2 + 1] = exact_soln_y2pp(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_y2 (x)
return(sin(x)) 
end
def exact_soln_y2p (x)
return( cos(x)) 
end
def exact_soln_y2pp (x)
return(  -sin(x)) 
end
def exact_soln_y1 (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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                      0.09983341664682815
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
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.6747903585133234e-258
estimated_step_error          2.6747903585133234e-258
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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                      0.09983341664682815
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                    1.5971914124998497e-21
est_needed_step_err           1.5971914124998497e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.8381019356630986e-247
estimated_step_error          1.8381019356630986e-247
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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                      0.09983341664682815
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                    2.258769757263128e-21
est_needed_step_err           2.258769757263128e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.263134028636665e-236
estimated_step_error          1.263134028636665e-236
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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                      0.09983341664682815
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                    3.1943828249996993e-21
est_needed_step_err           3.1943828249996993e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      8.680190902457671e-226
estimated_step_error          8.680190902457671e-226
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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                      0.09983341664682815
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                    4.517539514526256e-21
est_needed_step_err           4.517539514526256e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      5.964981703152478e-215
estimated_step_error          5.964981703152478e-215
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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                      0.09983341664682815
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                    6.388765649999399e-21
est_needed_step_err           6.388765649999399e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      4.0991041248780636e-204
estimated_step_error          4.0991041248780636e-204
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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                      0.09983341664682815
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                    9.035079029052512e-21
est_needed_step_err           9.035079029052512e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.816882783259633e-193
estimated_step_error          2.816882783259633e-193
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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
min_size                      0.09983341664682815
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                    1.2777531299998797e-20
est_needed_step_err           1.2777531299998797e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.935746940941988e-182
estimated_step_error          1.935746940941988e-182
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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2  0.09933466539749951 
Order of pole (three term test)                   32.00996671107996 
NO COMPLEX POLE (six term test) for Equation 2
SETTING H FOR POLE ACCURACY
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                             0.1 
y2[1] (closed_form)              0.09983341664682815 
y2[1] (numeric)                  0.09983341664682815 
absolute error                   0.0 
relative error                   0.0%
Desired digits                   16 
Estimated correct digits         13 
Correct digits                   16 
h                                0.000128 
y1[1] (closed_form)              0.9950041652780258 
y1[1] (numeric)                  0.9950041652780258 
absolute error                   0.0 
relative error                   0.0%
Desired digits                   16 
Estimated correct digits         13 
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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                             0.2000959999999943 
y2[1] (closed_form)              0.1987634162709156 
y2[1] (numeric)                  0.19876341627092092 
absolute error                   5.329070518200751e-15 
relative error                   2.6811123586934128e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.980047501069369 
y1[1] (numeric)                  0.9800475010693684 
absolute error                   5.551115123125783e-16 
relative error                   5.664128643834854e-14%
Desired digits                   16 
Estimated correct digits         12 
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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                             0.3000639999999968 
y2[1] (closed_form)              0.2955813475913734 
y2[1] (numeric)                  0.2955813475913767 
absolute error                   3.3306690738754696e-15 
relative error                   1.126819774324852e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.9553175738758645 
y1[1] (numeric)                  0.955317573875865 
absolute error                   5.551115123125783e-16 
relative error                   5.810753695866903e-14%
Desired digits                   16 
Estimated correct digits         12 
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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                             0.40003200000001005 
y2[1] (closed_form)              0.38944781606108064 
y2[1] (numeric)                  0.3894478160610709 
absolute error                   9.769962616701378e-15 
relative error                   2.508670536534493e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.9210485321443462 
y1[1] (numeric)                  0.921048532144352 
absolute error                   5.773159728050814e-15 
relative error                   6.268029888294798e-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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                             0.5000000000000233 
y2[1] (closed_form)              0.47942553860422343 
y2[1] (numeric)                  0.4794255386042027 
absolute error                   2.0761170560490427e-14 
relative error                   4.330426497706715e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.8775825618903615 
y1[1] (numeric)                  0.8775825618903754 
absolute error                   1.3877787807814457e-14 
relative error                   1.581365493170344e-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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                             0.6000960000000366 
y2[1] (closed_form)              0.5647217030121027 
y2[1] (numeric)                  0.5647217030120735 
absolute error                   2.919886554764162e-14 
relative error                   5.170487585637531e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.8252814054291484 
y1[1] (numeric)                  0.8252814054291694 
absolute error                   2.098321516541546e-14 
relative error                   2.542552761685468e-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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                             0.7000640000000499 
y2[1] (closed_form)              0.6442666358183241 
y2[1] (numeric)                  0.6442666358182869 
absolute error                   3.7192471324942744e-14 
relative error                   5.772838333883644e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.7648009557861044 
y1[1] (numeric)                  0.7648009557861374 
absolute error                   3.297362383136715e-14 
relative error                   4.311399401622746e-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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                             0.8000320000000631 
y2[1] (closed_form)              0.7173783851469757 
y2[1] (numeric)                  0.7173783851469342 
absolute error                   4.1522341120980855e-14 
relative error                   5.78806693659634e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.6966837535955014 
y1[1] (numeric)                  0.6966837535955481 
absolute error                   4.674038933671909e-14 
relative error                   6.708982245602476e-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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                             0.9000000000000764 
y2[1] (closed_form)              0.7833269096275309 
y2[1] (numeric)                  0.7833269096274866 
absolute error                   4.4297898682543746e-14 
relative error                   5.655097270130453e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.6216099682706046 
y1[1] (numeric)                  0.6216099682706662 
absolute error                   6.161737786669619e-14 
relative error                   9.91254661474032e-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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                             1.0000960000000896 
y2[1] (closed_form)              0.8415228499517303 
y2[1] (numeric)                  0.8415228499516865 
absolute error                   4.3853809472693683e-14 
relative error                   5.211244052993823e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.5402215221639338 
y1[1] (numeric)                  0.5402215221640109 
absolute error                   7.704947790898586e-14 
relative error                   1.4262570954291725e-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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                             1.1000640000000161 
y2[1] (closed_form)              0.8912363883880015 
y2[1] (numeric)                  0.8912363883880007 
absolute error                   7.771561172376096e-16 
relative error                   8.719977408499542e-14%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   16 
h                                0.000128 
y1[1] (closed_form)              0.45353908322559316 
y1[1] (numeric)                  0.4535390832256088 
absolute error                   1.5654144647214707e-14 
relative error                   3.451553620446915e-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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                             1.2000319999999427 
y2[1] (closed_form)              0.9320506809381428 
y2[1] (numeric)                  0.9320506809381703 
absolute error                   2.7533531010703882e-14 
relative error                   2.9540808857078873e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.36232792904045397 
y1[1] (numeric)                  0.362327929040402 
absolute error                   5.1958437552457326e-14 
relative error                   1.4340169053502955e-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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
 
TOP MAIN SOLVE Loop
x[1]                             1.2999999999998693 
y2[1] (closed_form)              0.963558185417158 
y2[1] (numeric)                  0.9635581854172003 
absolute error                   4.2299497238218464e-14 
relative error                   4.389926615579062e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.26749882862471336 
y1[1] (numeric)                  0.2674988286245888 
absolute error                   1.2456702336294256e-13 
relative error                   4.656731545456727e-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
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
Finished!
Maximum Time Reached before Solution Completed!
diff  (  y2  ,  x  ,  3  )   =  m1  *  cos  (  x  )   ; 
diff  (  y1  ,  x  ,  1  )   =  m1  *  y2  ; 
Iterations                      9451 
Total Elapsed Time              3 Minutes 0 Seconds
Elapsed Time(since restart)     2 Minutes 59 Seconds
Expected Time Remaining         9 Minutes 9.01237833271125 Seconds
Optimized Time Remaining        9 Minutes 5.962309564196175 Seconds
Expected Total Time             12 Minutes 5.962309564196175 Seconds
Time to Timeout                 0.0 Seconds
Percent Done                    24.690938775507384%