##############ECHO OF PROBLEM#################
##############temp/mtest7postode.ode#################
diff  (  y2  ,  x  ,  5  )   =  y1  ; 
diff  (  y1  ,  x  ,  1  )   =  m1  *  diff  ( y2  ,  x , 4 )   ; 
!
#BEGIN FIRST INPUT BLOCK
# Digits:=64; ELIMINATED in preodein.rb
max_terms=40 
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start=0.1 
x_end=0.7 
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
$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)
$array_y2_init[3 + 1] = exact_soln_y2ppp(x_start)
$array_y2_init[4 + 1] = exact_soln_y2pppp(x_start)
$glob_look_poles=true 
$glob_max_h=0.1 
#  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_y1 (x)
return(	 cos(x) ) 
end
def exact_soln_y2 (x)
return(	sin(x) + 10.0 * x + 10.0) 
end
def exact_soln_y2p (x)
return(	cos(x) + 10.0) 
end
def exact_soln_y2pp (x)
return( -sin(x)) 
end
def exact_soln_y2ppp (x)
return(	-cos(x)) 
end
def exact_soln_y2pppp (x)
return(   sin(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                         0.6
estimated_steps               600000.0
step_error                    3.227486121839514e-21
est_needed_step_err           3.227486121839514e-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                      11.099833416646828
min_size                      0.9950041652780258
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                         0.6
estimated_steps               600000.0
step_error                    3.227486121839514e-21
est_needed_step_err           3.227486121839514e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.6747903621399995e-258
estimated_step_error          2.6747903621399995e-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                      11.099833416646828
min_size                      0.9950041652780258
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                         0.6
estimated_steps               300000.0
step_error                    4.564354645876384e-21
est_needed_step_err           4.564354645876384e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.838101940647567e-247
estimated_step_error          1.838101940647567e-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                      11.099833416646828
min_size                      0.9950041652780258
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                         0.6
estimated_steps               150000.0
step_error                    6.454972243679028e-21
est_needed_step_err           6.454972243679028e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.2631340354872694e-236
estimated_step_error          1.2631340354872694e-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                      11.099833416646828
min_size                      0.9950041652780258
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                         0.6
estimated_steps               75000.0
step_error                    9.128709291752767e-21
est_needed_step_err           9.128709291752767e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      8.68019099661172e-226
estimated_step_error          8.68019099661172e-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                      11.099833416646828
min_size                      0.9950041652780258
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                         0.6
estimated_steps               37500.0
step_error                    1.2909944487358056e-20
est_needed_step_err           1.2909944487358056e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      5.964981832556958e-215
estimated_step_error          5.964981832556958e-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                      11.099833416646828
min_size                      0.9950041652780258
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                         0.6
estimated_steps               18750.0
step_error                    1.8257418583505535e-20
est_needed_step_err           1.8257418583505535e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      4.099104302730605e-204
estimated_step_error          4.099104302730605e-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                      11.099833416646828
min_size                      0.9950041652780258
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                         0.6
estimated_steps               9375.0
step_error                    2.5819888974716112e-20
est_needed_step_err           2.5819888974716112e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.8168830276993333e-193
estimated_step_error          2.8168830276993333e-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                      11.099833416646828
min_size                      0.9950041652780258
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                         0.6
estimated_steps               4687.5
step_error                    3.651483716701107e-20
est_needed_step_err           3.651483716701107e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.9357472769001758e-182
estimated_step_error          1.9357472769001758e-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)              11.099833416646828 
y2[1] (numeric)                  11.099833416646828 
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]                             0.16003199999999768 
y2[1] (closed_form)              11.759669797805712 
y2[1] (numeric)                  11.75966979780574 
absolute error                   2.842170943040401e-14 
relative error                   2.4168798885583793e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
y1[1] (closed_form)              0.9872221846875562 
y1[1] (numeric)                  0.9872221846875561 
absolute error                   1.1102230246251565e-16 
relative error                   1.1245928645500694e-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]                             0.22006399999999263 
y2[1] (closed_form)              12.418932080070569 
y2[1] (numeric)                  12.418932080070649 
absolute error                   7.993605777301127e-14 
relative error                   6.436628951477207e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
y1[1] (closed_form)              0.9758834806361015 
y1[1] (numeric)                  0.9758834806361013 
absolute error                   2.220446049250313e-16 
relative error                   2.2753188196227886e-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]                             0.2800959999999941 
y2[1] (closed_form)              13.077407908612539 
y2[1] (numeric)                  13.077407908612615 
absolute error                   7.638334409421077e-14 
relative error                   5.840862702149568e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
y1[1] (closed_form)              0.9610289037400077 
y1[1] (numeric)                  0.9610289037400073 
absolute error                   4.440892098500626e-16 
relative error                   4.620976623302523e-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]                             0.3400000000000021 
y2[1] (closed_form)              13.733487092140837 
y2[1] (numeric)                  13.733487092140832 
absolute error                   5.329070518200751e-15 
relative error                   3.880347709541577e-14%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   16 
h                                0.000128 
y1[1] (closed_form)              0.9427546655283455 
y1[1] (numeric)                  0.9427546655283474 
absolute error                   1.887379141862766e-15 
relative error                   2.0019833482394142e-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]                             0.40003200000001005 
y2[1] (closed_form)              14.38976781606118 
y2[1] (numeric)                  14.389767816061102 
absolute error                   7.815970093361102e-14 
relative error                   5.43161654397042e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
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]                             0.460064000000018 
y2[1] (closed_form)              15.044645453416312 
y2[1] (numeric)                  15.044645453416154 
absolute error                   1.580957587066223e-13 
relative error                   1.0508440308290694e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.8960240830115753 
y1[1] (numeric)                  0.8960240830115859 
absolute error                   1.0547118733938987e-14 
relative error                   1.177102148693333e-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]                             0.520096000000026 
y2[1] (closed_form)              15.697923446195517 
y2[1] (numeric)                  15.697923446195276 
absolute error                   2.4158453015843406e-13 
relative error                   1.538958518854183e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.8677714751855665 
y1[1] (numeric)                  0.8677714751855811 
absolute error                   1.454392162258955e-14 
relative error                   1.676008262368781e-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]                             0.5800000000000339 
y2[1] (closed_form)              16.34802393679224 
y2[1] (numeric)                  16.348023936791943 
absolute error                   2.984279490192421e-13 
relative error                   1.8254680209246055e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.8364626499151684 
y1[1] (numeric)                  0.8364626499151869 
absolute error                   1.8540724511240114e-14 
relative error                   2.2165633472242257e-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]                             0.6400320000000419 
y2[1] (closed_form)              16.99754110812133 
y2[1] (numeric)                  16.997541108120974 
absolute error                   3.552713678800501e-13 
relative error                   2.090133894191928e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
y1[1] (closed_form)              0.8020766472194742 
y1[1] (numeric)                  0.8020766472194995 
absolute error                   2.5202062658991053e-14 
relative error                   3.1421015368491274e-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
Finished!
diff  (  y2  ,  x  ,  5  )   =  y1  ; 
diff  (  y1  ,  x  ,  1  )   =  m1  *  diff  ( y2  ,  x , 4 )   ; 
Iterations                      4688 
Total Elapsed Time              56 Seconds
Elapsed Time(since restart)     56 Seconds
Time to Timeout                 2 Minutes 4.0 Seconds
Percent Done                    100.03200000000832%