##############ECHO OF PROBLEM#################
##############temp/expt_sin_cpostode.ode#################
diff  (  y  ,  x  ,  1  )   =   expt ( sin ( 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=0.2 
$array_y_init[0 + 1] = exact_soln_y(x_start)
$glob_look_poles=true 
$glob_max_iter=100000000 
$glob_max_h=0.00001 
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
$glob_desired_digits_correct=10 
$glob_display_interval=0.01 
$glob_look_poles=true 
$glob_max_iter=1000000000 
$glob_max_minutes=10.0 
$glob_subiter_method=3 
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
def exact_soln_y (x)
return(-2.5000000000000000000000000000000*sin(0.20000000000000000000000000000000*x+0.30000000000000000000000000000000)*cos(0.20000000000000000000000000000000*x+0.30000000000000000000000000000000)+0.50000000000000000000000000000000*x+0.75000000000000000000000000000000) 
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  10
estimated_h                   1.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-10
range                         0.1
estimated_steps               100000.00000000001
step_error                    9.999999999999999e-16
est_needed_step_err           9.999999999999999e-16
opt_iter                        1
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      9.321627682506412e-167
estimated_step_error          9.321627682506412e-167
best_h                        2.0e-06
opt_iter                        2
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      6.255636641280291e-159
estimated_step_error          6.255636641280291e-159
best_h                        4.0e-06
opt_iter                        3
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      4.1980842663104976e-151
estimated_step_error          4.1980842663104976e-151
best_h                        8.0e-06
opt_iter                        4
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.817283413329734e-143
estimated_step_error          2.817283413329734e-143
best_h                        1.6e-05
opt_iter                        5
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.890642535567966e-135
estimated_step_error          1.890642535567966e-135
best_h                        1.0e-05
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                             0.1 
y[1] (analytic)                  0.05350569829701002 
y[1] (numeric)                   0.05350569829701002 
absolute error                   0.0 
relative error                   0.0%
Correct digits                   16 
h                                1.0e-05 
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  1.6000946158257991 
Order of pole (three term test)                   1.099674507281389 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.11000999999999612 
y[1] (analytic)                  0.05450220365181602 
y[1] (numeric)                   0.05450220365180445 
absolute error                   1.156713613781335e-14 
relative error                   2.1223244864940303e-11%
Correct digits                   13 
h                                1.0e-05 
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  1.6101065655254412 
Order of pole (three term test)                   1.100911487908702 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.12000999999999225 
y[1] (analytic)                  0.05550972750817018 
y[1] (numeric)                   0.05550972750814715 
absolute error                   2.303018886706809e-14 
relative error                   4.1488564078572357e-11%
Correct digits                   13 
h                                1.0e-05 
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  1.6201085428081663 
Order of pole (three term test)                   1.102154583563257 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.13000999999999532 
y[1] (analytic)                  0.05652932327278937 
y[1] (numeric)                   0.056529323272753944 
absolute error                   3.54230533794464e-14 
relative error                   6.266314777643454e-11%
Correct digits                   13 
h                                1.0e-05 
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  1.6301105499222628 
Order of pole (three term test)                   1.103405019749035 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.14000000000000531 
y[1] (analytic)                  0.05756001681781853 
y[1] (numeric)                   0.05756001681777024 
absolute error                   4.82877626772904e-14 
relative error                   8.389115456676211e-11%
Correct digits                   13 
h                                1.0e-05 
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  1.6401025851331685 
Order of pole (three term test)                   1.1046615284276746 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.15000000000001532 
y[1] (analytic)                  0.058603935033209265 
y[1] (numeric)                   0.058603935033147946 
absolute error                   6.131900542882818e-14 
relative error                   1.0463291482744351e-10%
Correct digits                   12 
h                                1.0e-05 
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  1.650104652835389 
Order of pole (three term test)                   1.105926618491914 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.16000000000002532 
y[1] (analytic)                  0.05966011556928974 
y[1] (numeric)                   0.059660115569215424 
absolute error                   7.431555371084642e-14 
relative error                   1.2456488392908949e-10%
Correct digits                   12 
h                                1.0e-05 
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  1.66010675132982 
Order of pole (three term test)                   1.1071990291527933 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.17000000000003532 
y[1] (analytic)                  0.060728621527087134 
y[1] (numeric)                   0.060728621526999885 
absolute error                   8.724965194772949e-14 
relative error                   1.4367138550775934e-10%
Correct digits                   12 
h                                1.0e-05 
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  1.670108880942022 
Order of pole (three term test)                   1.1084787536825882 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.18000000000004532 
y[1] (analytic)                  0.06180951581042249 
y[1] (numeric)                   0.06180951581032218 
absolute error                   1.0030865027488289e-13 
relative error                   1.6228674332693701e-10%
Correct digits                   12 
h                                1.0e-05 
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  1.6801110420002103 
Order of pole (three term test)                   1.1097657853122216 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.19000000000005532 
y[1] (analytic)                  0.0629028611249034 
y[1] (numeric)                   0.06290286112479027 
absolute error                   1.1313172620930345e-13 
relative error                   1.7985147922709405e-10%
Correct digits                   12 
h                                1.0e-05 
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  1.6901132348352326 
Order of pole (three term test)                   1.111060117233256 
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff  (  y  ,  x  ,  1  )   =   expt ( sin ( 0.2  *  x  +  0.3 )   ,  2.0 )  ; 
Iterations                      10000 
Total Elapsed Time              12 Seconds
Elapsed Time(since restart)     12 Seconds
Time to Timeout                 9 Minutes 48.0 Seconds
Percent Done                    100.01000000006532%