##############ECHO OF PROBLEM#################
##############temp/sqrt_tonepostode.ode#################
diff  (  y  ,  x  ,  1  )   =  sqrt ( x )  ; 
!
#BEGIN FIRST INPUT BLOCK
# Digits:=32; ELIMINATED in preodein.rb
max_terms=40 
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start=c(0.5) 
x_end=c(0.6) 
$array_y_init[0 + 1] = exact_soln_y(x_start)
$glob_look_poles=true 
$glob_max_h=c(0.01) 
$glob_min_h=c(0.001) 
#  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=1 
#  ELIMINATED in preodein.rb
$array_given_rad_poles[1][1]=c(0.0) 
#  ELIMINATED in preodein.rb
$array_given_rad_poles[1][2]=c(0.0) 
#  ELIMINATED in preodein.rb
$array_given_ord_poles[1][1]=c(1.5) 
#  ELIMINATED in preodein.rb
$array_given_ord_poles[1][2]=c(0.0) 
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
$glob_desired_digits_correct=8 
$glob_max_minutes=(3.0) 
$glob_subiter_method=3 
$glob_max_iter=100000 
$glob_upper_ratio_limit=c(1.000001) 
$glob_lower_ratio_limit=c(0.999999) 
$glob_look_poles=true 
$glob_h=c(0.001) 
$glob_display_interval=c(0.01) 
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
def exact_soln_y (x)
x = c(x)
return(c(2.0)*expt(c(x),c(1.5))/c(3.0)) 
end
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
 
TOP MAIN SOLVE Loop
x[1]                             0.5 
y[1] (closed_form)               0.23570226039551587 
y[1] (numeric)                   0.23570226039551587 
absolute error                   0.0 
relative error                   0.0%
Desired digits                   8 
Estimated correct digits         14 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.5 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.4999999999999888 
Order of pole (three term test)                   1.5000000000006768 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.51 
y[1] (closed_form)               0.2428085665704569 
y[1] (numeric)                   0.24280856657045696 
absolute error                   5.551115123125783e-17 
relative error                   2.2862105738410962e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.51 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.5100000000000011 
Order of pole (three term test)                   1.4999999999999092 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.52 
y[1] (closed_form)               0.24998488843216993 
y[1] (numeric)                   0.24998488843217 
absolute error                   8.326672684688674e-17 
relative error                   3.330870412572161e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.52 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.5199999999999972 
Order of pole (three term test)                   1.500000000000124 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.53 
y[1] (closed_form)               0.257230549421245 
y[1] (numeric)                   0.25723054942124507 
absolute error                   5.551115123125783e-17 
relative error                   2.1580310486509067e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.53 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.5300000000000031 
Order of pole (three term test)                   1.4999999999997842 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.54 
y[1] (closed_form)               0.26454489222058325 
y[1] (numeric)                   0.26454489222058336 
absolute error                   1.1102230246251565e-16 
relative error                   4.1967282577485134e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.54 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.540000000000007 
Order of pole (three term test)                   1.499999999999392 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.55 
y[1] (closed_form)               0.27192727786017434 
y[1] (numeric)                   0.2719272778601745 
absolute error                   1.6653345369377348e-16 
relative error                   6.124190813229314e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.55 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.5499999999999974 
Order of pole (three term test)                   1.5000000000005258 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.56 
y[1] (closed_form)               0.279377084879121 
y[1] (numeric)                   0.2793770848791211 
absolute error                   1.1102230246251565e-16 
relative error                   3.973923004835992e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.56 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.5599999999999978 
Order of pole (three term test)                   1.5000000000002045 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5700000000000001 
y[1] (closed_form)               0.28689370854028856 
y[1] (numeric)                   0.28689370854028867 
absolute error                   1.1102230246251565e-16 
relative error                   3.8698061044069485e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.5700000000000001 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.5699999999999935 
Order of pole (three term test)                   1.5000000000004565 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5800000000000001 
y[1] (closed_form)               0.2944765600934045 
y[1] (numeric)                   0.2944765600934046 
absolute error                   1.1102230246251565e-16 
relative error                   3.77015754419641e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.5800000000000001 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.5800000000000031 
Order of pole (three term test)                   1.499999999999944 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5900000000000001 
y[1] (closed_form)               0.302125066082832 
y[1] (numeric)                   0.302125066082832 
absolute error                   0.0 
relative error                   0.0%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.5900000000000001 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.5899999999999986 
Order of pole (three term test)                   1.5000000000002272 
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff  (  y  ,  x  ,  1  )   =  sqrt ( x )  ; 
Iterations                      100 
Total Elapsed Time              0 Seconds
Elapsed Time(since restart)     0 Seconds
Time to Timeout                 3 Minutes 0.0 Seconds
Percent Done                    101.00000000000011%