##############ECHO OF PROBLEM#################
##############temp/sqrtpostode.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(0.1) 
x_end=c(0.2) 
$array_y_init[0 + 1] = exact_soln_y(x_start)
$glob_look_poles=true 
$glob_min_h=c(0.001) 
$glob_max_h=c(0.01) 
#  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]                             0.1 
y[1] (closed_form)               0.0210818510677892 
y[1] (numeric)                   0.0210818510677892 
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           0.1 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.10000000000000069 
Order of pole (three term test)                   1.499999999999913 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.11000000000000001 
y[1] (closed_form)               0.02432191512927294 
y[1] (numeric)                   0.024321915129272943 
absolute error                   3.469446951953614e-18 
relative error                   1.4264694755792147e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.11000000000000001 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.11000000000000036 
Order of pole (three term test)                   1.4999999999999207 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.12000000000000002 
y[1] (closed_form)               0.027712812921102045 
y[1] (numeric)                   0.02771281292110205 
absolute error                   3.469446951953614e-18 
relative error                   1.2519288322809658e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.12000000000000002 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.11999999999999968 
Order of pole (three term test)                   1.5000000000001754 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.13000000000000003 
y[1] (closed_form)               0.03124811105402125 
y[1] (numeric)                   0.03124811105402125 
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           0.13000000000000003 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.1299999999999993 
Order of pole (three term test)                   1.500000000000124 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.14000000000000004 
y[1] (closed_form)               0.03492213560989014 
y[1] (numeric)                   0.034922135609890124 
absolute error                   1.3877787807814457e-17 
relative error                   3.973923004835991e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.14000000000000004 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.13999999999999946 
Order of pole (three term test)                   1.5000000000002045 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.15000000000000005 
y[1] (closed_form)               0.03872983346207419 
y[1] (numeric)                   0.03872983346207417 
absolute error                   2.0816681711721685e-17 
relative error                   5.37484410618657e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.15000000000000005 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.14999999999999986 
Order of pole (three term test)                   1.4999999999998817 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.16000000000000006 
y[1] (closed_form)               0.042666666666666686 
y[1] (numeric)                   0.04266666666666666 
absolute error                   2.7755575615628914e-17 
relative error                   6.505213034913024e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.16000000000000006 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.1599999999999993 
Order of pole (three term test)                   1.500000000000195 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.17000000000000007 
y[1] (closed_form)               0.04672853042366685 
y[1] (numeric)                   0.04672853042366681 
absolute error                   4.163336342344337e-17 
relative error                   8.909623959061443e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.17000000000000007 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.1700000000000029 
Order of pole (three term test)                   1.4999999999996096 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.18000000000000008 
y[1] (closed_form)               0.050911688245431456 
y[1] (numeric)                   0.050911688245431415 
absolute error                   4.163336342344337e-17 
relative error                   8.17756488897799e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.18000000000000008 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.18000000000000008 
Order of pole (three term test)                   1.499999999999794 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.19000000000000009 
y[1] (closed_form)               0.05521271995151524 
y[1] (numeric)                   0.0552127199515152 
absolute error                   4.163336342344337e-17 
relative error                   7.54053838680715e-14%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
Radius of convergence (given) for eq  1           0.19000000000000009 
Order of pole (given)                             1.5 
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.18999999999999734 
Order of pole (three term test)                   1.5000000000004095 
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                    101.00000000000009%