##############ECHO OF PROBLEM#################
##############R:Temp/h5h3postode.ode#################
diff  (  y  ,  x  ,  5  )   =  neg ( diff  (  y  ,  x  ,  3 )  )   ; 
!
#BEGIN FIRST INPUT BLOCK
# Digits:=64; 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) 
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
$array_y_init[0 + 1] = exact_soln_y(x_start)
$array_y_init[1 + 1] = exact_soln_yp(x_start)
$array_y_init[2 + 1] = exact_soln_ypp(x_start)
$array_y_init[3 + 1] = exact_soln_yppp(x_start)
$array_y_init[4 + 1] = exact_soln_ypppp(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=12 
$glob_max_minutes=(3.0) 
$glob_subiter_method=2 
$glob_max_iter=1000000 
$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) 
$glob_h_reason=1 
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
def exact_soln_y (x)
x = c(x)
return(cos(c(x))) 
end
def exact_soln_yp (x)
x = c(x)
return(neg(sin(c(x)))) 
end
def exact_soln_ypp (x)
x = c(x)
return(neg(cos(c(x)))) 
end
def exact_soln_yppp (x)
x = c(x)
return(sin(x)) 
end
def exact_soln_ypppp (x)
x = c(x)
return(cos(c(x))) 
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)               0.9950041652780258 
y[1] (numeric)                   0.9950041652780258 
absolute error                   0.0 
relative error                   0.0%
Desired digits                   12 
Estimated correct digits         14 
Correct digits                   16 
h                                0.001 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.09933466539753055 
Order of pole (three term test)                   32.00996671107938 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.11000000000000001 
y[1] (closed_form)               0.9939560979566968 
y[1] (numeric)                   0.9939560979566969 
absolute error                   1.1102230246251565e-16 
relative error                   1.1169739054948934e-14%
Desired digits                   12 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.10911481154043472 
Order of pole (three term test)                   32.0120512753347 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.12000000000000002 
y[1] (closed_form)               0.9928086358538663 
y[1] (numeric)                   0.9928086358538663 
absolute error                   0.0 
relative error                   0.0%
Desired digits                   12 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.1188513132135672 
Order of pole (three term test)                   32.01433101257398 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.13000000000000003 
y[1] (closed_form)               0.9915618937147881 
y[1] (numeric)                   0.9915618937147881 
absolute error                   0.0 
relative error                   0.0%
Desired digits                   12 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.12854027594607761 
Order of pole (three term test)                   32.01680501093274 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.14000000000000004 
y[1] (closed_form)               0.9902159962126371 
y[1] (numeric)                   0.9902159962126372 
absolute error                   1.1102230246251565e-16 
relative error                   1.1211927790214664e-14%
Desired digits                   12 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.1381778242820568 
Order of pole (three term test)                   32.019472280844624 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.15000000000000005 
y[1] (closed_form)               0.9887710779360422 
y[1] (numeric)                   0.9887710779360421 
absolute error                   1.1102230246251565e-16 
relative error                   1.1228312087592942e-14%
Desired digits                   12 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.14776010333066994 
Order of pole (three term test)                   32.0223317554372 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.16000000000000006 
y[1] (closed_form)               0.9872272833756269 
y[1] (numeric)                   0.9872272833756267 
absolute error                   2.220446049250313e-16 
relative error                   2.2491741128323968e-14%
Desired digits                   12 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.15728328030805896 
Order of pole (three term test)                   32.02538229095879 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.17000000000000007 
y[1] (closed_form)               0.9855847669095607 
y[1] (numeric)                   0.9855847669095603 
absolute error                   3.3306690738754696e-16 
relative error                   3.3793836772855666e-14%
Desired digits                   12 
Estimated correct digits         13 
Correct digits                   15 
h                                0.001 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.1667435460704073 
Order of pole (three term test)                   32.02862266723583 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.18000000000000008 
y[1] (closed_form)               0.9838436927881214 
y[1] (numeric)                   0.9838436927881212 
absolute error                   2.220446049250313e-16 
relative error                   2.2569093703876634e-14%
Desired digits                   12 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.17613711663754497 
Order of pole (three term test)                   32.03205158816103 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.19000000000000009 
y[1] (closed_form)               0.9820042351172703 
y[1] (numeric)                   0.9820042351172701 
absolute error                   2.220446049250313e-16 
relative error                   2.261136937953377e-14%
Desired digits                   12 
Estimated correct digits         13 
Correct digits                   16 
h                                0.001 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.1854602347064912 
Order of pole (three term test)                   32.035667682211745 
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff  (  y  ,  x  ,  5  )   =  neg ( diff  (  y  ,  x  ,  3 )  )   ; 
Iterations                      100 
Total Elapsed Time              1 Seconds
Elapsed Time(since restart)     1 Seconds
Time to Timeout                 2 Minutes 59.0 Seconds
Percent Done                    101.00000000000009%