$ 
$       Mathieu's differential equation with damping
$
$               y" + cy' + ( a + b cos(x) )y = 0
$
$       as system ( U1=y, U2=y' T=x ):
$               
$               U1' = U2
$               U2' = -c*U2 - ( a + b*cos(T) )*U1
$
$
$ The data after the differential equation (terminated with ;;) means:
$
$ 1 0 12 0 20   :      out  = 1  ,  each 1st step ( i.e. each step )
$                                   will be printed out
$                 T_start   = 0  ,  start of integration interval
$                 T_end     = 12 ,  end of integration interval
$                 h_initial = 0,    inital step size chosen by AWA
$                    p      = 20 ,  order of method
$
$ 4             : enclosure method 4, i.e. intersection of interval-vector
$                 and QR-decomposition
$
$ 0             : output values : 0 = enclosures of the function values
$                                     of the solution
$
$ 1 0           : initial values for both components of the solution
$                 U1(0) = 1,  U2(0) = 0
$
$ 1e-16 1e-16   : Error tolerances E_a = 1e-16 and E_r = 1e-16
$
$ n             : do not continue integration
$ n             : no further initial values
$ n             : no other differential equation
$


a = 1    b = 1    c = 0.1

F1 = U2
F2 = -c*U2 - ( a+b*cos(T) )*U1

;;

1 0 12 0 20

4
0

1.0
0.0
 
1e-16 1e-16

n
n
n

 
