numerical solution of differential equation with convolution

Hi,
I would like to know if it's possible to solve this kind of differential equation numerically:

dx(t)/dt=v(t)
dv(t)/dt= convolution(x(t),a(t))

or

dx(t)/dt=v(t)
dv(t)/dt= -integral(n=0->infinity) ( x(n)*a(t-n) dn )

a(t) is a known function in time.

I tried to solve this by hand with Euler's method.
I'm stuck at the point where I have to evaluate dv/dt for a single value of t and x because the sum of the integral requires more than just one value of x.

I would appreciate very much any information on this problem.

Thanks,
Matthias
.

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