  We prove the convergence in a strong norm of a finite difference
semi-discrete scheme approximating a coupled Schr\"odinger--KdV system on a
bounded domain. This system models the interaction of short and long waves.
Since the energy estimates available in the continuous case do not carry over
to the discrete setting, we rely on a suitably truncated problem which we prove
reduces to the original one. We present some numerical examples to illustrate
our convergence result.
