  It is well accepted by physicists that the Manakov PMD equation is a good
model to describe the evolution of nonlinear electric fields in optical fibers
with randomly varying birefringence. In the regime of the diffusion
approximation theory, an effective asymptotic dynamics has recently been
obtained to describe this evolution. This equation is called the stochastic
Manakov equation. In this article, we propose a semidiscrete version of a Crank
Nicolson scheme for this limit equation and we analyze the strong error.
Allowing sufficient regularity of the initial data, we prove that the numerical
scheme has strong order 1/2.
