Strong order of convergence of a semidiscrete scheme for the stochastic Manakov equation

TL;DR

This paper introduces a semidiscrete Crank-Nicolson scheme for the stochastic Manakov equation, demonstrating a strong convergence order of 1/2 under certain regularity conditions, advancing numerical methods for optical fiber models.

Contribution

The paper develops and analyzes a new semidiscrete Crank-Nicolson scheme for the stochastic Manakov equation, establishing its strong convergence order of 1/2.

Findings

The scheme achieves strong order 1/2 convergence.

The analysis requires sufficient regularity of initial data.

The method provides a reliable numerical approach for the stochastic Manakov equation.

Abstract

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.