Simulating Stochastic Inertial Manifolds by a Backward-Forward Approach

TL;DR

This paper introduces a numerical method to approximate inertial manifolds in stochastic systems using a backward-forward scheme, demonstrated through stochastic ODEs and PDEs.

Contribution

It presents a novel numerical scheme for stochastic inertial manifolds by splitting equations into backward and forward parts, enabling effective approximation.

Findings

Successful approximation of stochastic inertial manifolds in examples

Numerical scheme effectively handles multiplicative noise

Method applicable to both stochastic ODEs and PDEs

Abstract

A numerical approach for the approximation of inertial manifolds of stochastic evolutionary equations with multiplicative noise is presented and illustrated. After splitting the stochastic evolutionary equations into a backward and a forward part, a numerical scheme is devised for solving this backward-forward stochastic system, and an ensemble of graphs representing the inertial manifold is consequently obtained. This numerical approach is tested in two illustrative examples: one is for a system of stochastic ordinary differential equations and the other is for a stochastic partial differential equation.