Simulating stochastic inertial manifolds by a backward-forward approach

Xingye Kan; Jinqiao Duan; Ioannis G. Kevrekidis; Anthony J. Roberts

doi:10.1137/120881968

Simulating stochastic inertial manifolds by a backward-forward approach

Xingye Kan, Jinqiao Duan, Ioannis G. Kevrekidis, Anthony J. Roberts

Mathematics

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11 Scopus citations

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.

Original language	English (US)
Pages (from-to)	487-514
Number of pages	28
Journal	SIAM Journal on Applied Dynamical Systems
Volume	12
Issue number	1
DOIs	https://doi.org/10.1137/120881968
State	Published - 2013

Keywords

Backward and forward stochastic differential equations
Inertial manifolds
Invariant manifolds
Numerical schemes
Random dynamical systems
Stochastic partial differential equations

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KW - Numerical schemes

KW - Random dynamical systems

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Simulating stochastic inertial manifolds by a backward-forward approach

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