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Type: Journal article
Title: Simulating stochastic inertial manifolds by a backward-forward approach
Author: Kan, X.
Duan, J.
Kevrekidis, I.
Roberts, A.
Citation: SIAM Journal on Applied Dynamical Systems, 2013; 12(1):487-514
Publisher: Society for Industrial and Applied Mathematics
Issue Date: 2013
ISSN: 1536-0040
Statement of
Xingye Kan, Jinqiao Duan, Ioannis G. Kevrekidis, and Anthony J. Roberts
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.
Keywords: invariant manifolds
inertial manifolds
random dynamical systems
backward and forward stochastic differential equations
stochastic partial differential equations
numerical schemes
Rights: © 2013, Society for Industrial and Applied Mathematics
DOI: 10.1137/120881968
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