Simulating stochastic inertial manifolds by a backward-forward approach

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

Research output: Contribution to journalArticle

8 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 languageEnglish (US)
Pages (from-to)487-514
Number of pages28
JournalSIAM Journal on Applied Dynamical Systems
Volume12
Issue number1
DOIs
StatePublished - May 15 2013

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation

Keywords

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

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