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) |
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Pages (from-to) | 487-514 |
Number of pages | 28 |
Journal | SIAM Journal on Applied Dynamical Systems |
Volume | 12 |
Issue number | 1 |
DOIs | |
State | Published - 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