Work

Lattice approximation for stochastic reaction diffusion equations with one-sided Lipschitz condition

Year: 2014

Type: article

Abstract: We consider strong convergence of the finite differences approximation in space for stochastic reaction diffusion equations in one dimension with multiplicative noise under a one-sided Lipschitz condition only. The equation may be additionally coupled with a noisy control variable with global Lipschitz condition but no diffusion. We derive convergence with an implicit rate depending on the regularity of the exact solution. This can be made explicit if the variational solution has more than its canonical spatial regularity. As an application, spatially extended FitzHugh-Nagumo systems with noise are considered.

Source: Mathematics of Computation

DOI: 10.1090/s0025-5718-2014-02873-1

Authors: Martin Sauer, Wilhelm Stannat

Institutions: Technische Universität Berlin, Bernstein Center for Computational Neuroscience Berlin

Language: English

Topic: Differential Equations and Numerical Methods

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Bundesministerium für Bildung und Forschung

Award: Verbundprojekt: Bernstein Zentrum für Computational Neuroscience, Berlin - 'Präzision und Variabilität' - Teilprojekt B2, B3, B5, Professur und Nachwuchsgruppe