Numerical Approximation of the Invariant Distribution for a Class of Stochastic Damped Wave Equations
Year: 2025
Author: Ziyi Lei, Siqing Gan
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 4 : pp. 976–1015
Abstract
We study a class of stochastic semilinear damped wave equations driven by additive Wiener noise. Owing to the damping term, under appropriate conditions on the nonlinearity, the solution admits a unique invariant distribution. We apply semi-discrete and fully-discrete methods in order to approximate this invariant distribution, using a spectral Galerkin method and an exponential Euler integrator for spatial and temporal discretization respectively. We prove that the considered numerical schemes also admit unique invariant distributions, and we prove error estimates between the approximate and exact invariant distributions, with identification of the orders of convergence. To the best of our knowledge this is the first result in the literature concerning numerical approximation of invariant distributions for stochastic damped wave equations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2404-m2023-0144
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 4 : pp. 976–1015
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 40
Keywords: Stochastic damped wave equation Invariant distribution Exponential integrator Spectral Galerkin method Weak error estimates Infinite dimensional Kolmogorov equations.