TY - JOUR
T1 - Numerical Approximation of the Invariant Distribution for a Class of Stochastic Damped Wave Equations
AU - Lei , Ziyi
AU - Gan , Siqing
JO - Journal of Computational Mathematics
VL - 4
SP - 976
EP - 1015
PY - 2025
DA - 2025/07
SN - 43
DO - http://doi.org/10.4208/jcm.2404-m2023-0144
UR - https://global-sci.org/intro/article_detail/jcm/24267.html
KW - Stochastic damped wave equation, Invariant distribution, Exponential integrator, Spectral Galerkin method, Weak error estimates, Infinite dimensional Kolmogorov equations.
AB - <p style="text-align: justify;">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.</p>