Work

Approximation of the invariant measure for stochastic Burgers–Huxley equation via an explicit fully discrete scheme

Year: 2025

Type: article

Abstract: This paper investigates the long-time behavior of an explicit fully discrete scheme for the stochastic Burgers–Huxley equation driven by an additive noise, employing the spectral Galerkin spatial discretization with a temporally tamed accelerated exponential Euler method. Through a crucial monotone condition that effectively controls the Burgers-type nonlinearity, we establish the moment bound for numerical solution, which exhibits sublinear dependence with respect to the time horizon. We apply this result to present the strong convergence rate of proposed scheme and the approximation error of invariant measure. Notably, our scheme demonstrates the computational efficiency when applied to numerically approximate the invariant measure of the original equation, despite the time dependence of numerical solution. This paper constitutes the first study of invariant measure approximation for a class of stochastic partial differential equations involving Burgers-type nonlinearity.

Source: Discrete and Continuous Dynamical Systems - S

DOI: 10.3934/dcdss.2025084

Authors: Yibo Wang, Shuhan Zhang, Wanrong Cao

Institution: Southeast University

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Natural Science Foundation of China

Award: G2864589926