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arXiv · 2408.00947

Strong convergence of an explicit full-discrete scheme for stochastic Burgers-Huxley equation

Yibo Wang·Wanrong Cao·Yanzhao Cao
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Abstract

The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise, which possesses both Burgers-type and cubic nonlinearities. To discretize the continuous problem in space, we utilize a spectral Galerkin method. Subsequently, we introduce a nonlinear-tamed exponential integrator scheme, resulting in a fully discrete scheme. Within the framework of semigroup theory, this study provides precise estimations of the Sobolev regularity, $L^\infty$ regularity in space, and Hölder continuity in time for the mild solution, as well as for its semi-discrete and full-discrete approximations. Building upon these results, we establish moment boundedness for the numerical solution and obtain strong convergence rates in both spatial and temporal dimensions. A numerical example is presented to validate the theoretical findings.

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Yibo Wang, Wanrong Cao, Yanzhao Cao. 2026-04-19. Strong convergence of an explicit full-discrete scheme for stochastic Burgers-Huxley equation. https://doi.org/10.4208/jcm.2408-m2024-0110

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