Strong convergence of an explicit full-discrete scheme for stochastic Burgers-Huxley equation
<|reference_start|>Strong convergence of an explicit full-discrete scheme for stochastic Burgers-Huxley equation: 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 H\"older 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.<|reference_end|>
@article{wang2024strong,
    title={Strong convergence of an explicit full-discrete scheme for stochastic
  Burgers-Huxley equation},
    author={Yibo Wang and Wanrong Cao and Yanzhao Cao},
    journal={arXiv preprint arXiv:2408.00947},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.00947},
    primaryClass={math.NA cs.NA}
}