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.

翻译：本文研究了由加性时空白噪声驱动的随机Burgers-Huxley方程显式全离散格式的强收敛性，该方程同时包含Burgers型非线性和三次非线性项。为对连续问题进行空间离散，我们采用谱Galerkin方法。随后引入非线性驯化指数积分器格式，从而构建出全离散格式。在半群理论框架下，本研究给出了温和解及其半离散与全离散逼近的Sobolev正则性、空间$L^\infty$正则性以及时间Hölder连续性的精确估计。基于这些结果，我们建立了数值解的矩有界性，并获得了空间与时间维度上的强收敛速率。最后通过数值算例验证了理论结果。