Strong convergence of an explicit full-discrete scheme for stochastic Burgers-Huxley equation
This work provides rigorous convergence guarantees for a numerical method applied to a challenging stochastic PDE with multiple nonlinearities, benefiting researchers in computational stochastics.
The authors developed an explicit full-discrete scheme for the stochastic Burgers-Huxley equation with additive space-time white noise and proved its strong convergence with rates in both space and time, validated by a numerical example.
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.