Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations
Provides the first strong convergence proof for explicit numerical methods for stochastic Burgers equations with space-time white noise, addressing a gap in numerical analysis for SPDEs.
The authors propose explicit space-time discrete numerical approximations for stochastic Burgers equations with space-time white noise and prove strong convergence, which is the first such result in the literature.
In this paper we propose and analyze explicit space-time discrete numerical approximations for additive space-time white noise driven stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities such as the stochastic Burgers equation with space-time white noise. The main result of this paper proves that the proposed explicit space-time discrete approximation method converges strongly to the solution process of the stochastic Burgers equation with space-time white noise. To the best of our knowledge, the main result of this work is the first result in the literature which establishes strong convergence for a space-time discrete approximation method in the case of the stochastic Burgers equations with space-time white noise.