Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations
This work provides a provably convergent explicit numerical method for a class of SPDEs with non-globally monotone nonlinearities, which is important for computational practitioners in stochastic PDEs.
The authors propose a new explicit, full-discrete accelerated exponential Euler-type scheme for stochastic Kuramoto-Sivashinsky equations with additive space-time white noise, proving strong and numerical weak convergence. The scheme handles non-globally monotone nonlinearities and achieves strong convergence.
This article introduces and analyzes a new explicit, easily implementable, and full discrete accelerated exponential Euler-type approximation scheme for additive space-time white noise driven stochastic partial differential equations (SPDEs) with possibly non-globally monotone nonlinearities such as stochastic Kuramoto-Sivashinsky equations. The main result of this article proves that the proposed approximation scheme converges strongly and numerically weakly to the solution process of such an SPDE. Key ingredients in the proof of our convergence result are a suitable generalized coercivity-type condition, the specific design of the accelerated exponential Euler-type approximation scheme, and an application of Fernique's theorem.