Strong convergence of full-discrete nonlinearity-truncated accelerated exponential euler-type approximations for stochastic Kuramoto–Sivashinsky equations

摘要

This article introduces and analyzes a new explicit, easily implementable,and full discrete accelerated exponential Euler-type approximation scheme foradditive space-time white noise driven stochastic partial differentialequations (SPDEs) with possibly non-globally monotone nonlinearities such asstochastic Kuramoto-Sivashinsky equations. The main result of this articleproves that the proposed approximation scheme converges strongly andnumerically weakly to the solution process of such an SPDE. Key ingredients inthe proof of our convergence result are a suitable generalized coercivity-typecondition, the specific design of the accelerated exponential Euler-typeapproximation scheme, and an application of Fernique's theorem.