  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.
