An Exponential Wagner--Platen Type Scheme for SPDEs

The strong numerical approximation of semilinear stochastic partial differential equations (SPDEs) driven by infinite dimensional Wiener processes is investigated. There are a number of results in the literature that show that Euler-type approximation methods converge, under suitable assumptions, to the exact solutions of such SPDEs with strong order 1/2 or at least with strong order 1/2 - ε, where ε > 0 is arbitrarily small. Recent results extend these results and show that Milstein-type approximation methods converge, under suitable assumptions, to the exact solutions of such SPDEs with strong order 1 - ε. It has also been shown that splitting-up approximation methods converge, under suitable assumptions, with strong order $ 1 $ to the exact solutions of such SPDEs. In this article an exponential Wagner--Platen type numerical approximation method for such SPDEs is proposed and shown to converge, under suitable assumptions, with strong order 3/2 - ε to the exact solutions of such SPDEs.