  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 strongly, under suitable assumptions,
to the exact solutions of such SPDEs with strong order 1/2 or at least with
strong order 1/2 - epsilon where epsilon > 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 - epsilon. 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 -
epsilon to the exact solutions of such SPDEs.
