  Recently, in a paper by Jentzen and Kloeden [Proc. R. Soc. Lond. Ser. A Math.
Phys. Eng. Sci. 465 (2009) 649-667], a new method for simulating nearly linear
stochastic partial differential equations (SPDEs) with additive noise has been
introduced. The key idea was to use suitable linear functionals of the noise
process in the numerical scheme which allow a higher approximation order to be
obtained. Following this approach, a new simplified version of the scheme in
the above named reference is proposed and analyzed in this article. The main
advantage of the convergence result given here is the higher convergence order
for nonlinear parabolic SPDEs with additive noise, although the used numerical
scheme is very simple to simulate and implement.
