  This article proposes and analyzes explicit and easily implementable temporal
numerical approximation schemes for additive noise-driven stochastic partial
differential equations (SPDEs) with polynomial nonlinearities such as, e.g.,
stochastic Ginzburg-Landau equations. We prove essentially sharp strong
convergence rates for the considered approximation schemes. Our analysis is
carried out for abstract stochastic evolution equations on separable Banach and
Hilbert spaces including the above mentioned SPDEs as special cases. We also
illustrate our strong convergence rate results by means of a numerical
simulation in Matlab.
