Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations

摘要

This article proposes and analyzes explicit and easily implementable temporalnumerical approximation schemes for additive noise-driven stochastic partialdifferential equations (SPDEs) with polynomial nonlinearities such as, e.g.,stochastic Ginzburg-Landau equations. We prove essentially sharp strongconvergence rates for the considered approximation schemes. Our analysis iscarried out for abstract stochastic evolution equations on separable Banach andHilbert spaces including the above mentioned SPDEs as special cases. We alsoillustrate our strong convergence rate results by means of a numericalsimulation in Matlab.