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

by S. Becker and A. Jentzen

(Report number 2016-07)

Abstract
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.

Keywords:

@Techreport{BJ16_644,
  author = {S. Becker and A. Jentzen},
  title = {Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2016-07},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2016/2016-07.pdf },
  year = {2016}
}

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