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

TL;DR

This paper develops explicit numerical schemes for stochastic Ginzburg-Landau equations with polynomial nonlinearities, proving sharp strong convergence rates and validating them through numerical simulations.

Contribution

It introduces and analyzes new explicit Euler-type schemes for SPDEs with polynomial nonlinearities, establishing sharp convergence rates.

Findings

Proved sharp strong convergence rates for the schemes.

Validated theoretical results with numerical simulations.

Applicable to a broad class of stochastic evolution equations.

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.