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

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  • Becker, Sebastian
  • Jentzen, Arnulf

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–Landauequations. 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.

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  • Becker, Sebastian & Jentzen, Arnulf, 2019. "Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg–Landau equations," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 28-69.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:1:p:28-69
    DOI: 10.1016/j.spa.2018.02.008
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    Cited by:

    1. Junmei Wang & James Hoult & Yubin Yan, 2021. "Spatial Discretization for Stochastic Semi-Linear Subdiffusion Equations Driven by Fractionally Integrated Multiplicative Space-Time White Noise," Mathematics, MDPI, vol. 9(16), pages 1-38, August.
    2. Cui, Jianbo & Hong, Jialin & Sun, Liying, 2021. "Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 55-93.
    3. Wang, Xiaojie, 2020. "An efficient explicit full-discrete scheme for strong approximation of stochastic Allen–Cahn equation," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6271-6299.

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