Pathwise convergence of a numerical method for stochastic partial differential equations with correlated noise and local Lipschitz condition

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:323

Article

Kamrani, Minoo^1,2  Bloemker, Dirk³ 

[1] Razi Univ, Dept Math, Fac Sci, Kermanshah, Iran

[2] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran

[3] Univ Augsburg, Inst Math, D-86159 Augsburg, Germany

关键词: Stochastic partial differential equations;    Spectral Galerkin approximation;    Time discretization;    Colored noise;    Order of convergence;    Uniform bounds;   

DOI  :  10.1016/j.cam.2017.04.012

来源: Elsevier

【 摘 要 】

In this paper we obtain a general statement concerning pathwise convergence of the full discretization of certain stochastic partial differential equations (SPDEs) with non globally Lipschitz continuous drift coefficients. We focus on non-diagonal colored noise instead of the usual space-time white noise. By applying a spectral Galerkin method for spatial discretization and a numerical scheme in time introduced by Jentzen, Kloeden and Winkel we obtain the rate of path-wise convergence in the uniform topology. The main assumptions are either uniform bounds on the spectral Galerkin approximation or uniform bounds on the numerical data. Numerical examples illustrate the theoretically predicted convergence rate. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free