High order operator splitting methods based on an integral deferred correction framework

JOURNAL OF COMPUTATIONAL PHYSICS

卷:294

Article

Christlieb, Andrew J.^1,2  Liu, Yuan¹  Xu, Zhengfu³ 

[1] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[2] Michigan State Univ, Dept Elect & Comp Engn, E Lansing, MI 48824 USA

[3] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA

关键词: Integral deferred correction;    Initial-boundary value problem;    High-order accuracy;    Operator splitting;   

DOI  :  10.1016/j.jcp.2015.03.032

来源: Elsevier

【 摘 要 】

Integral deferred correction (IDC) methods have been shown to be an efficient way to achieve arbitrary high order accuracy and possess good stability properties. In this paper, we construct high order operator splitting schemes using the IDC procedure to solve initial value problems (IVPs). We present analysis to show that the IDC methods can correct for both the splitting and numerical errors, lifting the order of accuracy by r with each correction, where r is the order of accuracy of the method used to solve the correction equation. We further apply this framework to solve partial differential equations (PDEs). Numerical examples in two dimensions of linear and nonlinear initial-boundary value problems are presented to demonstrate the performance of the proposed IDC approach. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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