A reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for Burgers equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:229

Article

Luo, Zhendong²  Yang, Xiaozhong²  Zhou, Yanjie¹ 

[1] Beijing Technol & Business Univ, Dept Math & Phys, Beijing 100037, Peoples R China

[2] N China Elect Power Univ, Sch Math & Phys, Beijing 102206, Peoples R China

关键词: Finite difference scheme;    Singular value decomposition;    Proper orthogonal decomposition;    Burgers equation;    Error estimate;   

DOI  :  10.1016/j.cam.2008.10.026

来源: Elsevier

【 摘 要 】

In this article, a reduced optimizing finite difference scheme (FDS) based on singular value decomposition (SVD) and proper orthogonal decomposition (POD) for Burgers equation is presented. Also the error estimates between the usual finite difference solution and the POD solution of reduced optimizing FDS are analyzed. It is shown by considering the results obtained for numerical simulations of cavity flows that the error between the POD solution of reduced optimizing FDS and the solution of the usual FDS is consistent with theoretical results. Moreover, it is also shown that the reduced optimizing FDS is feasible and efficient. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

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