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

Authors:
Zhendong Luo;Xiaozhong Yang;Yanjie Zhou
Affiliations:
School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;Department of Mathematics and Physics, Beijing Technology and Business University, Beijing 100037, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

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.