A reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for Burgers equation
type: Item
instance of: scholarly article
title: A reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for Burgers equation
zbMATH Open document ID: 1179.65111
published in: Journal of Computational and Applied Mathematics
publication date: 2009-06-11T00:00:00Z
review text: By using reduced basis techniques for solving partial differential equation, the computational cost can be decreased both in terms of memory and time. In this article the authors consider the Burgers' equation. By singular value decomposition of the matrix where the columns are snapshots of the solution to the equation, the reduced basis is taken as the set of singular vectors corresponding to the singular values larger than some prescribed constant. In the numerical experiments the snapshots are taken from the finite difference solution of the corresponding equation. The author also proves some error bounds for the solution obtained with the developed reduced basis technique.
reviewed by: Stefan Jakobsson
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 5564248
zbMATH Keywords: finite difference scheme
zbMATH Keywords: singular value decomposition
zbMATH Keywords: proper orthogonal decomposition
zbMATH Keywords: Burgers equation
zbMATH Keywords: error estimate
zbMATH Keywords: reduced basis techniques
zbMATH Keywords: numerical experiments
author: Zhendong Luo
author: Xiaozhong Yang
author: Yan Jie Zhou
MaRDI profile type: Publication
full work available at URL: j.cam.2008.10.026
OpenAlex ID: W2017785494
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DOI: 10.1016/J.CAM.2008.10.026
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description: scientific article; zbMATH DE number 5564248