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	The von Neumann analysis and modified equation approach for finite difference schemes
	Li, Jiequan ; Yang, Zhicheng
	2013
关键词	Finite difference schemes Von Neumann analysis Modified equation approach Amplification factor Full equivalence SECOND-ORDER METHODS HYPERBOLIC PROBLEMS CONSERVATION-LAWS PHASE ERROR STABILITY OSCILLATIONS
英文摘要	The von Neumann (discrete Fourier) analysis and modified equation technique have been proven to be two effective tools in the design and analysis of finite difference schemes for linear and nonlinear problems. The former has merits of simplicity and intuition in practical applications, but only restricted to problems of linear equations with constant coefficients and periodic boundary conditions. The later PDE approach has more extensive potential to nonlinear problems and error analysis despite its kind of relative complexity. The dissipation and dispersion properties can be observed directly from the PDE point of view: Even-order terms supply dissipation and odd-order terms reflect dispersion. In this paper we will show rigorously their full equivalence via the construction of modified equation of two-level finite difference schemes around any wave number only in terms of the amplification factor used in the von Neumann analysis. Such a conclusion fills in the gap between these two approaches in literatures. (C) 2013 Elsevier Inc. All rights reserved.; Mathematics, Applied; SCI(E); EI; 0; ARTICLE; 610-621; 225
语种	英语
出处	SCI ; EI
出版者	applied mathematics and computation
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/219216]
专题	数学科学学院
推荐引用方式 GB/T 7714	Li, Jiequan,Yang, Zhicheng. The von Neumann analysis and modified equation approach for finite difference schemes. 2013-01-01.

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