Abstract
This paper concerns theL2-stability analysis for a family of finite difference schemes for the initial value problem of space 1 dimensional linear constant coefficient convection diffusion equation. The space difference operators of the schemes have the order of accuracy greater than or equal to 2. In this paper we say that the scheme satisfies the von Neumann condition if the maximum of the absolute value of the amplification coefficient of the scheme is less than or equal to 1. The problem is to characterize, in terms of the space mesh and the time mesh, the scheme which satisfies the von Neumann condition. To investigate the toughness of the scheme in the computation of the modes in a range of relatively shorter wave length in the relevant discrete problem, the concept of e-stability is introduced, and characterized in this paper. The principal aim of the paper is to give the proof of the characterization.
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