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Symbolic-Numerical Method for the Stability Analysis of Difference Schemes on the Basis of the Catastrophe Theory

✍ Scribed by E.V. Vorozhtsov; B.Yu. Scobelev; V.G. Ganzha

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
644 KB
Volume
116
Category
Article
ISSN
0021-9991

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✦ Synopsis

We propose a symbolic-numerical method for the stability analysis of diflerence initial-value problems approximating initial-value problems for the systems of partial differential equations of hyperbolic or parabolic type. The basis of the method is constituted by the Fourier method. It is proposed to use the catastrophe theory for an analysis of the manifold of characteristic equation zeros. This equation is derived automatically by symbolic computations which also enables us to automatically generate some FORTRAN subroutines needed for the analysis within the framework of the catastrophe theory. Examples of the application of the developed method are presented. In particular, the necessary stability condition has been obtained for the two-cycle MacCormack scheme of 1969 . (c) 1995 Academic Press, Inc.

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✍ Yue-Kuen Kwok πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 647 KB

The accuracy and stability properties of several two-level and three-level difference schemes for solving the shallow water model are analyzed by the linearized Fourier Method. The effects of explicit or implicit treatments of the gravity, Coriolis, convective and friction terms on accuracy and stab