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Excerpt from Aec Computing and Applied Mathematics Center: Aec Research and Development Report
This report is based on a lecture given at the Courant Institute of Mathematical Sciences in July 1964, in a special series of lectures arranged by P. D. Lax on the numerical treatment of boundary conditions in finite difference cal culations. The stability criterion introduced by Godunov and Ryabenkii as a guide to the effect of boundary calculations on stability is described here together with an application made by D. A. Quarles, Jr. To shock fitting in fluid dynamics. The criterion is in the spirit of the von Neumann condition in that it is concerned with local normal modes of the linearized difference equations; it is formalized in terms of the concept, defined by Godunov and Ryabenkii, of the spectrum of an infinite family of linear operators, and the main theorem of the theory, reproduced in a simplified form here, Shows how to test this criterion, in the case of one space variable, by the study of the local normal modes near the boundary, as well as in the.
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