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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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Aec Computing and Applied Mathematics Center (Classic Reprint)
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Paperback. Condizione: New. Print on Demand. This book addresses the stability of numerical difference schemes, particularly when auxiliary techniques like shock fitting are used. Traditional methods like the von Neumann condition, though helpful for interior calculations, struggle to predict stability when boundary conditions apply. The author introduces a revised criterion by Godunov and Ryabenkii to bridge this gap. By examining local normal modes near boundaries and interiors, this criterion provides a more comprehensive stability analysis. Furthermore, it is formalized in terms of the "spectrum of an infinite family of linear operators," a concept introduced by the authors to describe the full range of amplification factors possible in a given scheme. The book explores the theoretical underpinnings of this notion and demonstrates its application to practical fluid dynamics problems involving shock waves. Overall, this book offers valuable insights into the stability of numerical difference schemes, providing a deeper understanding of their behavior and enabling the development of more robust and reliable numerical methods. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Codice articolo 9781332199457_0
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Aec Computing and Applied Mathematics Center Aec Research and Development Report Classic Reprint
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LW-9781332199457
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Aec Computing and Applied Mathematics Center Aec Research and Development Report Classic Reprint
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LW-9781332199457
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Aec Computing and Applied Mathematics Center : Aec Research and Development Report (Classic Reprint)
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Condizione: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher. Codice articolo 26075360/2
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