Title: Aec Computing and Applied Mathematics Center Aec Research and Development Report Classic Reprint
Publisher: Forgotten Books
Publication Date: 2019
Language: English
ISBN 10: 1332199453
ISBN 13: 9781332199457
Binding: PAP
Condition: New
Weight: 130 grams

About this title

Synopsis

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.

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