Stability Studies for Difference Equations: I Non-Linear Stability; II Coupled Sound and Heat Flow (Classic Reprint) - Rilegato

Richtmyer, R. D.

Rilegato

ISBN 10: 0267435436 ISBN 13: 9780267435432

Casa editrice: Forgotten Books, 2018

Riassunto

Excerpt from Stability Studies for Difference Equations: I Non-Linear Stability; II Coupled Sound and Heat Flow

In part II, the difference equations for coupled sound and heat flow, in which the latter is treated implicitly, are considered. The stability condition is known to be c at/ax l, where c is the isothermal sound speed. This seems somewhat paradoxical, for if the thermal conductivity is small, signals travel at practically the adiabatic sound speed, V7 0, which is larger than c. For such problems, stability, as usually defined, is inadequate for an actual calculation, since it considers only the limit At, Ax O. A practical stability criterion for such problems is proposed and is applied to the problem at hand, with complete success, as judged by numerical tests, which are also described; the criterion leads, in this problem, to a stability condition intermediate between c at/ax 1 and 'v7 c at/ax 1, depending on various parameters, includ ing At (or Ax) itself. The condition is shown to be necessary (by the Fourier analysis) and sufficient (by the energy method).

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Dettagli dell'edizione

• Editore: Forgotten Books
• Data di pubblicazione: 2018
• Lingua: Inglese
• ISBN 10: 0267435436
• ISBN 13: 9780267435432
• Rilegatura: Copertina rigida
• Numero di pagine: 62
• Contatto del produttore: non disponibile
• Persona responsabile: Bärenreiter-Verlag Karl Vötterle GmbH & Co. KG; bscheuch@baerenreiter.com; ; Heinrich-Schütz-Allee 35-37; Kassel; Germania; 34131; Germania