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Stability Studies for Difference Equations: I Non-Linear Stability; II Coupled Sound and Heat Flow (Classic Reprint) - Softcover
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).
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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.
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.
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- PublisherForgotten Books
- Publication date2024
- ISBN 10 1333526881
- ISBN 13 9781333526887
- BindingPaperback
- Number of pages63
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Stability Studies for Difference Equations I NonLinear Stability II Coupled Sound and Heat Flow Classic Reprint
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Stability Studies for Difference Equations: I Non-Linear Stability
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Book Description Paperback. Condition: New. Print on Demand. Excerpt from Stability Studies for Difference Equations. About the Publisher, Forgotten Books publishes hundreds of thousands of rare and classic books. 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. This text has been digitally restored from a historical edition. Some errors may persist, however we consider it worth publishing due to the work's historical value. The digital edition of all books may be viewed on our website before purchase. print-on-demand item. Seller Inventory # 9781333526887_0
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Stability Studies for Difference Equations I NonLinear Stability II Coupled Sound and Heat Flow Classic Reprint
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