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Stability Studies for Difference Equations: I Non-Linear Stability; II Coupled Sound and Heat Flow (Classic Reprint) - Softcover
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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.
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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.
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Stability Studies for Difference Equations: I Non-Linear Stability
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Paperback. Zustand: New. Print on Demand. This book investigates numerical techniques, known as difference schemes, applied to solving partial differential equations in mathematical physics. The author explores the stability of various difference schemes, comparing their strengths and weaknesses when applied to specific problems. The stability of these schemes is crucial for accurate and reliable numerical solutions. This book delves into the intricacies of these schemes, providing valuable insights for researchers and practitioners working in numerical analysis and computational science. 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. Bestandsnummer des Verkäufers 9781333526887_0
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Stability Studies for Difference Equations I NonLinear Stability II Coupled Sound and Heat Flow Classic Reprint
Anbieter: PBShop.store US, Wood Dale, IL, USA
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PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781333526887
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Stability Studies for Difference Equations I NonLinear Stability II Coupled Sound and Heat Flow Classic Reprint
Anbieter: PBShop.store UK, Fairford, GLOS, Vereinigtes Königreich
Verkäuferbewertung 5 von 5 Sternen
PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781333526887
Anzahl: 15 verfügbar