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Alternating Direction and Semi-Explicit Difference Methods for Parabolic Partial Differential Equations (Classic Reprint) - Softcover
Synopsis
Excerpt from Alternating Direction and Semi-Explicit Difference Methods for Parabolic Partial Differential Equations
For the model problem, the first boundary value problem for the heat conduction equation in a rectangular domain, the unconditional stability of the alternating direction methods was proved in [3] and The proof consists in showing, with the aid of Fourier analysis, that the von Neumann stability condition [11] is always satisfied. It can be shown however, that this method of proof cannot be extended beyond the model problem.
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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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- PublisherForgotten Books
- Publication date2024
- ISBN 10 1333553579
- ISBN 13 9781333553579
- BindingPaperback
- LanguageEnglish
- Number of pages47
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Alternating Direction and Semi-Explicit Difference Methods for Parabolic
Print on DemandSeller: Forgotten Books, London, United Kingdom
Seller rating 5 out of 5 stars
Paperback. Condition: New. Print on Demand. This book introduces two methods of approximating parabolic partial differential equations through the lens of difference methods: alternating direction techniques, and a new semi-explicit method. While the unconditional stability of alternating direction methods for the heat conduction equation has been proven in the past, the author extends these proofs to a far broader range of parabolic equations. The semi-explicit method is an unconditionally stable explicit method, and is self-starting unlike other explicit methods. The author applies the energy method to the problem of establishing the rate of convergence of iterative methods in elliptic difference equations, providing a path forward in solving these types of equations. Ultimately, this book aims to provide a deeper understanding of difference methods for solving parabolic partial differential equations, offering new insights for researchers and practitioners in computational mathematics. 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. Seller Inventory # 9781333553579_0
Quantity: Over 20 available
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Alternating Direction and SemiExplicit Difference Methods for Parabolic Partial Differential Equations Classic Reprint
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
Seller rating 5 out of 5 stars
PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333553579
Quantity: 15 available
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Alternating Direction and SemiExplicit Difference Methods for Parabolic Partial Differential Equations Classic Reprint
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
Seller rating 4 out of 5 stars
PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333553579
Quantity: 15 available