Synopsis
Excerpt from On Some Iterative Methods for Solving Elliptic Difference Equations
The theorems are used to define three subclasses, called complete image classes, of the general family. These classes contain many of the schemes in current use as well as generalizations of them. Thus it is shown that a variety of independently proposed and seemingly unrelated iterative methods are special cases of a general class of methods. These complete image classes are such that each of the eigenvalues of any scheme in the class is a given algebraic function of at least one of the eigenvalues of a particular reference scheme of the class.
Thus a knowledge of the eigenvalues of the reference schemepermits, in principle, the determination of the best scheme of the given class.
A special class of equations is considered for which all the eigenvalues of each reference scheme can be explicitly written in terms of the eigenvalues of two matrices. It is then possible to determine which of the reference schemes is best and hence it is also possible to determine that scheme which is best of all those in the complete image classes.
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On Some Iterative Methods for Solving Elliptic Difference Equations
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Paperback. Condition: New. Print on Demand. This book introduces a new mathematical methodology for tackling elliptical equations. These are commonly found in physics and engineering, and describe phenomena such as heat flow through materials or interactions between charged particles. Current approaches to solving these equations rely on extensive computation, which becomes impractical as problem size and precision demands increase. The author introduces a framework for iterative methods, which significantly reduces computational requirements without sacrificing results quality. The methods are conceptually presented and explored via a specific example, but the techniques are generalizable to other elliptical equations. This book will be of great interest to applied mathematicians and computational scientists who work on modeling and solving real-world problems. 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 # 9781332092321_0
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