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Analysis of Discretization Methods for Ordinary Differential Equations

Analysis of Discretization Methods for Ordinary Differential Equations (Hardback)

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Synopsis

Due to the fundamental role of differential equations in science and engineering it has long been a basic task of numerical analysts to generate numerical values of solutions to differential equations. Nearly all approaches to this task involve a "finitization" of the original differential equation problem, usually by a projection into a finite-dimensional space. By far the most popular of these finitization processes consists of a reduction to a difference equation problem for functions which take values only on a grid of argument points. Although some of these finite- difference methods have been known for a long time, their wide applica- bility and great efficiency came to light only with the spread of electronic computers. This in tum strongly stimulated research on the properties and practical use of finite-difference methods.

While the theory or partial differential equations and their discrete analogues is a very hard subject, and progress is consequently slow, the initial value problem for a system of first order ordinary differential equations lends itself so naturally to discretization that hundreds of numerical analysts have felt inspired to invent an ever-increasing number of finite-difference methods for its solution. For about 15 years, there has hardly been an issue of a numerical journal without new results of this kind; but clearly the vast majority of these methods have just been variations of a few basic themes. In this situation, the classical text- book by P.

Science & MathematicsMathematicsCalculus & mathematical analysisDifferential calculus & equations Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Publication Date: 09/04/1973 ISBN-13: 9783540060086  Details: Type: Hardback Format: Books
Availability: Unavailable. This title is Out of Print.  

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