Numerical Methods for Ordinary Differential Systems: The Initial Value Problem [Hardcover]

J. D. Lambert (Author)

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Product Details

Hardcover: 304 pages
Publisher: Wiley (Sep 13 1991)
Language: English
ISBN-10: 0471929905
ISBN-13: 978-0471929901
Product Dimensions: 24.2 x 16.3 x 2.3 cm
Shipping Weight: 644 g
Amazon Bestsellers Rank: #1,297,394 in Books (See Top 100 in Books)

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Book Description

Numerical Methods for Ordinary Differential Systems The Initial Value Problem J. D. Lambert Professor of Numerical Analysis University of Dundee Scotland In 1973 the author published a book entitled Computational Methods in Ordinary Differential Equations. Since then, there have been many new developments in this subject and the emphasis has changed substantially. This book reflects these changes; it is intended not as a revision of the earlier work but as a complete replacement for it. Although some basic material appears in both books, the treatment given here is generally different and there is very little overlap. In 1973 there were many methods competing for attention but more recently there has been increasing emphasis on just a few classes of methods for which sophisticated implementations now exist. This book places much more emphasis on such implementations--and on the important topic of stiffness--than did its predecessor. Also included are accounts of the structure of variable-step, variable-order methods, the Butcher and the Albrecht theories for Runge--Kutta methods, order stars and nonlinear stability theory. The author has taken a middle road between analytical rigour and a purely computational approach, key results being stated as theorems but proofs being provided only where they aid the reader's understanding of the result. Numerous exercises, from the straightforward to the demanding, are included in the text. This book will appeal to advanced students and teachers of numerical analysis and to users of numerical methods who wish to understand how algorithms for ordinary differential systems work and, on occasion, fail to work.

From the Publisher

The numerical methods for initial value problems in ordinary differential systems reflect an important change in emphasis from the author's previous work on this subject. The new treatment limits the number of methods used and emphasizes sophisticated and well-analyzed implementations. It covers the Runge-Kutta methods including the non-rigorous account of Butcher theory, Albrecht approach and stiffness and non-linear stability theory. Also contains are exercises and experiments.

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First Sentence
The level of mathematical background needed for this book is not particularly high; in general, a knowledge of the calculus and of some aspects of numerical linear algebra (vector and matrix norms, LU-decomposition) together with some familiarity with complex numbers will suffice. Read the first page

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