Scientific Computing with Ordinary Differential Equations

By: Peter Deuflhard, W.C. Rheinboldt (Translator), Folkmar Bornemann

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Hardcover | 9 July 2002

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516 Pages

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24.77 x 15.88 x 3.18

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This text provides an introduction to the numerical solution of initial and boundary value problems in ordinary differential equations on a firm theoretical basis. The book strictly presents numerical analysis as part of the more general field of scientific computing. Important algorithmic concepts are explained down to questions of software implementation. For initial value problems a dynamical systems approach is used to develop Runge-Kutta, extrapolation, and multistep methods. For boundary value problems including optimal control problems both multiple shooting and collocation methods are worked out in detail. Graduate students and researchers in mathematics, computer science, and engineering will find this book useful. Chapter summaries, detailed illustrations, and exercises are contained throughout the book with many interesting applications taken from a rich variety of areas.Peter Deuflhard is founder and president of the Zuse Institute Berlin (ZIB) and full professor of scientific computing at the Free University of Berlin, department of mathematics and computer science.Folkmar Bornemann is full professor of scientific computing at the Center of Mathematical Sciences, Technical University of Munich.

Industry Reviews

P. Deuflhard and F. Bornemann

Scientific Computing with Ordinary Differential Equations

"Provides a sound fundamental introduction to the mathematical and numerical aspects of discretization methods for solving initial value problems in ordinary differential equations . . . This book would make an interesting (non-conventional) textbook for a graduate course in numerical analysis of ODEs. It is written at a level which is accessible to such an audience, covers a wide variety of topics, both classical and modern, and contains a generous supply of homework exercises. In summary, this is an excellent and timely book."-MATHEMATICAL REVIEWS

"As indicated by the title, this is not a treatise merely on the numerical analysis of ordinary differential equations (ODEs). ... the reader is made acquainted with nontrivial examples of ODEs arising in diverse areas and with intrinsic properties of these equations. ... The consideration of all the various components ... makes for a very informative reading which is further aided by the undogmatic style of presentation. The volume can be recommended to newcomers, but also to instructors in this area." (H. Muthsam, Monatshefte fuer Mathematik, Vol. 143 (1), 2004)

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Preface
Outline
Time-Dependent Processes in Science and Engineering	p. 1
Existence and Uniqueness for Initial Value Problems	p. 33
Condition of Initial Value Problems	p. 75
One-Step Methods for Nonstiff IVPs	p. 121
Adaptive Control of One-Step Methods	p. 191
One-Step Methods for Stiff ODE and DAE IVPs	p. 219
Multistep Methods for ODE and DAE IVPs	p. 313
Boundary Value Problems for ODEs	p. 389
References	p. 461
Software	p. 475
Index	p. 477
Table of Contents provided by Blackwell. All Rights Reserved.

Scientific Computing with Ordinary Differential Equations

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Hardcover

Industry Reviews

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How to return your order

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