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Texts in Applied Mathematics

Scientific Computing with Ordinary Differential Equations

Authors: Deuflhard, Peter, Bornemann, Folkmar

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  • ISBN 978-0-387-21582-2
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  • ISBN 978-0-387-95462-2
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  • ISBN 978-1-4419-3011-8
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About this Textbook

This text provides an introduction to the numerical solution of initial and boundary value problems in ordinary differential equations on a firm theoretical basis. This book strictly presents numerical analysis as a 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.
This book was translated by Werner Rheinboldt, professor emeritus of numerical analysis and scientific computing at the Department of Mathematics, University of Pittsburgh.

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 für Mathematik, Vol. 143 (1), 2004)


Table of contents (8 chapters)

  • Time-Dependent Processes in Science and Engineering

    Deuflhard, Peter (et al.)

    Pages 1-31

  • Existence and Uniqueness for Initial Value Problems

    Deuflhard, Peter (et al.)

    Pages 33-73

  • Condition of Initial Value Problems

    Deuflhard, Peter (et al.)

    Pages 75-119

  • One-Step Methods for Nonstiff IVPs

    Deuflhard, Peter (et al.)

    Pages 121-190

  • Adaptive Control of One-Step Methods

    Deuflhard, Peter (et al.)

    Pages 191-218

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-0-387-21582-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-0-387-95462-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA
  • ISBN 978-1-4419-3011-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Scientific Computing with Ordinary Differential Equations
Authors
Translated by
Rheinboldt, W.C.
Series Title
Texts in Applied Mathematics
Series Volume
42
Copyright
2002
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-387-21582-2
DOI
10.1007/978-0-387-21582-2
Hardcover ISBN
978-0-387-95462-2
Softcover ISBN
978-1-4419-3011-8
Series ISSN
0939-2475
Edition Number
1
Number of Pages
XX, 486
Additional Information
Original German edition published by DeGruyter, Germany
Topics