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© 2002

Scientific Computing with Ordinary Differential Equations

Textbook

Part of the Texts in Applied Mathematics book series (TAM, volume 42)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Peter Deuflhard, Folkmar Bornemann
    Pages 1-31
  3. Peter Deuflhard, Folkmar Bornemann
    Pages 33-73
  4. Peter Deuflhard, Folkmar Bornemann
    Pages 75-119
  5. Peter Deuflhard, Folkmar Bornemann
    Pages 121-190
  6. Peter Deuflhard, Folkmar Bornemann
    Pages 191-218
  7. Peter Deuflhard, Folkmar Bornemann
    Pages 219-311
  8. Peter Deuflhard, Folkmar Bornemann
    Pages 313-387
  9. Peter Deuflhard, Folkmar Bornemann
    Pages 389-460
  10. Back Matter
    Pages 461-486

About this book

Introduction

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.

Keywords

BVP Boundary value problem calculus numerical analysis ordinary differential equation ordinary differential equations scientific computing

Authors and affiliations

  1. 1.Konrad-Zuse-Zentrum BerlinBerlin-DahlemGermany
  2. 2.Center for Mathematical SciencesMunich University of Technology (TUM)MunichGermany

Bibliographic information

  • Book Title Scientific Computing with Ordinary Differential Equations
  • Authors Peter Deuflhard
    Folkmar Bornemann
  • Series Title Texts in Applied Mathematics
  • DOI https://doi.org/10.1007/978-0-387-21582-2
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-95462-2
  • Softcover ISBN 978-1-4419-3011-8
  • eBook ISBN 978-0-387-21582-2
  • Series ISSN 0939-2475
  • Edition Number 1
  • Number of Pages XX, 486
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Original German edition published by DeGruyter, Germany
  • Topics Ordinary Differential Equations
    Computational Mathematics and Numerical Analysis
  • Buy this book on publisher's site

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)