Lecture Notes in Mathematics

The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods

Authors: Hairer, Ernst, Lubich, Christian, Roche, Michel

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About this book

The term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations on manifolds) and singular implicit differential equations. Such problems arise in a variety of applications, e.g. constrained mechanical systems, fluid dynamics, chemical reaction kinetics, simulation of electrical networks, and control engineering. From a more theoretical viewpoint, the study of differential-algebraic problems gives insight into the behaviour of numerical methods for stiff ordinary differential equations. These lecture notes provide a self-contained and comprehensive treatment of the numerical solution of differential-algebraic systems using Runge-Kutta methods, and also extrapolation methods. Readers are expected to have a background in the numerical treatment of ordinary differential equations. The subject is treated in its various aspects ranging from the theory through the analysis to implementation and applications.

Table of contents (2 chapter)

  • Runge-Kutta methods for differential-algebraic equations

    Pages 14-22

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  • Solution of nonlinear systems by simplified Newton

    Pages 92-98

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Buy this book

eBook $29.99 net
( price for USA )
  • The eBook version of this title will be available soon
  • ISBN 978-3-540-46832-5
  • digitally watermarked, no DRM
  • included format:
  • eBooks can be used on all Reading Devices
Softcover $39.99 net
( price for USA )
  • ISBN 978-3-540-51860-0
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods
Series Title
Lecture Notes in Mathematics
Series Volume
1409
Copyright
1989
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-46832-5
DOI
10.1007/BFb0093947
Softcover ISBN
978-3-540-51860-0
Series ISSN
0075-8434
Edition Number
1
Topics