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

  • Authors
  • Ernst Hairer
  • Michel Roche
  • Christian Lubich

Part of the Lecture Notes in Mathematics book series (LNM, volume 1409)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Ernst Hairer, Michel Roche, Christian Lubich
    Pages 1-13
  3. Ernst Hairer, Michel Roche, Christian Lubich
    Pages 14-22
  4. Ernst Hairer, Michel Roche, Christian Lubich
    Pages 23-29
  5. Ernst Hairer, Michel Roche, Christian Lubich
    Pages 30-54
  6. Ernst Hairer, Michel Roche, Christian Lubich
    Pages 55-70
  7. Ernst Hairer, Michel Roche, Christian Lubich
    Pages 71-91
  8. Ernst Hairer, Michel Roche, Christian Lubich
    Pages 92-98
  9. Ernst Hairer, Michel Roche, Christian Lubich
    Pages 99-105
  10. Ernst Hairer, Michel Roche, Christian Lubich
    Pages 106-123
  11. Back Matter
    Pages 124-139

About this book

Introduction

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.

Keywords

Nonlinear system Simula algebra behavior control convergence differential equation implementation kinetics network networks numerical method online ordinary differential equation simulation

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0093947
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-51860-0
  • Online ISBN 978-3-540-46832-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site