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

  • Book
  • © 1989

Overview

Authors:
  1. Ernst Hairer
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  2. Michel Roche
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  3. Christian Lubich
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1409)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-VII
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  2. Description of differential-algebraic problems

    • Ernst Hairer, Michel Roche, Christian Lubich
    Pages 1-13

  3. Runge-Kutta methods for differential-algebraic equations

    • Ernst Hairer, Michel Roche, Christian Lubich
    Pages 14-22

  4. Convergence for index 1 problems

    • Ernst Hairer, Michel Roche, Christian Lubich
    Pages 23-29

  5. Convergence for index 2 problems

    • Ernst Hairer, Michel Roche, Christian Lubich
    Pages 30-54

  6. Order conditions of Runge-Kutta methods for index 2 systems

    • Ernst Hairer, Michel Roche, Christian Lubich
    Pages 55-70

  7. Convergence for index 3 problems

    • Ernst Hairer, Michel Roche, Christian Lubich
    Pages 71-91

  8. Solution of nonlinear systems by simplified Newton

    • Ernst Hairer, Michel Roche, Christian Lubich
    Pages 92-98

  9. Local error estimation

    • Ernst Hairer, Michel Roche, Christian Lubich
    Pages 99-105

  10. Examples of differential-algebraic systems and their solution

    • Ernst Hairer, Michel Roche, Christian Lubich
    Pages 106-123

  11. Back Matter

    Pages 124-139
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Keywords

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.

Bibliographic Information

  • Book Title: The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods

  • Authors: Ernst Hairer, Michel Roche, Christian Lubich

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0093947

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • Softcover ISBN: 978-3-540-51860-0Published: 28 November 1989

  • eBook ISBN: 978-3-540-46832-5Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 146

  • Topics: Numerical Analysis

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