The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods (Lecture Notes in Mathematics, 1409)

Hairer, Ernst; Lubich, Christian; Roche, Michel

ISBN 10: 3540518606 / ISBN 13: 9783540518600

Published by Springer, 1989

About this Item

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Bibliographic Details

• Title: The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods (Lecture Notes in Mathematics, 1409)
• Publisher: Springer
• Publication Date: 1989
• Language: English
• ISBN 10: 3540518606
• ISBN 13: 9783540518600
• Binding: Soft cover
• Condition: good

About this title

Synopsis

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.