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

Lubich, Christian
Roche, Michel
Publication Berlin: Springer, 1989
Collection Lecture Notes in Mathematics; 1409
Description 139 p., Softcover
Abstract 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.
ISBN: 978-3-540-51860-0
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HAIRER, Ernst, LUBICH, Christian, ROCHE, Michel. The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods. Berlin : Springer, 1989. (Lecture Notes in Mathematics; 1409) https://archive-ouverte.unige.ch/unige:12339

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Deposited on : 2010-11-05

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