The numerical solution of differential-algebraic systems by Runge-Kutta methods

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Springer, 1989 - Mathematics - 139 pages
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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.

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Description of differentialalgebraic problems
RungeKutta methods for differentialalgebraic equations
Convergence for index 1 problems

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About the author (1989)

Ernst Hairer is a Professor of Mathematics at the University of Geneva and has been awarded the Henrici Prize by the Society of Industrial and Applied Mathematics.

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