The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods: 1409 - Brossura

Hairer, Ernst

Brossura

ISBN 10: 3540518606 ISBN 13: 9783540518600

Casa editrice: Springer, 2009

Riassunto

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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Contenuti

Description of differential-algebraic problems.- Runge-Kutta methods for differential-algebraic equations.- Convergence for index 1 problems.- Convergence for index 2 problems.- Order conditions of Runge-Kutta methods for index 2 systems.- Convergence for index 3 problems.- Solution of nonlinear systems by simplified Newton.- Local error estimation.- Examples of differential-algebraic systems and their solution.

Product Description

Numerical Solution Of Differential-Algebraic Systems By Runge-Kutta Methods (Lecture Notes In Mathematics) by Hairer,E., Lubich, C., Roche, M., 9783540518600, Springer, 1989, Paperback

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2009
• Lingua: Inglese
• ISBN 10: 3540518606
• ISBN 13: 9783540518600
• Rilegatura: Copertina flessibile
• Numero di pagine: 156
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