Ernst Hairer, Christian Lubich, Michel Roche

The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 146
• Erscheinungstermin: 14. November 2006
• Englisch
• ISBN-13: 9783540468325
• Artikelnr.: 53391472

Inhaltsangabe

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.