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The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods
Ernst HairerChristian LubichMichel Roche
出版Springer, 2006-11-14
主題Mathematics / Number SystemsMathematics / Numerical AnalysisMathematics / Algebra / General
ISBN35404683239783540468325
URLhttp://books.google.com.hk/books?id=Qp98CwAAQBAJ&hl=&source=gbs_api
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註釋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.