The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods [electronic resource] / by Ernst Hairer, Michel Roche, Christian Lubich.
Material type: TextSeries: Lecture Notes in Mathematics ; 1409Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1989Description: X, 146 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540468325Subject(s): Mathematics | Numerical analysis | Mathematics | Numerical AnalysisAdditional physical formats: Printed edition:: No titleDDC classification: 518 LOC classification: QA297-299.4Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK1467 |
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.
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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