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Record Nr. |
UNISA996466626303316 |
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Autore |
Hairer E (Ernst) |
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Titolo |
The numerical solution of differential-algebraic systems by Runge-Kutta methods. / / Ernst Hairer, Michel Roche, Christian Lubich |
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Pubbl/distr/stampa |
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Berlin, Germany : , : Springer-Verlag, , [1989] |
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©1989 |
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ISBN |
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Edizione |
[1st ed. 1989.] |
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Descrizione fisica |
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1 online resource (X, 146 p.) |
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Collana |
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Lecture Notes in Mathematics ; ; 1409 |
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Disciplina |
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Soggetti |
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Differential-algebraic equations - Numerical solutions |
Numerical analysis |
Runge-Kutta formulas |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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