The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods [electronic resource] /
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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Format: | Texto biblioteca |
Language: | eng |
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Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,
1989
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Subjects: | Mathematics., Numerical analysis., Numerical Analysis., |
Online Access: | http://dx.doi.org/10.1007/BFb0093947 |
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KOHA-OAI-TEST:2082262018-07-30T23:38:54ZThe Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods [electronic resource] / Hairer, Ernst. author. Roche, Michel. author. Lubich, Christian. author. SpringerLink (Online service) textBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,1989.engThe 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.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.Mathematics.Numerical analysis.Mathematics.Numerical Analysis.Springer eBookshttp://dx.doi.org/10.1007/BFb0093947URN:ISBN:9783540468325 |
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Mathematics. Numerical analysis. Mathematics. Numerical Analysis. Mathematics. Numerical analysis. Mathematics. Numerical Analysis. Hairer, Ernst. author. Roche, Michel. author. Lubich, Christian. author. SpringerLink (Online service) The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods [electronic resource] / |
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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 various aspects ranging from the theory through the analysis to implementation and applications. |
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Texto |
topic_facet |
Mathematics. Numerical analysis. Mathematics. Numerical Analysis. |
author |
Hairer, Ernst. author. Roche, Michel. author. Lubich, Christian. author. SpringerLink (Online service) |
author_facet |
Hairer, Ernst. author. Roche, Michel. author. Lubich, Christian. author. SpringerLink (Online service) |
author_sort |
Hairer, Ernst. author. |
title |
The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods [electronic resource] / |
title_short |
The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods [electronic resource] / |
title_full |
The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods [electronic resource] / |
title_fullStr |
The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods [electronic resource] / |
title_full_unstemmed |
The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods [electronic resource] / |
title_sort |
numerical solution of differential-algebraic systems by runge-kutta methods [electronic resource] / |
publisher |
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, |
publishDate |
1989 |
url |
http://dx.doi.org/10.1007/BFb0093947 |
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