The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods
Series: Lecture Notes in Mathematics; 1409;
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Product details:
- Edition number 1989
- Publisher Springer
- Date of Publication 28 November 1989
- Number of Volumes 1 pieces, Book
- ISBN 9783540518600
- Binding Paperback
- No. of pages146 pages
- Size 235x155 mm
- Weight 510 g
- Language English
- Illustrations X, 146 p. 0
Categories
Long description:
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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Table of Contents:
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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The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods
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