UID:
almafu_9959185692902883
Format:
1 online resource (X, 146 p.)
Edition:
1st ed. 1989.
Edition:
Online edition Springer Lecture Notes Archive ; 041142-5
ISBN:
3-540-46832-3
Series Statement:
Lecture Notes in Mathematics, 1409
Content:
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.
Note:
Bibliographic Level Mode of Issuance: Monograph
,
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.
,
English
In:
Springer eBooks
Additional Edition:
ISBN 3-540-51860-6
Language:
English
URL:
http://dx.doi.org/10.1007/BFb0093947
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