1.

Record Nr.

UNISA996466626303316

Autore

Hairer E (Ernst)

Titolo

The numerical solution of differential-algebraic systems by Runge-Kutta methods. / / Ernst Hairer, Michel Roche, Christian Lubich

Pubbl/distr/stampa

Berlin, Germany : , : Springer-Verlag, , [1989]

©1989

ISBN

3-540-46832-3

Edizione

[1st ed. 1989.]

Descrizione fisica

1 online resource (X, 146 p.)

Collana

Lecture Notes in Mathematics ; ; 1409

Disciplina

511.4

Soggetti

Differential-algebraic equations - Numerical solutions

Numerical analysis

Runge-Kutta formulas

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di contenuto

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.

Sommario/riassunto

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.