The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods

✍ Scribed by Ernst Hairer, Christian Lubich, Michel Roche

• Book ID: 127405762
• Publisher: Springer
• Year: 1989
• Tongue: English
• Weight: 893 KB
• Series: Lecture Notes in Mathematics
• Edition: 1
• Category: Library
• ISBN: 3540518606

✦ Synopsis

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.