The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods / Edition 1

by Ernst Hairer, Christian Lubich, Michel Roche

Overview

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.

Product Details

ISBN-13:	9783540518600
Publisher:	Springer Berlin Heidelberg
Publication date:	12/11/1989
Series:	Lecture Notes in Mathematics , #1409
Edition description:	1989
Pages:	146
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

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.