TY  - BOOK
AU  - Hairer,Ernst
AU  - Roche,Michel
AU  - Lubich,Christian
ED  - SpringerLink (Online service)
TI  - The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods
T2  - Lecture Notes in Mathematics,
SN  - 9783540468325
AV  - QA297-299.4 
U1  - 518 23
PY  - 1989///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Numerical analysis
KW  - Numerical Analysis
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/BFb0093947
ER  -