Formulating differential algebraic equations properly

Inmaculada Higueras, Roswitha März

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 30

MSC 2000

34A09 Implicit equations, differential-algebraic equations
65L80 Methods for differential-algebraic equations
65L06 Multistep, Runge-Kutta and extrapolation methods
Abstract

When modeling complex processes by means of DAEs, one should carefully investigate the leading term. In this paper we study properly formulated problems, i.e. problems of the form f((Dx)',x,t)=0 with some additional condition on im D(t). From the numerical point of view, working with properly formulated problems in some sense means that the ODE method is used to discretize only the differential components. We provide stability inequalities and prove convergence in compact integration intervals for Runge-Kutta methods and BDFs. The case of a time invariant im D(t) is essentially favourable for the qualitative behaviour of the approximation on infinite intervals. This study is extended to the nonlinear version f((d(x,t))', x, t)=0.

Keywords: Differential algebraic equation, Runge-Kutta methods, backward differentiation formulas