On logarithmic norms for differential-algebraic equations

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

MSC 2000

65L07 Numerical investigation of stability of solutions

65L80 Methods for differential-algebraic equations

CR: G.1.7

Abstract
Logarithmic matrix norms are well known in the theory of ordinary differential equations (ODEs) where they supply estimates for error growth and the growth of the solutions. In this paper we present a natural generalization of logarithmic norms which makes it applicable to differential- algebraic equations (DAEs) and yield sense-full estimates for the growth of the solutions of the DAE. As there are various possibilities we show how they correspond to each other.

Keywords:logarithmic norm, differential-algebraic equations, error estimation, solution growth