Preprint 719-2001

Index reduction for differential-algebraic equations by minimal extension

Author(s) : Peter Kunkel , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 719-2001

MSC 2000

65L05 Initial value problems

34H05 Control problems

Abstract :
In this paper a new index reduction technique is discussed for the treatment of differential-algebraic systems for which extra structural information is available. Based on this information reduced derivative arrays are formed and instead of using expensive subspace computations the index reduction is obtained by introducing new variables. The new approach is demonstrated for several important classes of differential-algebraic systems, where the structural information is available. These include multibody systems and circuit simulation problems. The effectiveness of the new approach is demonstrated via numerical examples.

Keywords : differential-algebraic equation,index reduction, minimal extension, circuit simulation, multibody system, strangeness index, regularization