A New Software Package for Linear Differential-Algebraic Equations

Abstract

We describe the new software package GELDA for the numerical solution of linear differential-algebraic equations with variable coefficients. The implementation is based on the new discretization scheme introduced in [P. Kunkel and V. Mehrmann, SIAM J. Numer. Anal., 33 (1996), pp. 1941--1961]. It can deal with systems of arbitrary index and with systems that do not have unique solutions or inconsistencies in the initial values or the inhomogeneity. The package includes a computation of all the local invariants of the system, a regularization procedure, and an index reduction scheme, and it can be combined with every solution method for standard index-1 systems. Nonuniqueness and inconsistencies are treated in a least square sense. We give a brief survey of the theoretical analysis of linear differential-algebraic equations with variable coefficients and discuss the algorithms used in GELDA. Furthermore, we include a series of numerical examples as well as comparisons with results from other codes, as far as this is possible.