A NEW SOFTWARE PACKAGE FOR LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS

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 introduc ed 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 syst ems that do not have unique solutions or inconsistencies in the initia l values or the inhomogeneity. The package includes a computation of a ll 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 inconsistencie s are treated in a least square sense. We give a brief survey of the t heoretical analysis of linear differential-algebreic equations with va riable coefficients and discuss the algorithms used in GELDA. Furtherm ore, we include a series of numerical examples as well as comparisons with results from other codes, as far as this is possible.