swMATH ID: 331
Software Authors: Peter Kunkel, Volker Mehrmann, Werner Rath and Jörg Weickert
Description: GELDA is a Fortran77 sofware package for the numerical solution of linear differential-algebraic equations (DAEs) with variable coefficients of arbitrary index An important invariant in the analysis of linear DAEs is the so called strangeness index, which generalizes the differentiation index ([2],[3],[5]]) for systems with undetermined components which occur, for example, in the solution of linear quadratic optimal control problems and differential-algebraic Riccati equations, see e.g. [8], [9],[10]. It is known that many of the standard integration methods for general DAEs require the system to have differentiation index not higher than one, which corresponds to a vanishing strangeness index, see [B]. If this condition is not valid or if the DAE has undetermined components, then the standard methods as implemented in codes like DASSL of Petzold [11], LIMEX of Deuflhard/Hairer/Zugck [4], or RADAU5 of Hairer/Wanner [6], [7] may fail. The implementation of GELDA is based on the construction of the discretization scheme introduced in [B], which first determines all the local invariants and then transforms the system (1) into an equivalent strangeness-free DAE with the same solution set. The resulting strangeness-free system is allowed to have nonuniqueness in the solution set or inconsistency in the initial values or inhomogeneities. But this information is now available to the user and systems with such properties can be treated in a least squares sense. In the case that the DAE is found to be uniquely solvable, GELDA is able to compute a consistent initial value and apply the well-known integration schemes for DAEs. In GELDA the BDF methods [1] and Runge-Kutta schemes [6],[7] are implemented.
Homepage: http://www3.math.tu-berlin.de/multiphysics/Software/GELDA/
Keywords: orms; canonical form; backward difference formula; Runge-Kutta method; least squares regularization; singular pencils; strangeness index; software package GELDA; differential-algebraic equations; inconsistencies; comparison; variable coefficients
Related Software: GENDA; RODAS; Modelica; DASSL; NewtonLib; MBSPACK; SIMPACK; MANPAK; Matlab; GEOMS; KELLEY; LAPACK; SolveDAE; COLNEW; Python; DFVLR-SQP; AlgoPy; DAETS; Dymola; GESDA
Cited in: 33 Publications
This software is also referenced in ORMS.

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