GELDA
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 differentialalgebraic 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 differentialalgebraic 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 strangenessfree DAE with the same solution set. The resulting strangenessfree 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 wellknown integration schemes for DAEs. In GELDA the BDF methods [1] and RungeKutta schemes [6],[7] are implemented. 
Homepage:  http://www3.math.tuberlin.de/multiphysics/Software/GELDA/ 
Keywords:  orms; canonical form; backward difference formula; RungeKutta method; least squares regularization; singular pencils; strangeness index; software package GELDA; differentialalgebraic equations; inconsistencies; comparison; variable coefficients 
Related Software:  GENDA; RODAS; Modelica; DASSL; NewtonLib; MBSPACK; SIMPACK; MANPAK; Matlab; GEOMS; KELLEY; LAPACK; SolveDAE; COLNEW; Python; DFVLRSQP; AlgoPy; DAETS; Dymola; GESDA 
Cited in: 
33 Publications
This software is also referenced in ORMS. 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

A new software package for linear differentialalgebraic equations. Zbl 0868.65041 Kunkel, Peter; Mehrmann, Volker; Rath, Werner; Weickert, Jörg 
1997

all
top 5
Cited by 28 Authors
all
top 5
Cited in 18 Serials
all
top 5