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 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. Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A new software package for linear differential-algebraic equations. Zbl 0868.65041Kunkel, Peter; Mehrmann, Volker; Rath, Werner; Weickert, Jörg 1997 all top 5 Cited by 28 Authors 16 Mehrmann, Volker 15 Kunkel, Peter 6 Campbell, Stephen LaVern 3 Stöver, Ronald 2 Bobinyec, Karen S. 2 Linh, Vu Hoang 2 Rath, Werner 2 Scholz, Lena 2 Shi, Chunchao 2 Steinbrecher, Andreas 1 Arnold, Martin 1 Brachtendorf, Hans Georg 1 Byers, Ralph 1 Estévez Schwarz, Diana 1 Hamann, Peter 1 Lamour, René 1 Laur, Rainer 1 Manickam, A. V. 1 Marszałek, Wiesław 1 Moudgalya, Kannan M. 1 Okay, Irfan 1 Pani, Amiya Kumar 1 Reinschke, Kurt J. 1 Röbenack, Klaus 1 Van Vleck, Erik S. 1 Weickert, Jörg 1 Wunderlich, Lena 1 Yeomans, Kevin D. all top 5 Cited in 18 Serials 4 MCSS. Mathematics of Control, Signals, and Systems 3 Numerische Mathematik 2 Computers & Mathematics with Applications 2 Applied Numerical Mathematics 2 Numerical Algorithms 1 Computer Methods in Applied Mechanics and Engineering 1 SIAM Journal on Control and Optimization 1 SIAM Journal on Numerical Analysis 1 Mathematical and Computer Modelling 1 IEEE Transactions on Circuits and Systems. I: Fundamental Theory and Applications 1 Linear Algebra and its Applications 1 Journal of Dynamics and Differential Equations 1 SIAM Journal on Scientific Computing 1 ETNA. Electronic Transactions on Numerical Analysis 1 Advances in Computational Mathematics 1 ELA. The Electronic Journal of Linear Algebra 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 International Journal of Applied Mathematics and Computer Science all top 5 Cited in 10 Fields 23 Ordinary differential equations (34-XX) 22 Numerical analysis (65-XX) 6 Systems theory; control (93-XX) 4 Mechanics of particles and systems (70-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Information and communication theory, circuits (94-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Partial differential equations (35-XX) 1 Fluid mechanics (76-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year