GELDA

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.

This software is also referenced in ORMS.


References in zbMATH (referenced in 31 articles , 1 standard article )

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  1. Bobinyec, Karen S.; Campbell, Stephen L.: Linear differential algebraic equations and observers (2015)
  2. Kunkel, Peter; Mehrmann, Volker; Scholz, Lena: Self-adjoint differential-algebraic equations (2014)
  3. Campbell, Stephen L.; Kunkel, Peter; Bobinyec, Karen: A minimal norm corrected underdetermined Gauß-Newton procedure (2012)
  4. Linh, Vu Hoang; Mehrmann, Volker; Van Vleck, Erik S.: $QR$ methods and error analysis for computing Lyapunov and Sacker--Sell spectral intervals for linear differential-algebraic equations (2011)
  5. Röbenack, Klaus; Reinschke, Kurt: On generalized inverses of singular matrix pencils (2011)
  6. Linh, Vu Hoang; Mehrmann, Volker: Lyapunov, Bohl and Sacker-Sell spectral intervals for differential-algebraic equations (2009)
  7. Arnold, Martin: Numerical methods for simulation in applied dynamics (2008)
  8. Hamann, Peter; Mehrmann, Volker: Numerical solution of hybrid systems of differential-algebraic equations (2008)
  9. Kunkel, Peter; Mehrmann, Volker: Optimal control for unstructured nonlinear differential-algebraic equations of arbitrary index (2008)
  10. Wunderlich, Lena: Analysis and numerical solution of structured and switched differential-algebraic systems (2008)
  11. Okay, Irfan; Campbell, Stephen L.; Kunkel, Peter: The additional dynamics of least squares completions for linear differential algebraic equations (2007)
  12. Kunkel, Peter; Mehrmann, Volker: Differential-algebraic equations. Analysis and numerical solution (2006)
  13. Mehrmann, Volker; Shi, Chunchao: Transformation of high order linear differential-algebraic systems to first order (2006)
  14. Steinbrecher, Andreas: Numerical solution of quasi-linear differential-algebraic equations and industrial simulation of multibody systems. (2006)
  15. Kunkel, Peter; Mehrmann, Volker: Characterization of classes of singular linear differential-algebraic equations (2005)
  16. Kunkel, Peter; Mehrmann, Volker; Stöver, Ronald: Multiple shooting for unstructured nonlinear differential-algebraic equations of arbitrary index (2005)
  17. Arévalo, C.; Campbell, S.L.; Selva, M.: Unitary partitioning in general constraint preserving DAE integrators (2004)
  18. Kunkel, P.; Mehrmann, V.: Index reduction for differential-algebraic equations by minimal extension (2004)
  19. Shi, Chunchao: Linear differential-algebraic equations of higher-order and the regularity or singularity of matrix polynomials. (2004)
  20. Kunkel, Peter; Stöver, Ronald: Symmetric collocation methods for linear differential-algebraic boundary value problems (2002)

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