GENDA

GENDA is a Fortran77 sofware package for the numerical solution of nonlinear differential-algebraic equations (DAEs) of arbitrary index0=F(x,x”,t) (1)on the domain [t0,tf] together with an initial conditionx(t0)=x0An important invariant in the analysis of DAEs is the so called strangeness index, which generalizes the differentiation index [2], [3], [5] for systems with undetermined components [B]. It is known that many of the standard integration methods for general DAEs require the system to have differentiation index not higher than one. 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 [8] or LIMEX of Deuflhard/Hairer/Zugck [4] may fail.The implementation of GENDA is based on the construction of the discretization scheme introduced in [A], which transforms the system into a strangeness-free DAE with the same local 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, GENDA is able to compute a consistent initial value and apply an integration scheme for DAEs. In GENDA Runge-Kutta scheme of type RADAU IIa of order 5 [6], [7] is implemented.


References in zbMATH (referenced in 13 articles )

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  1. Campbell, Stephen; Kunkel, Peter: Solving higher index DAE optimal control problems (2016)
  2. Scholz, Lena; Steinbrecher, Andreas: DAEs in applications (2015)
  3. Estévez Schwarz, Diana; Lamour, René: Projector based integration of DAEs with the Taylor series method using automatic differentiation (2014)
  4. Campbell, Stephen L.; Kunkel, Peter; Bobinyec, Karen: A minimal norm corrected underdetermined Gauß-Newton procedure (2012)
  5. Lamour, René; Monett, Dagmar: A new algorithm for index determination in DAEs using algorithmic differentiation (2011)
  6. Campbell, Stephen L.; Kunkel, Peter: Completions of nonlinear DAE flows based on index reduction techniques and their stabilization (2009)
  7. Hamann, Peter; Mehrmann, Volker: Numerical solution of hybrid systems of differential-algebraic equations (2008)
  8. Wunderlich, Lena: Analysis and numerical solution of structured and switched differential-algebraic systems (2008)
  9. Kunkel, Peter; Mehrmann, Volker: Differential-algebraic equations. Analysis and numerical solution (2006)
  10. Voigtmann, Steffen: General linear methods for integrated circuit design. (2006)
  11. Kunkel, Peter; Mehrmann, Volker; Stöver, Ronald: Multiple shooting for unstructured nonlinear differential-algebraic equations of arbitrary index (2005)
  12. Kunkel, Peter; Mehrmann, Volker; Stöver, Ronald: Symmetric collocation for unstructered nonlinear differential-algebraic equations of arbitrary index (2004)
  13. Kunkel, P.; Mehrmann, V.: Index reduction for differential-algebraic equations by minimal extension (2004)