GENDA

GENDA is a Fortran77 sofware package for the numerical solution of nonlinear differential-algebraic equations (DAEs) of arbitrary index

0=F(x,x',t)

(1)

on the domain [t₀,t_f] together with an initial condition

x(t0)=x0

An 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.