## GELDA

### Summary

GELDA is a Fortran77 software package for the numerical integration of general linear differential-algebraic equations (DAE) with variable coefficients of arbitrary index.

The implementation of GELDA is based on the construction of the discretization scheme, which first determines all the local invariants and then transforms the linear DAE 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.

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 and Runge-Kutta schemes are implemented.

### Authors

Prof. Dr. Peter Kunkel (Universität Leipzig, Mathematisches Institut), Prof. Dr. Volker Mehrmann (Technische Universität Berlin, Institut für Mathematik), Dr. Werner Rath and Dr. Jörg Weickert

### Links

### Status

incomplete information or not officially approved by the authors### Aims and scope

### Mathematical Classification

### Keywords

- backward differentiation formulae method
- computing consistent initial conditions
- DAE solvers
- derivative
- differentiation index
- general linear differential algebraic equation solver
- implicit Runge-Kutta scheme
- inconsistencies in the initial
- initial-value problem
- linear algebra
- linear differential equations
- local invariants
- new discretization scheme
- non-unique solutions
- numerical dae solver
- numerical integration
- reduction
- regularization of DAEs
- stepsize
- strangeness index
- transformation into strangeness-free DAE
- values
- variable coefficients of arbitrary index