Gilles Villard, LMC-IMAG / Equipe Calcul Formel, Grenoble, France.

Computer Algebra for Differential-Algebraic Equations (DAEs).

Joint work with R. Aid, G. Thomas, J. Visconti

This talk will survey the activities of a five year project (95-99) of the computer algebra team of Grenoble on DAEs. The ACTE project has been supported by "Electricite de France" (EDF) in relation with the development of the Eurostag software for power systems simulation.
Answering to questions of the compagy EDF, ACTE main concerns have been to investigate how computer algebra could be involved for the study and the numerical integration of DAEs. Three main topics have been be distinguished and will be presented:

The validation of numerical solutions of low index DAEs using global error estimators. Convergence analysis and numerical tests are proposed.
A fully symbolic index reduction algorithm is designed as an effective implementation of Rabier and Rheinbold's method for quasi-linear DAEs.
A cheap hybrid numeric / symbolic is proposed for the numerical integration of high index quasi-linear DAEs. It is based on fast exact linear algebra for a preliminary reduction of the index.