From Équipe Calcul Formel

MasterI: Determining consistent initial values for DAE

Team and Contacts

Computer Algebra François Boulier Francois.Boulier@univ-lille1.fr

Keywords

Numerical Integration. Differential Equations.

Context

This training is part of the ANR LEDA project.

Subject

DAE are systems of algebraic differential equations. Their numerical integrations raise specific difficulties. In particular, initial values cannot be chosen freely: they must satisfy some constraints (consistency). These constraints can be determined by a preliminary step of differential elimination. We would like to determine how to take advantage of these constraints in order to compute consistent initial values.

Work to be done

• Determining a set of DAE which will serve as examples
• Testing and comparing different methods for computing consistent initial values (computation time, numerical conditioning)
• Development of a software prototype (C language)
• Bibliography

Follow up

Continuation in a PhD thesis is possible

References

• Les bibliothèques BLAD
• Solving ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Ernst Hairer and Gerhard Wanner. Springer Verlag. 1996