Sequential Regularization Methods for

Nonlinear Higher Index DAEs

Uri Ascher?

Institute of Applied Mathematics
Department of Computer Science
University of British Columbia
Vancouver, British Columbia
Canada V6T 1Z4
[email protected]

Ping Liny

Institute of Applied Mathematics
Department of Mathematics
University of British Columbia
Vancouver, British Columbia
Canada V6T 1Z2
[email protected]

June, 1995

Abstract

Sequential regularization methods relate to a combination of stabilization methods and the usual penalty method for differential equations with algebraic equality constraints. The present paper extends an earlier work [4] to nonlinear problems and to DAEs with index higher than 2. Rather than having one winning" method, this is a class of methods from which a number of variants are singled out as being particularly effective methods in certain circumstances.

We propose sequential regularization methods for index-2 and index-3 DAEs, both with and without constraint singularities. In the case of no constraint singularity we prove convergence results. Numerical experiments confirm our theoretical predictions and demonstrate the viability of the proposed methods. The examples include constrained multibody systems.

?The work of this author was partially supported under NSERC Canada Grant OGP0004306. yThe work of this author was partially supported under a Killam postgraduate grant