Numerical Solution of Differential-Algebraic Equations with Ill-Conditioned Constraints.

摘要

In this paper we consider the numerical solution of higher-index differential algebraic equations with ill-conditioned or rank-deficient constraints. These types of problems arise for example in the solution of constrained mechanical systems, when a mechanism's trajectory passes through or near a kinematic singularity. We derive a class of methods for these problems which are based on minimization of the norm of the constraints. The new methods are analogous to trust-region methods of numerical optimization. We give error estimates and convergence and stability results for the new methods, and present SCM numerical experiments which illustrate their effectiveness.