Numerical Solution of Nonlinear Differential Equations with Algebraic Constraints II: Practical Implications

In this paper we investigate the behavior of numerical ODE methods for the solution of systems of differential equations coupled with algebraic constraints. Systems of this form arise frequently in the modelling of problems from physics and engineering; we study some particular examples from fluid dynamics and constrained mechanical systems. We investigate some of the practical difficulties of implementing variable-stepsize backward differentiation formulas for the solution of these equations, showing how to overcome problems of matrix ill-conditioning, and giving convergence tests and error tests which are supported by theory.