One-step collocation methods for differential-algebraic systems of index 1

摘要

In this paper we propose one-step collocation methods for linear differential-algebraic equation (DAE) systems of index 1. The proposed methods give a continuous approximate solution on the integration interval [t0, tN]. We study the uniform convergence properties of the proposed collocation methods. Some of the methods show an order reduction phenomenon, at the nodes, similar to that observed for Runge-Kutta methods (Petzold, 1986). Since DAE systems may be considered as a kind of very stiff differential systems, the collocation methods for DAE systems have to verify strong stability properties. For example, collocation methods at Radau points are particularly suitable for solving DAE systems. However the numerical results will also show that Gauss-Legendre collocation methods may be applied successfully to DAE systems also if these are only A-stable methods.