Multistep Discretization of Index 3 DAEs

Abstract

In the past Index-3 DAEs were solved by BDF methods as multistep methods or implicit Runge-Kutta methods as one-step methods. But if the equations are nonstiff, not only BDF but other multistep methods may be applied. This paper considers four different types of multistep discretization of index 3 DAEs in hessenberg form. The convergence of these methods is proven under the condition that the multistep formula is strictly infinite stable. Numerical tests also confirm the results.