Stabilized multistep methods for index 2 Euler-Lagrange DAEs

Abstract:
We consider multistep discretizations, stabilized by β-blocking, for Euler-Lagrange DAEs of index 2. Thus we may use “nonstiff” multistep methods with an appropriate stabilizing difference correction applied to the Lagrangian multiplier term. We show that order p =k + 1 can be achieved for the differential variables with order p =k for the Lagrangian multiplier fork-step difference corrected BDF methods as well as for low order k-step Adams-Moulton methods. This approach is related to the recently proposed “half-explicit” Runge-Kutta methods.