β-blocked multistep methods for Euler-Lagrange DAEs: Linear analysis

Many different methods have been suggested for the numerical solution of index 2 and 3 Euler-Lagrange equations. We focus on 0-stability of multistep methods (φ, σ) and investigate the relations between some well-known computational techniques. By various modifications, referred to as β-blocking of the σ polynomial, some basic shortcomings of multistep methods may be overcome. This approach is related to projection techniques and has a clear and well-known analogy in control theory. In particular, it is not necessary to use BDF methods for the solution of high index problems; indeed, “nonstiff” methods may be used for part of the system provided that the state-space form is nonstiff. We illustrate the techniques and demonstrate the results with a simplified multibody model of a truck.