BETA-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 O-stability of multistep methods (rho, sigma) and investigate the relations between s ome well-known computational techniques. By various modifications, ref erred to as P-blocking of the a polynomial, some basic shortcomings of multistep methods may be overcome. This approach is related to projec tion techniques and has a clear and well-known analogy in control theo ry. In. particular, it is not necessary to use BDF methods for the sol ution 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 simp lified multibody model of a truck.