Efficient High-Order Methods for ODEs and DAEs
by
Jens Hoefkens
Coauthors: Martin Berz and Kyoko Makino

Methods for the high-order differentiation through ordinary differential equations, and more importantly, differential algebraic equations, are presented. First, methods are developed that assert that the requested derivatives are really those of the solution of the ODE, and not those of the algorithm used to solve the ODE. Next, high-order solvers for DAEs are developed that in a fully automatic way turn an n-th order solution step of the DAEs into a corresponding step for an (enlarged) set of ODEs. In particular, this requires the automatic high-order solution of implicit constraint conditions, which is achieved using an iterative algorithm that converges to the exact result in precisely n steps. Examples for the performance of the method are given.

http://bt.nscl.msu.edu/~hoefkens/ad2000-dae.ps

Date received: March 3, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cads-96.