New Paper ‘General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes’ published in Numerische Mathematik

The paper General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes of Lajos Lóczi, David I. Ketcheson, and me has been published in Numerische Mathematik. As usual, you can find the preprint on arXiv.

Recently, an approach known as relaxation has been developed for preserving the correct evolution of a functional in the numerical solution of initial-value problems, using Runge-Kutta methods. We generalize this approach to multistep methods, including all general linear methods of order two or higher, and many other classes of schemes. We prove the existence of a valid relaxation parameter and high-order accuracy of the resulting method, in the context of general equations, including but not limited to conservative or dissipative systems. The theory is illustrated with several numerical examples.