General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes
Numerical Analysis
2020-11-26 v2 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2003.03012,
title = {General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes},
author = {Hendrik Ranocha and Lajos Lóczi and David I. Ketcheson},
journal= {arXiv preprint arXiv:2003.03012},
year = {2020}
}