153973 - A comparison of explicit runge kutta methods.pdf (6.84 MB)
A comparison of explicit Runge-Kutta methods
journal contribution
posted on 2023-05-21, 14:29 authored by Stephen WaltersStephen Walters, Ross TurnerRoss Turner, Lawrence ForbesLawrence ForbesRecent higher-order explicit Runge–Kutta methods are compared with the classic fourth-order (RK4) method in long-term integration of both energy-conserving and lossy systems. By comparing quantity of function evaluations against accuracy for systems with and without known solutions, optimal methods are proposed. For a conservative system, we consider positional accuracy for Newtonian systems of two or three bodies and total angular momentum for a simplified Solar System model, over moderate astronomical timescales (tens of millions of years). For a nonconservative system, we investigate a relativistic two-body problem with gravitational wave emission. We find that methods of tenth and twelfth order consistently outperform lower-order methods for the systems considered here.
History
Publication title
The ANZIAM JournalVolume
64Pagination
227 - 249ISSN
1446-1811Department/School
School of Natural SciencesPublisher
Cambridge University PressPlace of publication
United KingdomRights statement
© The Author(s), 2022. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly citedRepository Status
- Open