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A comparison of explicit Runge-Kutta methods

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posted on 2023-05-21, 14:29 authored by Stephen WaltersStephen Walters, Ross TurnerRoss Turner, Lawrence ForbesLawrence Forbes
Recent 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 Journal

Volume

64

Pagination

227 - 249

ISSN

1446-1811

Department/School

School of Natural Sciences

Publisher

Cambridge University Press

Place of publication

United Kingdom

Rights 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 cited

Repository Status

  • Open

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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