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A comparison of explicit Runge-Kutta methods

Citation

Walters, SJ and Turner, RJ and Forbes, LK, A comparison of explicit Runge-Kutta methods, The ANZIAM Journal pp. 1-29. ISSN 1446-1811 (2022) [Refereed Article]

Copyright Statement

© The Author(s), 2022.

DOI: doi:10.1017/S1446181122000141

Abstract

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.

Item Details

Item Type:Refereed Article
Keywords:numerical methods, Runge–Kutta method, differential equations
Research Division:Mathematical Sciences
Research Group:Numerical and computational mathematics
Research Field:Numerical solution of differential and integral equations
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Walters, SJ (Mr Stephen Walters)
UTAS Author:Turner, RJ (Dr Ross Turner)
UTAS Author:Forbes, LK (Professor Larry Forbes)
ID Code:153973
Year Published:2022
Deposited By:Physics
Deposited On:2022-10-19
Last Modified:2022-11-09
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