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 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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