A COMPARISON OF EXPLICIT RUNGE-KUTTA METHODS

被引：0
|
作者：
Walters, Stephen J. [1 ]
Turner, Ross J. [1 ]
Forbes, Lawrence K. [1 ]
机构：
[1] Univ Tasmania, Math Dept, Hobart, Tas 7005, Australia
来源：
ANZIAM JOURNAL | 2022年 / 64卷 / 03期
关键词：
numerical methods; Runge-Kutta method; differential equations;
D O I：
10.1017/S1446181122000141
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：227 / 249
页数：23
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