A comparison of explicit Runge-Kutta methods
| Autor: | Stephen J. Walters, Ross J. Turner, Lawrence K. Forbes |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | ANZIAM Journal. 64:227-249 |
| ISSN: | 1445-8810 1446-1811 |
| DOI: | 10.21914/anziamj.v64.17438 |
| Popis: | 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. doi: 10.1017/S1446181122000141 |
| Databáze: | OpenAIRE |
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