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- W4306750178 abstract "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." @default.
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- W4306750178 date "2022-07-01" @default.
- W4306750178 modified "2023-09-27" @default.
- W4306750178 title "A COMPARISON OF EXPLICIT RUNGE–KUTTA METHODS" @default.
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- W4306750178 doi "https://doi.org/10.1017/s1446181122000141" @default.
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