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A Comparison of Explicit Runge-Kutta Methods

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.

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Informasi Detail

Judul Seri

THE ANZIAM JOURNAL; Vol.64 Issue 3 July 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 227-249

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

DIFFERENTIAL EQUATIONS
NUMERICAL METHODS

Info Detail Spesifik

DOI: https://doi.org/10.1017/S1446181122000141

Pernyataan Tanggungjawab

Stephen J. Walters, Ross J. Turner, Lawrence K. Forbes

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