Explicit Almost P-Stable Runge-Kutta-Nyström Methods for the Numerical Solution of the Two-Body Problem

Date

2014-04-01

Advisors

Journal Title

Journal ISSN

ISSN

0101-8205

Volume Title

Publisher

Springer

Type

Article

Peer reviewed

Yes

Abstract

In this paper, three families of explicit Runge–Kutta–Nyström methods with three stages and third algebraic order are presented. Each family consists of one method with constant coefficients and one corresponding optimized “almost” P-stable method with variable coefficients, zero phase-lag and zero amplification error. The firstmethod with constant coefficients is new, while the second and third have been constructed by Chawla and Sharma. The newmethod with constant coefficients, constructed in this paper has larger interval of stability than the two methods of Chawla and Sharma. Furthermore, the optimized methods possess an infinite interval of periodicity, excluding some discrete values, while being explicit, which is a very desired combination. The preservation of the algebraic order is examined, local truncation error and stability/periodicity analysis are performed and the efficiency of the new methods is measured via the integration of the two-body problem.

Description

The Publisher's final version can be found by following the DOI link.

Keywords

Numerical solution, Initial value problems (IVPs), Runge–Kutta–Nyström methods, Phase-lag, Amplification error

Citation

Kosti, A.A. and Anastassi, Z.A. (2015) Explicit Almost P-Stable Runge-Kutta-Nyström Methods for the Numerical Solution of the Two-Body Problem. Computational and Applied Mathematics, 34, pp. 647-659.

Rights

Research Institute

Institute of Artificial Intelligence (IAI)