Using neural networks for the derivation of Runge-Kutta-Nystrom pairs for integration of orbits

被引：10

作者：

Tsitouras, Ch ^{[1
]}

Famelis, I. Th ^{[2
]}

机构：

[1] TEI Chalkis, Dept Appl Sci, GR-34400 Psahna, Greece

[2] TEI Athens, Dept Math, GR-12210 Egaleo, Greece

来源：

NEW ASTRONOMY | 2012年 / 17卷 / 04期

关键词：

Neural networks; Runge-Kutta; Kepler problem; Differential evolution;

D O I：

10.1016/j.newast.2011.11.009

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

In this paper we present Runge-Kutta-Nystrom (RKN) pairs of orders 4(3) and 6(4). We choose a test orbit from the Kepler problem to integrate for a specific tolerance. Then we train the free parameters of the above RKN4(3) and RKN6(4) families to perform optimally. For that we form a neural network approach and minimize its objective function using a differential evolution optimization technique. Finally we observe that the produced pairs outperform standard pairs from the literature for Pleiades orbits and Kepler problem over a wide range of eccentricities and tolerances. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：469 / 473

页数：5

共 12 条

[1]

Butcher JC., 1987, The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods

[2] FAMILIES OF RUNGE-KUTTA-NYSTROM FORMULAS [J].