New methods for oscillatory systems based on ARKN methods

被引：122
作者：
Franco, J. M. [1 ]
机构：
[1] Univ Zaragoza, Dept Matemat Aplicada, CPS Ingn, Zaragoza 50018, Spain
来源：
APPLIED NUMERICAL MATHEMATICS | 2006年 / 56卷 / 08期
关键词：
numerical integration; adapted RKN methods; oscillatory systems;
D O I：
10.1016/j.apnum.2005.09.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A one-parameter family of explicit fourth-order methods for oscillatory systems of the form y" + Ky = f (t, y), K being a symmetric positive semi-definite matrix, is obtained. The new methods possess eighth order for the unperturbed problem (f (t, y) = 0), and the free parameter is chosen so that the dispersion or the dissipation are optimized. The stability and phase properties of the new methods are analyzed, obtaining generalized stability regions for the second-order homogeneous linear test model. The numerical experiments carried out show that the new methods are very competitive when they are compared with standard, symplectic and special codes proposed in the scientific literature. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：1040 / 1053
页数：14
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