Long-Term Stability of Multi-Value Methods for Ordinary Differential Equations

被引：21

作者：

D'Ambrosio, R. ^{[1
]}

Hairer, E. ^{[2
]}

机构：

[1] Univ Salerno, Dipartimento Matemat, I-84084 Fisciano, SA, Italy

[2] Univ Geneva, Sect Mathemat, CH-1211 Geneva 4, Switzerland

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2014年 / 60卷 / 03期

关键词：

Multi-value methods; General linear methods; Backward error analysis; Modulated Fourier expansion; Parasitic components; Hamiltonian systems; Long-term integration;

D O I：

10.1007/s10915-013-9812-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Much effort is put into the construction of general linear methods with the aim of achieving an excellent long-time behavior for the integration of Hamiltonian systems. In this article, a backward error analysis is presented, which permits to get sharp estimates for the parasitic solution components and for the error in the Hamiltonian. For carefully constructed methods (symmetric and zero growth parameters) the error in the parasitic components typically grows like , where is the order of the method, and depends on the problem and on the coefficients of the method. This is confirmed by numerical experiments.

引用

页码：627 / 640

页数：14