Numerical stability and oscillation of the Runge-Kutta methods for the differential equations with piecewise continuous arguments alternately of retarded and advanced type

doi:10.1186/1029-242X-2012-290

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	Numerical stability and oscillation of the Runge-Kutta methods for the differential equations with piecewise continuous arguments alternately of retarded and advanced type
	Song,Minghui; Liu,Mingzhu
	2012-12-10
发表期刊	Journal of Inequalities and Applications
ISSN	1029-242X
卷号	2012 期号:1
摘要	AbstractThis paper is concerned with the numerical properties of Runge-Kutta methods for the alternately of retarded and advanced equation x˙(t)=ax(t)+a0x(2[t+12]). The stability region of Runge-Kutta methods is determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained. A?necessary and sufficient condition for the oscillation of the numerical solution is given. And it is proved that the Runge-Kutta methods preserve the oscillations of the analytic solutions. Some numerical experiments are illustrated.
关键词	stability oscillation delay differential equation piecewise continuous arguments
DOI	10.1186/1029-242X-2012-290
语种	英语
WOS记录号	BMC:10.1186/1029-242X-2012-290
出版者	Springer International Publishing
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/288
专题	中国科学院数学与系统科学研究院
通讯作者	Song,Minghui
作者单位	Harbin Institute of Technology; Department of Mathematics
推荐引用方式 GB/T 7714	Song,Minghui,Liu,Mingzhu. Numerical stability and oscillation of the Runge-Kutta methods for the differential equations with piecewise continuous arguments alternately of retarded and advanced type[J]. Journal of Inequalities and Applications,2012,2012(1).
APA	Song,Minghui,&Liu,Mingzhu.(2012).Numerical stability and oscillation of the Runge-Kutta methods for the differential equations with piecewise continuous arguments alternately of retarded and advanced type.Journal of Inequalities and Applications,2012(1).
MLA	Song,Minghui,et al."Numerical stability and oscillation of the Runge-Kutta methods for the differential equations with piecewise continuous arguments alternately of retarded and advanced type".Journal of Inequalities and Applications 2012.1(2012).