THE l(1)-STABILITY OF A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH DISCONTINUOUS POTENTIALS

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	THE l(1)-STABILITY OF A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH DISCONTINUOUS POTENTIALS
	Wen, Xin 1; Jin, Shi 2
	2009
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	27 期号:1 页码:45-67
摘要	We study the l(1)-stability of a Hamiltonian-preserving scheme, developed in [Jin and Wen, Comm. Math. Sci., 3 (2005), 285-315], for the Liouville equation with a discontinuous potential in one. space dimension. We prove that, for suitable initial data, the scheme is stable in the l(1)-norm under a hyperbolic CFL, condition which is in consistent with the l(1)-convergence results established in [Wen and Jin, SIAM J. Numer. Anal., 46 (2008), 2688-2714] for the same scheme. The stability constant is shown to be independent of the computational time. We also provide a counter example to show that for other initial data, in particular, the measure-valued initial data, the numerical solution may become l(1)-unstable.
关键词	Liouville equations Hamiltonian preserving schemes Discontinuous potentials l(1)-stability Semiclassical limit
语种	英语
资助项目	Knowledge Innovation Project of the Chinese Academy of Sciences[K5501312S1] ; Knowledge Innovation Project of the Chinese Academy of Sciences[K5502212F1] ; Knowledge Innovation Project of the Chinese Academy of Sciences[K7290312G7] ; Knowledge Innovation Project of the Chinese Academy of Sciences[K7502712F7] ; NSFC[10601062] ; NSF[DMS-0608720] ; NSAF[10676017]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000263626900002
出版者	VSP BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7390
专题	中国科学院数学与系统科学研究院
通讯作者	Wen, Xin
作者单位	1.Chinese Acad Sci, LSEC, ICMSEC, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Wisconsin, Dept Math, Madison, WI 53706 USA
推荐引用方式 GB/T 7714	Wen, Xin,Jin, Shi. THE l(1)-STABILITY OF A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH DISCONTINUOUS POTENTIALS[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2009,27(1):45-67.
APA	Wen, Xin,&Jin, Shi.(2009).THE l(1)-STABILITY OF A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH DISCONTINUOUS POTENTIALS.JOURNAL OF COMPUTATIONAL MATHEMATICS,27(1),45-67.
MLA	Wen, Xin,et al."THE l(1)-STABILITY OF A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH DISCONTINUOUS POTENTIALS".JOURNAL OF COMPUTATIONAL MATHEMATICS 27.1(2009):45-67.