THE L-1-ERROR ESTIMATES FOR A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH PIECEWISE CONSTANT POTENTIALS AND PERTURBED INITIAL DATA

doi:10.4208/jcm.1006-m3057

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	THE L-1-ERROR ESTIMATES FOR A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH PIECEWISE CONSTANT POTENTIALS AND PERTURBED INITIAL DATA
	Wen, Xin
	2011
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	29 期号:1 页码:26-48
摘要	We study the L-1-error of a Hamiltonian-preserving scheme, developed in [19], for the Liouville equation with a piecewise constant potential in one space dimension when the initial data is given with perturbation errors. We extend the l(1)-stability analysis in [46] and apply the L-1-error estimates with exact initial data established in [45] for the same scheme. We prove that the scheme with the Dirichlet incoming boundary conditions and for a class of bounded initial data is L-1-convergent when the initial data is given with a wide class of perturbation errors, and derive the L-1-error bounds with explicit coefficients. The convergence rate of the scheme is shown to be less than the order of the initial perturbation error, matching with the fact that the perturbation solution can be L-1-unstable.
关键词	Liouville equations Hamiltonian preserving schemes Piecewise constant potentials Error estimate Perturbed initial data Semiclassical limit
DOI	10.4208/jcm.1006-m3057
语种	英语
资助项目	Chinese Academy of Sciences[K3502012S8] ; NSFC[10601062] ; National Basic Research Program[2010CB731505]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000286296700003
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/12630
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	Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wen, Xin. THE L-1-ERROR ESTIMATES FOR A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH PIECEWISE CONSTANT POTENTIALS AND PERTURBED INITIAL DATA[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2011,29(1):26-48.
APA	Wen, Xin.(2011).THE L-1-ERROR ESTIMATES FOR A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH PIECEWISE CONSTANT POTENTIALS AND PERTURBED INITIAL DATA.JOURNAL OF COMPUTATIONAL MATHEMATICS,29(1),26-48.
MLA	Wen, Xin."THE L-1-ERROR ESTIMATES FOR A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH PIECEWISE CONSTANT POTENTIALS AND PERTURBED INITIAL DATA".JOURNAL OF COMPUTATIONAL MATHEMATICS 29.1(2011):26-48.