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

	THE L-1-ERROR ESTIMATES FOR A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH PIECEWISE CONSTANT POTENTIALS AND PERTURBED INITIAL DATA
	Wen, Xin
刊名	JOURNAL OF COMPUTATIONAL MATHEMATICS
	2011
卷号	29 期号:1 页码:26-48
关键词	Liouville equations Hamiltonian preserving schemes Piecewise constant potentials Error estimate Perturbed initial data Semiclassical limit
ISSN号	0254-9409
DOI	10.4208/jcm.1006-m3057
英文摘要	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.
语种	英语
出版者	VSP BV
WOS记录号	WOS:000286296700003
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/12629]
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.