The l(1)-error estimates for a Hamiltonian-preserving scheme for the Liouville equation with piecewise constant potentials

doi:10.1137/070700681

CSpace

	The l(1)-error estimates for a Hamiltonian-preserving scheme for the Liouville equation with piecewise constant potentials
	Wen, Xin 1; Jin, Shi 2
	2008
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	46 期号:5 页码:2688-2714
摘要	We study the l(1)-error of a Hamiltonian-preserving scheme, developed in [ S. Jin and X. Wen, Commun. Math. Sci., 3 ( 2005), pp. 285 - 315], for the Liouville equation with a piecewise constant potential in one space dimension. This problem has important applications in computations of the semiclassical limit of the linear Schrodinger equation through barriers, and of the high frequency waves through interfaces. We use the l(1)-error estimates established in [ X. Wen and S. Jin, J. Comput. Math., 26 ( 2008), pp. 1-22; X. Wen, Convergence of an Immersed Interface Upwind Scheme for Linear Advection Equations with Piecewise Constant Coefficients II: Some Related Binomial Coefficient Inequalities, preprint, 2008] for the immersed interface upwind scheme to the linear advection equations with piecewise constant coefficients. We prove that the scheme with the Dirichlet incoming boundary conditions is l(1)-convergent for a class of bounded initial data and derive the half order l(1)-error bounds with explicit coefficients. The initial conditions can be satisfied by applying the decomposition technique proposed in [ S. Jin, H. L. Liu, S. Osher, and R. Tsai, J. Comput. Phys., 205 ( 2005), pp. 222 - 241] for solving the Liouville equation with measure-valued initial data, which arises in the semiclassical limit of the linear Schrodinger equation.
关键词	Liouville equations Hamiltonian preserving schemes piecewise constant potentials error estimate half order error bound semiclassical limit
DOI	10.1137/070700681
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000257746600021
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6737
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, Inst Computat Math, LSEC, 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)-error estimates for a Hamiltonian-preserving scheme for the Liouville equation with piecewise constant potentials[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2008,46(5):2688-2714.
APA	Wen, Xin,&Jin, Shi.(2008).The l(1)-error estimates for a Hamiltonian-preserving scheme for the Liouville equation with piecewise constant potentials.SIAM JOURNAL ON NUMERICAL ANALYSIS,46(5),2688-2714.
MLA	Wen, Xin,et al."The l(1)-error estimates for a Hamiltonian-preserving scheme for the Liouville equation with piecewise constant potentials".SIAM JOURNAL ON NUMERICAL ANALYSIS 46.5(2008):2688-2714.