The l(1)-error estimates for a Hamiltonian-preserving scheme for the Liouville equation with piecewise constant potentials
文献类型：期刊论文
| 作者 | Wen, Xin1; Jin, Shi2 |
| 刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| 出版日期 | 2008 |
| 卷号 | 46期号:5页码:2688-2714 |
| 关键词 | Liouville equations Hamiltonian preserving schemes piecewise constant potentials error estimate half order error bound semiclassical limit |
| ISSN号 | 0036-1429 |
| DOI | 10.1137/070700681 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000257746600021 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/6736]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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