THE L1-ERROR ESTIMATES FOR A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH PIECEWISE CONSTANT POTENTIALS AND PERTURBED INITIAL DATA  

作　　者：Xin Wen 

机构地区：[1]LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Journal of Computational Mathematics》2011年第1期26-48,共23页计算数学（英文）

摘　　要：We study the Ll-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 l1-stability analysis in [46] and apply the Ll-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 Ll-convergent when the initial data is given with a wide class of perturbation errors, and derive the Ll-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 l1-unstable.We study the Ll-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 l1-stability analysis in [46] and apply the Ll-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 Ll-convergent when the initial data is given with a wide class of perturbation errors, and derive the Ll-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 l1-unstable.

关 键 词：Liouville equations Hamiltonian preserving schemes Piecewise constant po-tentials Error estimate Perturbed initial data Semiclassical limit. 

分 类 号：O241.82[理学—计算数学] TU311[理学—数学]