e1-ERROR ESTIMATES ON THE HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH PIECEWISE CONSTANT POTENTIALS： A SIMPLE PROOF  

作　　者：Xinchun Li 

机构地区：[1]School of Mathematical Science, Shanghai Jiao Tong University, Shanghai 200230, China

出　　处：《Journal of Computational Mathematics》2017年第6期814-827,共14页计算数学（英文）

摘　　要：This work is concerned with e1-error estimates on a Hamiltonian-preserving scheme for the Liouville equation with pieeewise constant potentials in one space dimension. We provide an analysis much simpler than these in literature and obtain the same half-order convergence rate. We formulate the Liouville equation with discretized velocities into a series of linear convection equations with piecewise constant coefficients, and rewrite the numerical scheme into some immersed interface upwind schemes. The e1-error estimates are then evaluated by comparing the derived equations and schemes.This work is concerned with e1-error estimates on a Hamiltonian-preserving scheme for the Liouville equation with pieeewise constant potentials in one space dimension. We provide an analysis much simpler than these in literature and obtain the same half-order convergence rate. We formulate the Liouville equation with discretized velocities into a series of linear convection equations with piecewise constant coefficients, and rewrite the numerical scheme into some immersed interface upwind schemes. The e1-error estimates are then evaluated by comparing the derived equations and schemes.

关 键 词：Liouville equations Hamiltonian-preserving schemes Piecewise constant po-tentials e1-error estimate Half-order error bound Semiclassical limit. 

分 类 号：O241.82[理学—计算数学] TU311[理学—数学]