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

• 来源期刊: 计算数学（英文版）
• 关键词: Liouville equations Hamiltonian-preserving schemes Piecewise constant potentials e1-error estimate Half-order error bound Semiclassical limit
• 年，卷（期）: 2017,（6）
• 页码范围: 814-827
• 页数: 14页
• 语种: 英文
• DOI: 10.4208/jcm.1701-m2016-0717

摘要

This work is concerned with e1-error estimates on a Hamiltonian-preserving scheme for the Liouville equation with piecewise 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.