THE l1-STABILITY OF A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH DISCONTINUOUS POTENTIALS

• 来源期刊: 计算数学（英文版）
• 关键词: Liouville equations Hamiltonian preserving schemes Discontinuous potentials l1-stability Semiclassical limit
• 年，卷（期）: 2009,（1）
• 页码范围: 45-67
• 页数: 23页
• 语种: 英文

摘要

We study the l1-stability of a Hamiltonian-preserving scheme,developed in Jin and Wen,Comm.Math.Sci.,3(2005),285-315],for the Liouville equation with a discontinuous potential in one space dimension.We prove that,for suitable initial data,the scheme is stable in the l1-norm under a hyperbolic CFL condition which is in consistent with the l1-convergence results established in[Wen and Jin,SIAM J.Numer.Anal.,46(2008),2688.2714] for the same scheme.The stability constant is shown to be independent of the computational time.We also provide a counter example to show that for other initial data,in particular,the measure-valued initial data,the numerical solution may become l1-unstable.