$ℓ^1$-Error Estimates on the Hamiltonian-Preserving Scheme for the Liouville Equation with Piecewise Constant Potentials: A Simple Proof
Year: 2017
Author: Xinchun Li
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 6 : pp. 814–827
Abstract
This work is concerned with $ℓ^1$-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 $ℓ^1$-error estimates are then evaluated by comparing the derived equations and schemes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1701-m2016-0717
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 6 : pp. 814–827
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Liouville equations Hamiltonian-preserving schemes Piecewise constant potentials $ℓ^1$-error estimate Half-order error bound Semiclassical limit.