@Article{JCM-35-6,
author = {Xinchun, Li},
title = {$ℓ^1$-Error Estimates on the Hamiltonian-Preserving Scheme for the Liouville Equation with Piecewise Constant Potentials: A Simple Proof},
journal = {Journal of Computational Mathematics},
year = {2017},
volume = {35},
number = {6},
pages = {814--827},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1701-m2016-0717},
url = {https://global-sci.com/article/84540/1-error-estimates-on-the-hamiltonian-preserving-scheme-for-the-liouville-equation-with-piecewise-constant-potentials-a-simple-proof}
}