The L1-Error Estimates for a Hamiltonian-Preserving Scheme for the Liouville Equation with Piecewise Constant Potentials and Perturbed Initial Data
Year: 2011
Journal of Computational Mathematics, Vol. 29 (2011), Iss. 1 : pp. 26–48
Abstract
We study the L1-error of a Hamiltonian-preserving scheme, developed in [19], for the Liouville equation with a piecewise constant potential in one space dimension when the initial data is given with perturbation errors. We extend the l1-stability analysis in [46] and apply the L1-error estimates with exact initial data established in [45] for the same scheme. We prove that the scheme with the Dirichlet incoming boundary conditions and for a class of bounded initial data is L1-convergent when the initial data are given with a wide class of perturbation errors, and derive the L1-error bounds with explicit coefficients. The convergence rate of the scheme is shown to be less than the order of the initial perturbation error, matching with the fact that the perturbation solution can be l1-unstable.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1006-m3057
Journal of Computational Mathematics, Vol. 29 (2011), Iss. 1 : pp. 26–48
Published online: 2011-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Liouville equations Hamiltonian preserving schemes Piecewise constant potentials Error estimate Perturbed initial data Semiclassical limit.