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2021. $ℓ^1$-Error Estimates on the Hamiltonian-Preserving Scheme for the Liouville Equation with Piecewise Constant Potentials: A Simple Proof. Journal of Computational Mathematics. 35, 6 (Jul. 2021), 814–827. DOI:https://doi.org/10.4208/jcm.1701-m2016-0717.