(untitled) (Journal of Computational Mathematics, 2021)
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.