The ${l}^1$-Error Estimates for a Hamiltonian-Preserving Scheme for the Liouville Equation with Piecewise Constant Potentials

DOI10.1137/070700681zbMath1176.65100OpenAlexW2035974650MaRDI QIDQ3642898

Xin Wen, Shih Jin

Publication date: 6 November 2009

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/070700681

zbMATH Keywords

error estimateLiouville equationssemiclassical limitHamiltonian preserving schemeshalf order error boundpiecewise constant potentials

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) Initial value problems for first-order hyperbolic systems (35L45) Hamiltonian and Lagrangian mechanics (70H99)

Related Items (4)

Hamiltonian-Preserving Discontinuous Galerkin Methods for the Liouville Equation With Discontinuous Potential ⋮ A high order numerical method for computing physical observables in the semiclassical limit of the one-dimensional linear Schrödinger equation with discontinuous potentials ⋮ \(l^1\)-error estimates on the immersed interface upwind scheme for linear convection equations with piecewise constant coefficients: a simple proof ⋮ Redheffer Products and Numerical Approximation of Currents in One-Dimensional Semiconductor Kinetic Models

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