Hamiltonian-preserving schemes for the Liouville equation with discontinuous potentials. (English) Zbl 1094.35074

Jin, Shi; Wen, Xin

Commun. Math. Sci. 3, No. 3, 285-315 (2005).

The authors propose two classes for Hamiltonian preserving schemes for Liouville equation with a discontinues potential. They introduce a selection criterion for a unique, physically relevant solution to the underlying linear hyperbolic equation with singular coefficients. These schemes have CFL condition, which is significant improvement over a conventional discretization. These schemes are proved to be positive, and stable in both \(\lambda^{\infty}\) and \(l'\) norms. There are a number of numerical experiments which illustrate the theory.

Reviewer: Qin Mengzhao (Beijing)

MSC:

35L45	Initial value problems for first-order hyperbolic systems
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
70H99	Hamiltonian and Lagrangian mechanics

Keywords:

Liouville equation; discontinuous potential; Hamiltonian-preserving; semiclassical limit; singular coefficients