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

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.


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
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