# zbMATH — the first resource for mathematics

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.

##### 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
Full Text: