Generalization of the finite difference method in distributions spaces

Stéphane Labbé (1) , Emmanuel Trélat (2)

1 EDP
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

The aim of this article is to propose a generalization of the finite difference scheme suitable with solutions of Dirac distribution type. This type of solution is for example encountered in earthquake or explosion simulations. In such problems, the difficulty is to catch sharply a moving singular front modeled by a Dirac type distribution. We give a general framework to deal with numerical methods, and use it to build finite difference methods in distribution spaces. Numerical examples are provided for a one-dimensional wave equation.

Mots clés: finite differences; partial differential equation; wave equation

Domaines: Analyse numérique [math.NA]

Stéphane Labbé, Emmanuel Trélat. Generalization of the finite difference method in distributions spaces. 2006. ⟨hal-00097806⟩