Work

Fast weak-KAM integrators for separable Hamiltonian systems

Year: 2012

Type: preprint

Abstract: We consider a numerical scheme for Hamilton-Jacobi equations based on a direct discretization of the Lax-Oleinik semi-group. We prove that this method is convergent with respect to the time and space stepsizes provided the solution is Lipschitz, and give an error estimate. Moreover, we prove that the numerical scheme is a geometric integrator satisfying a discrete weak-KAM theorem which allows to control its long time behavior. Taking advantage of a fast algorithm for computing min-plus convolutions based on the decomposition of the function into concave and convex parts, we show that the numerical scheme can be implemented in a very efficient way.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1210.4090

Authors: Bouillard, Anne, Faou, Erwan, Zavidovique, Maxime

Institutions: Institut national de recherche en sciences et technologies du numérique, École Normale Supérieure - PSL, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Pierre-et-Marie-Curie, École Normale Supérieure Paris-Saclay

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2952080104

Cites: 24

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Related to: 10