Structure preserving schemes for mean-field equations of collective behavior
Numerical Analysis
2017-05-19 v1 Adaptation and Self-Organizing Systems
Abstract
In this paper we consider the development of numerical schemes for mean-field equations describing the collective behavior of a large group of interacting agents. The schemes are based on a generalization of the classical Chang-Cooper approach and are capable to preserve the main structural properties of the systems, namely nonnegativity of the solution, physical conservation laws, entropy dissipation and stationary solutions. In particular, the methods here derived are second order accurate in transient regimes whereas they can reach arbitrary accuracy asymptotically for large times. Several examples are reported to show the generality of the approach.
Keywords
Cite
@article{arxiv.1705.06360,
title = {Structure preserving schemes for mean-field equations of collective behavior},
author = {Lorenzo Pareschi and Mattia Zanella},
journal= {arXiv preprint arXiv:1705.06360},
year = {2017}
}
Comments
Proceedings of the XVI International Conference on Hyperbolic Problems