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Structure Preserving Schemes for Mean-Field Equations of Collective Behavior

  • Lorenzo Pareschi
  • Mattia Zanella
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 237)

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

Collective behavior Fokker-Planck equations Mean-field equations Structure preserving methods 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of FerraraFerraraItaly
  2. 2.Department of Mathematical Computer SciencesPolitecnico di TorinoTorinoItaly

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