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.

Structure preserving schemes for mean-field equations of collective behavior

Pareschi, Lorenzo
Primo
;
2018

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.
2018
9783319915470
Collective behavior; Fokker-Planck equations Mean-field equations; Structure preserving methods; Mathematics (all)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2397773
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