Structure Preserving Schemes for Nonlinear Fokker–Planck Equations and Applications

Structure Preserving Schemes for Nonlinear Fokker–Planck Equations and Applications In this paper we focus on the construction of numerical schemes for nonlinear Fokker–Planck equations that preserve the structural properties, like non negativity of the solution, entropy dissipation and large time behavior. The methods here developed are second order accurate, they do not require any restriction on the mesh size and are capable to capture the asymptotic steady states with arbitrary accuracy. These properties are essential for a correct description of the underlying physical problem. Applications of the schemes to several nonlinear Fokker–Planck equations with nonlocal terms describing emerging collective behavior in socio-economic and life sciences are presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Scientific Computing Springer Journals

Structure Preserving Schemes for Nonlinear Fokker–Planck Equations and Applications

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Algorithms; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics
ISSN
0885-7474
eISSN
1573-7691
D.O.I.
10.1007/s10915-017-0510-z
Publisher site
See Article on Publisher Site

Abstract

In this paper we focus on the construction of numerical schemes for nonlinear Fokker–Planck equations that preserve the structural properties, like non negativity of the solution, entropy dissipation and large time behavior. The methods here developed are second order accurate, they do not require any restriction on the mesh size and are capable to capture the asymptotic steady states with arbitrary accuracy. These properties are essential for a correct description of the underlying physical problem. Applications of the schemes to several nonlinear Fokker–Planck equations with nonlocal terms describing emerging collective behavior in socio-economic and life sciences are presented.

Journal

Journal of Scientific ComputingSpringer Journals

Published: Jul 26, 2017

References

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