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Structure preserving stochastic Galerkin methods for Fokker–Planck equations with background interactions

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  • Zanella, Mattia

Abstract

This paper is devoted to the construction of structure preserving stochastic Galerkin schemes for Fokker–Planck type equations with uncertainties and interacting with an external distribution, that we refer to as a background distribution. The proposed methods are capable to preserve physical properties in the approximation of statistical moments of the problem like nonnegativity, entropy dissipation and asymptotic behaviour of the expected solution. The introduced methods are second order accurate in the transient regimes and high order for large times. We present applications of the developed schemes to the case of fixed and dynamic background distribution for models of collective behaviour.

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  • Zanella, Mattia, 2020. "Structure preserving stochastic Galerkin methods for Fokker–Planck equations with background interactions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 168(C), pages 28-47.
    • Handle: RePEc:eee:matcom:v:168:y:2020:i:c:p:28-47
    DOI: 10.1016/j.matcom.2019.07.012
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    References listed on IDEAS

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    1. Lorenzo Pareschi & Giuseppe Toscani, 2014. "Wealth distribution and collective knowledge. A Boltzmann approach," Papers 1401.4550, arXiv.org.
    2. Gualandi, Stefano & Toscani, Giuseppe, 2018. "Pareto tails in socio-economic phenomena: A kinetic description," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 12, pages 1-17.
    3. Pareschi, Lorenzo & Vellucci, Pierluigi & Zanella, Mattia, 2017. "Kinetic models of collective decision-making in the presence of equality bias," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 201-217.
    4. Pareschi, Lorenzo & Toscani, Giuseppe, 2013. "Interacting Multiagent Systems: Kinetic equations and Monte Carlo methods," OUP Catalogue, Oxford University Press, number 9780199655465.
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    Cited by:

    1. Andrea Medaglia & Andrea Tosin & Mattia Zanella, 2022. "Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties," Partial Differential Equations and Applications, Springer, vol. 3(4), pages 1-30, August.

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