IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v188y2021icp342-362.html
   My bibliography  Save this article

Structure preserving schemes for Fokker–Planck equations with nonconstant diffusion matrices

Author

Listed:
  • Loy, Nadia
  • Zanella, Mattia

Abstract

In this work we consider an extension of a recently proposed structure preserving numerical scheme for nonlinear Fokker–Planck-type equations to the case of nonconstant full diffusion matrices. While in existing works the schemes are formulated in a one-dimensional setting, here we consider exclusively the two-dimensional case. We prove that the proposed schemes preserve fundamental structural properties like nonnegativity of the solution without restriction on the size of the mesh and entropy dissipation. Moreover, all the methods presented here are at least second order accurate in the transient regimes and arbitrarily high order for large times in the hypothesis in which the flux vanishes at the stationary state. Suitable numerical tests will confirm the theoretical results.

Suggested Citation

  • Loy, Nadia & Zanella, Mattia, 2021. "Structure preserving schemes for Fokker–Planck equations with nonconstant diffusion matrices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 342-362.
    • Handle: RePEc:eee:matcom:v:188:y:2021:i:c:p:342-362
    DOI: 10.1016/j.matcom.2021.04.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421001464
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.04.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Pareschi, Lorenzo & Toscani, Giuseppe, 2013. "Interacting Multiagent Systems: Kinetic equations and Monte Carlo methods," OUP Catalogue, Oxford University Press, number 9780199655465.
    2. da Silva, P.C. & da Silva, L.R. & Lenzi, E.K. & Mendes, R.S. & Malacarne, L.C., 2004. "Anomalous diffusion and anisotropic nonlinear Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 16-21.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lorenzo Pareschi & Giuseppe Toscani, 2014. "Wealth distribution and collective knowledge. A Boltzmann approach," Papers 1401.4550, arXiv.org.
    2. Giuseppe Toscani, 2016. "Kinetic and mean field description of Gibrat's law," Papers 1606.04796, arXiv.org.
    3. Nicola Bellomo & Richard Bingham & Mark A.J. Chaplain & Giovanni Dosi & Guido Forni & Damian A. Knopoff & John Lowengrub & Reidun Twarock & Maria Enrica Virgillito, 2020. "A multi-scale model of virus pandemic: Heterogeneous interactive entities in a globally connected world," LEM Papers Series 2020/16, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    4. Xia Zhou & Shaoyong Lai, 2023. "The mutual influence of knowledge and individual wealth growth," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(6), pages 1-22, June.
    5. Maira Aguiar & Giovanni Dosi & Damian A. Knopoff & Maria Enrica Virgillito, 2021. "A multiscale network-based model of contagion dynamics: heterogeneity, spatial distancing and vaccination," LEM Papers Series 2021/24, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    6. G. Dimarco & L. Pareschi & G. Toscani & M. Zanella, 2020. "Wealth distribution under the spread of infectious diseases," Papers 2004.13620, arXiv.org.
    7. Albi, Giacomo & Chignola, Roberto & Ferrarese, Federica, 2022. "Efficient ensemble stochastic algorithms for agent-based models with spatial predator–prey dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 317-340.
    8. Lachowicz, Mirosław & Leszczyński, Henryk & Topolski, Krzysztof A., 2022. "Approximations of kinetic equations of swarm formation: Convergence and exact solutions," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    9. Borsche, Raul & Klar, Axel & Zanella, Mattia, 2022. "Kinetic-controlled hydrodynamics for multilane traffic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    10. Kayser, Kirk & Armbruster, Dieter, 2019. "Social optima of need-based transfers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    11. Ghosh, Asim & Chatterjee, Arnab & Inoue, Jun-ichi & Chakrabarti, Bikas K., 2016. "Inequality measures in kinetic exchange models of wealth distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 465-474.
    12. Mirosław Lachowicz & Henryk Leszczyński, 2020. "Modeling Asymmetric Interactions in Economy," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
    13. Stefania Monica & Federico Bergenti, 2017. "Opinion dynamics in multi-agent systems: selected analytic models and verifying simulations," Computational and Mathematical Organization Theory, Springer, vol. 23(3), pages 423-450, September.
    14. Düring, Bertram & Georgiou, Nicos & Merino-Aceituno, Sara & Scalas, Enrico, 2022. "Continuum and thermodynamic limits for a simple random-exchange model," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 248-277.
    15. Wang, Shengxian & Chen, Xiaojie & Xiao, Zhilong & Szolnoki, Attila, 2022. "Decentralized incentives for general well-being in networked public goods game," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    16. Pedraza, Lucía & Pinasco, Juan Pablo & Saintier, Nicolas & Balenzuela, Pablo, 2021. "An analytical formulation for multidimensional continuous opinion models," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    17. 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.
    18. Trimborn, Torsten & Frank, Martin & Martin, Stephan, 2018. "Mean field limit of a behavioral financial market model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 613-631.
    19. 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.
    20. Gualandi, Stefano & Toscani, Giuseppe, 2019. "Size distribution of cities: A kinetic explanation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 221-234.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:188:y:2021:i:c:p:342-362. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.