IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v221y2024icp55-78.html
   My bibliography  Save this article

A random free-boundary diffusive logistic differential model: Numerical analysis, computing and simulation

Author

Listed:
  • Casabán, M.-C.
  • Company, R.
  • Egorova, V.N.
  • Jódar, L.

Abstract

A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this paper we extend the diffusive logistic model with unknown moving front to the random scenario by assuming that the involved parameters have a finite degree of randomness. The resulting mathematical model becomes a random free boundary partial differential problem and it is addressed numerically combining the finite difference method with two approaches for the treatment of the moving front. Firstly, we propose a front-fixing transformation, reshaping the original random free boundary domain into a fixed deterministic one. A second approach is using the front-tracking method to capture the evolution of the moving front adapted to the random framework. Statistical moments of the approximating solution stochastic process and the stochastic moving boundary solution are calculated by the Monte Carlo technique. Qualitative numerical analysis establishes the stability and positivity conditions. Numerical examples are provided to compare both approaches, study the spreading-vanishing dichotomy, prove qualitative properties of the schemes and show the numerical convergence.

Suggested Citation

  • Casabán, M.-C. & Company, R. & Egorova, V.N. & Jódar, L., 2024. "A random free-boundary diffusive logistic differential model: Numerical analysis, computing and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 55-78.
    • Handle: RePEc:eee:matcom:v:221:y:2024:i:c:p:55-78
    DOI: 10.1016/j.matcom.2024.02.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847542400065X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.02.016?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. Durrett, Rick & Foo, Jasmine & Leder, Kevin & Mayberry, John & Michor, Franziska, 2010. "Evolutionary dynamics of tumor progression with random fitness values," Theoretical Population Biology, Elsevier, vol. 78(1), pages 54-66.
    2. Casabán, M.-C. & Company, R. & Jódar, L., 2023. "Numerical difference solution of moving boundary random Stefan problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 878-901.
    3. María Consuelo Casabán & Rafael Company & Lucas Jódar, 2021. "Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
    4. Vynnycky, M., 2023. "On boundary immobilization for one-dimensional Stefan-type problems with a moving boundary having initially parabolic-logarithmic behaviour," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    5. María Consuelo Casabán & Rafael Company & Vera N. Egorova & Lucas Jódar, 2023. "Qualitative Numerical Analysis of a Free-Boundary Diffusive Logistic Model," Mathematics, MDPI, vol. 11(6), pages 1-19, March.
    6. Nepal, Surendra & Wondmagegne, Yosief & Muntean, Adrian, 2023. "Analysis of a fully discrete approximation to a moving-boundary problem describing rubber exposed to diffusants," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    7. Acevedo, Miguel A. & Marcano, Mariano & Fletcher, Robert J., 2012. "A diffusive logistic growth model to describe forest recovery," Ecological Modelling, Elsevier, vol. 244(C), pages 13-19.
    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. Bonneau, Mathieu & Johnson, Fred A. & Romagosa, Christina M., 2016. "Spatially explicit control of invasive species using a reaction–diffusion model," Ecological Modelling, Elsevier, vol. 337(C), pages 15-24.
    2. Lucas Jódar & Rafael Company, 2022. "Preface to “Mathematical Methods, Modelling and Applications”," Mathematics, MDPI, vol. 10(9), pages 1-2, May.
    3. Foo, Jasmine & Leder, Kevin & Schweinsberg, Jason, 2020. "Mutation timing in a spatial model of evolution," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6388-6413.
    4. Delitala, Marcello & Lorenzi, Tommaso, 2011. "A mathematical model for progression and heterogeneity in colorectal cancer dynamics," Theoretical Population Biology, Elsevier, vol. 79(4), pages 130-138.
    5. Hwai-Ray Tung & Rick Durrett, 2021. "Signatures of neutral evolution in exponentially growing tumors: A theoretical perspective," PLOS Computational Biology, Public Library of Science, vol. 17(2), pages 1-12, February.
    6. Foo, Jasmine & Leder, Kevin & Zhu, Junfeng, 2014. "Escape times for branching processes with random mutational fitness effects," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3661-3697.
    7. Casabán, M.-C. & Company, R. & Jódar, L., 2023. "Numerical difference solution of moving boundary random Stefan problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 878-901.
    8. Safarzynska, Karolina, 2020. "Collective punishment promotes resource conservation if it is not enforced," Forest Policy and Economics, Elsevier, vol. 113(C).

    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:221:y:2024:i:c:p:55-78. 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.