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Qualitative Numerical Analysis of a Free-Boundary Diffusive Logistic Model

Author

Listed:
  • María Consuelo Casabán

    (Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain)

  • Rafael Company

    (Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain)

  • Vera N. Egorova

    (Depto de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Avda. de los Castros, s/n, 39005 Santander, Spain)

  • Lucas Jódar

    (Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain)

Abstract

A two-dimensional free-boundary diffusive logistic model with radial symmetry is considered. This model is used in various fields to describe the dynamics of spreading in different media: fire propagation, spreading of population or biological invasions. Due to the radial symmetry, the free boundary can be treated by a front-fixing approach resulting in a fixed-domain non-linear problem, which is solved by an explicit finite difference method. Qualitative numerical analysis establishes the stability, positivity and monotonicity conditions. Special attention is paid to the spreading–vanishing dichotomy and a numerical algorithm for the spreading–vanishing boundary is proposed. Theoretical statements are illustrated by numerical tests.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1296-:d:1090891
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    References listed on IDEAS

    as
    1. Mandel, Jan & Bennethum, Lynn S. & Beezley, Jonathan D. & Coen, Janice L. & Douglas, Craig C. & Kim, Minjeong & Vodacek, Anthony, 2008. "A wildland fire model with data assimilation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 584-606.
    2. R. Company & V. N. Egorova & L. Jódar, 2014. "Solving American Option Pricing Models by the Front Fixing Method: Numerical Analysis and Computing," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, April.
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