Qualitative Numerical Analysis of a Free-Boundary Diffusive Logistic Model

María Consuelo Casabán, Rafael Company (), Vera N. Egorova and Lucas Jódar
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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

Mathematics, 2023, vol. 11, issue 6, 1-19

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.

Keywords: free-boundary problem; diffusive logistic model; radial symmetry; spreading–vanishing dichotomy; numerical analysis; finite-difference method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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