A TPS-based numerical method for simulating the non-linear diffusion logistic population model
Year: 2025
Type: article
Abstract: The Fisher–Kolmogorov–Petrovsky–Piskunov equation is a diffusive logistic model for the population density of an invasive species. This paper presents a one-level numerical simulation of the non-linear diffusion logistic population model using the thin plate spline (TPS) radial basis function (RBF) collocation method. Based on the combination of time and space variables, the time–space points are constructed. During the collocation procedure, the non-uniform point distribution case is considered for comparison with the traditional uniform point distribution case. Numerical examples show that the one-level TPS-RBF collocation method avoids the complexities of mesh generation and re-meshing. We can conclude that non-uniform point distributions yield higher accuracy in simulating the non-linear diffusion logistic population model than uniform distributions, especially with increased collocation point density. The efficiency, accuracy, and stability of the proposed method are demonstrated through numerical experiments.
Source: Frontiers in Physics
Authors: Yingjie Mei, Fuzhang Wang, Enran Hou
Institutions: Xuzhou University of Technology, Huaibei Normal University
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,077
OpenAlex ID: W4413867828