AUTHOR=Mei Yingjie , Wang Fuzhang , Hou Enran 

TITLE=A TPS-based numerical method for simulating the non-linear diffusion logistic population model

JOURNAL=Frontiers in Physics

VOLUME=Volume 13 - 2025

YEAR=2025

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2025.1643625

DOI=10.3389/fphy.2025.1643625

ISSN=2296-424X

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.