BRIEF RESEARCH REPORT article
Front. Phys.
Sec. Interdisciplinary Physics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1643625
TPS-based numerical method for simulating the nonlinear diffusion logistic population model
Provisionally accepted
- 1Xuzhou University of Technology, Xuzhou, China
- 2Huaibei Normal University, Huaibei, China
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The Fisher-Kolmogorov-Petrovsky-Piskunov equation is a diffusive logistic model for the density of population of the invasive species. This paper presents a one-level numerical simulation of the nonlinear 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 traditional uniform point distribution case. Numerical examples show that the one-level TPS-RBF collocation method avoids the complexities associated with mesh generation and re-meshing. We can conclude that non-uniform point distributions yield higher accuracy in simulating the nonlinear 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.
Keywords: Fisher-Kolmogorov-Petrovsky-Piskunov equation, Thin plate spline, Radial basis function, numerical simulation, meshless method
Received: 09 Jun 2025; Accepted: 13 Aug 2025.
Copyright: © 2025 Mei, Wang and Hou. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence:
Fuzhang Wang, Xuzhou University of Technology, Xuzhou, China
Enran Hou, Huaibei Normal University, Huaibei, China
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