BRIEF RESEARCH REPORT article
Front. Phys.
Sec. Statistical and Computational Physics
A local meshless method for the one-dimensional Fisher's equation
Provisionally accepted
- 1Wuxi Taihu University, Wuxi, China
- 2Huaibei Normal University, Huaibei, China
- 3Xuzhou University of Technology, Xuzhou, China
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This study presents a novel local meshless approach for solving one-dimensional Fisher's equation, combining a local scheme, Gaussian radial basis functions (G-RBF), and a collocation technique. The method leverages the Gaussian basis's nonlinear fitting capability, the sparsity of the local scheme to avoid ill-conditioned matrices, and the simplicity of collocation. After time discretization using a finite difference scheme, the method constructs local approximations at each collocation point using G-RBFs over small subsets of neighboring nodes. Numerical experiments confirm its effectiveness in solving Fisher-type problems, with errors decreasing smoothly as collocation points increase and maintaining stable accuracy over time. The proposed method demonstrates computational efficiency, robustness, and potential for handling large-scale reaction-diffusion systems.
Keywords: Fisher's equation, Gaussian radial basis function, Local Meshless Method, numerical simulation, Partial differential equation
Received: 21 Jan 2026; Accepted: 06 Feb 2026.
Copyright: © 2026 Cao, An, Hou and Wang. 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:
Bailing An
Fuzhang Wang
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