Affiliations: [a] School of Mathematics and Statistics, Guangxi Teachers Education University, Nanning, China
| [b] College of Computer and Information Science, Zunyi Normal College, Zunyi, China
| [c] Guangxi High School Key Laboratory of Complex System and Computational Intelligence, Nanning, China
Correspondence:
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Corresponding author. Li-Bin Liu, School of Mathematics and Statistics, Guangxi Teachers Education University, Nanning 530001, China. E-mail: liulibin969@gxtc.edu.cn.
Abstract: In this paper, a numerical method on a Shishkin mesh to solve the singularly perturbed reaction-diffusion problem with Robin boundary conditions is considered. Especially, for the Robin boundary conditions, a high precision discrete scheme is developed. Then, we first transform the Shishkin mesh transition parameter selection problem into a nonlinear unconstrained optimization problem which is solved by using the basic particle swarm optimization (PSO) algorithm. The experimental results show that the accuracy of numerical solution to singularly perturbed problem on the boundary layers is improved by using the PSO algorithm to optimize Shishkin mesh parameters. It further verifies the feasibility and effectiveness of the proposed method.
