Numerical solution of a singularly perturbed problem with Robin boundary conditions using particle swarm optimization algorithm

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.