Solving Two-dimensional Elliptic Singular Perturbation Problems by Particle Swarm Optimization Algorithm

We study a class of elliptic singular perturbation problems on Bakhvalov-Shishkin mesh in this paper. In the process of solving the numerical scheme, we take the error norm between the exact solution and the numerical solution as the objective function, and use particle swarm optimization algorithm to obtain two optimal mesh parameters, so as to obtain the optimal value of error norm. From the results of numerical experimental research, it can be seen that we obtain higher precision numerical solution than selecting mesh transition points manually by the particle swarm optimization algorithm at a low cost, and the numerical solution reflect the singular perturbation characteristics of the exact solutions well.