A dual mutation differential evolution algorithm for singularly perturbed problems with two small parameters

A novel high accuracy numerical method for a singularly perturbed convection-diffusion problem with two small parameters is presented. At first, the given problem is discretized by using a rational spectral collocation method in barycentric form with sinh transformation. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near to the boundary layers of the domain. Them, a nonlinear unconstrained optimization problem is designed to determine the widths of boundary layers in sinh transform. Finally, a dual mutation differential evolution (DMDE) algorithm is proposed to solve the nonlinear unconstrained optimization problem, and a comparison of the DMDE algorithm with other algorithms has been made, which shows that DMDE algorithm can get fast convergence and find better results.