Numerical Solution of Singularly Perturbed Convection Delay Problems Using Self-adaptive Differential Evolution Algorithm

Abstract

In this paper, a new numerical technique is constructed to solve singularly perturbed convection delay problems. First of all, based on Taylor’s series expansion, the given problem is transformed into a singularly perturbed convection-diffusion problem without delay term, which is discretized by using the rational spectral collocation method with a sinh transformation. It should be pointed out that the width of boundary layer, which is chosen as a parameter in the sinh transformation, can be determined. Then, a nonlinear unconstrained optimization problem is designed to determine the width of boundary layer. Finally, the numerical solution of the singularly perturbed problem is converted into minimizing the nonlinear unconstrained optimization problem, which is solved by using a self-adaptive differential evolution (SADE). The numerical results show that the proposed algorithm is a robust and accurate procedure for solving singularly perturbed convection delay problems. Furthermore, the obtained accuracy for the solutions using SADE is much better than results obtained using some others algorithms.