A numerical method for singularly perturbed turning point problems with an interior layer

The objective of this paper is to present a numerical method for solving singularly perturbed turning point problems exhibiting an interior layer. The method is based on the asymptotic expansion technique and the reproducing kernel method (RKM). The original problem is reduced to interior layer and regular domain problems. The regular domain problems are solved by using the asymptotic expansion method. The interior layer problem is treated by the method of stretching variable and the RKM. Four numerical examples are provided to illustrate the effectiveness of the present method. The results of numerical examples show that the present method can provide very accurate approximate solutions.