A New Technique For Solving Singularly Perturbed Boundary Value Problems Based On The Sinc-collocation Method

Singularly perturbed boundary value problems are a kind of differential equations, and in these problems a small parameter ε multiplies to the highest derivative. A well-known fact is that the solution of such problems displays sharp boundary layers when the singular para-meter is very small, while away from the layers it behaves regularly. Numerically, the pre-sence of the perturbation parameter leads to difficulties when classical numerical techniques are used to solve such problems.The sine method is a highly efficient numerical method developed by F.Stenger. In com-parison with the finite difference and the finite element methods, the sine approach is more suitable for handling singularities in boundary layers. It is well known that the approximations by the sinc functions are characterized by exponentially decaying errors.In this paper we consider the singularly perturbed boundary value problems using the sine-collocation method. An improved technique is adopted to solve these problems with very thin boundary layers. The major advantage of the proposed method is that it can control the number of the collocation points which are within the boundary layer. The scheme is tested on five examples and compared with some other methods. Numerical experiments show that the proposed method can obtain better results even for very thin boundary layers.