Computational Method for Singularly Perturbed Boundary Value Problems with Dual Boundary Layer

In this paper, we proposed a computational method on a uniform mesh for solving singularly perturbed two-point boundary value problems exhibiting dual boundary layers using exponentially fitting factor. In this method, we extended the Numerov Scheme to the singularly perturbed two-point boundary value problem with first order derivative. By using non symmetric finite differences and mixed finite difference for the first order derivative, the finite difference scheme is derived. An exponential fitting factor is introduced in this finite difference scheme which takes care of the rapid behaviour occurs in the boundary layers. Using the asymptotic approximate solution of singular perturbations, the fitting factor is derived. Discrete invariant imbedding algorithm is used to solve the tridiagonal system of the fitted finite difference method. The method is analyzed for convergence. Numerical experiments are presented to demonstrate the utility and efficiency of the proposed computational method.