Numerical Solution of Singular Perturbation Problems Via Deviating Argument and Exponential Fitting

In this paper, an exponential fitted method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point via deviating argument. The original second order boundary value problem is transformed to first order differential equation with a small deviating argument. This problem is solved efficiently by using exponential fitting and discrete invariant imbedding method. Maximum absolute errors of several standard examples are presented to support the method.