Non-standard fitted operator scheme for singularly perturbed boundary value problem

Abstract

A non-standard fitted operator finite difference technique is designed for the solution of singularly perturbed two-point boundary value problems. Using the solution of reduced problem of the singular perturbation problem, it is transformed to an equivalent equation of first order. This first order singularly perturbed problem is solved by using an exact non-standard fitted operator method with an appropriate condition. To demonstrate the method computationally, it is implemented on several examples. From the numerical results, it is noticed that the proposed scheme is in respectable agreement with the exact solution with minimal computational effort.