A New Initial Value Technique for Singular Perturbation Problems Using Exponentially Finite Difference Scheme

Abstract

In the present analysis, an \( \upvarepsilon \)-uniform initial value technique is presented for solving singularly perturbed problems for linear and semi-linear second-order ordinary differential equations arising in a chemical reactor theory having a boundary layer at one end point. In this computational technique, the original problem is reduced to an asymptotically equivalent first-order singular initial value problem and a terminal boundary value problem. The required approximate solution is obtained using Box and Trapezoidal schemes after introducing an exponential factor to the singular perturbed initial value problem. Accuracy and efficiency of this technique are validated by considering error estimates and with well-established numerical examples.