Numerical Simulation of Multi Parameter Singularly Perturbed Two Point Boundary Value Problem

Abstract

A second-order singularly perturbed differential-difference equation involving both negative and positive shifts is examined in this paper. To obtain an approximate solution, a fitted nonpolynomial spline method is employed. The approach begins with a Taylor series expansion to derive an approximated form of the original problem, after which a fitted non-polynomial spline scheme is constructed in the form of a three-term recurrence relation. The convergence properties of the proposed method are rigorously analyzed, demonstrating a quadratic rate of convergence. Numerical experiments confirm this rate, with the maximum absolute errors reported accordingly. Additionally, the layer behaviour of the solution is investigated and illustrated through graphical representations.