Computational Approach for a Singularly Perturbed Differential Equations With Mixed Shifts Using a Non-Polynomial Spline

Abstract

In this paper, a second order singularly perturbed differential difference equation with both the negative and positive shifts is considered. A fitted non-polynomial spline approach is applied to solve the problem. Taylor series expansion process is being used to produce an approximated form of the considered problem, and then a fitted non-polynomial spline approach is devised in the form of a three-term recurrence relation. The convergence of the method is examined, and a quadratic rate of convergence is achieved. The maximum absolute error with quadratic rate of convergence of the solution is recorded. Layer profile is examined using the graphs.