Non-polynomial spline method for singularly perturbed differential difference equations with delay and advance terms

Abstract

In this study, we introduced a non-polynomial spline technique to address singularly perturbed differential difference equations involving both delay and advanced parameters. This method exhibits a linear rate of convergence, and we have thoroughly analyzed its convergence properties. To demonstrate the effectiveness of this approach, we provided two numerical examples. We presented the maximum absolute errors in tabular form and displayed the pointwise absolute errors using graphical representations. Additionally, we included tables showing the numerically obtained rate of convergence.