Numerical Solution of a Singularly - Perturbed Boundary-Value Problems by Using A Non-Polynomial Spline

TL;DR

This paper introduces non-polynomial cubic spline methods for numerically solving singularly perturbed boundary value problems, achieving second and fourth order accuracy and demonstrating efficiency through numerical comparisons.

Contribution

It develops new non-polynomial spline-based methods for singularly perturbed problems, with proven accuracy and applicability to both singular and non-singular cases.

Findings

Methods are second and fourth order accurate.

Numerical results show high efficiency.

Compared favorably with existing methods.

Abstract

We consider a non-polynomial cubic spline to develop the classes of methods for the numerical solution of singularly perturbed two-point boundary value problems. The proposed methods are second and fourth order accurate and applicable to problems both in singular and non-singular cases. Numerical results are given to illustrate the efficiency of our methods and compared with the methods given by different authors.