A New Algorithm for Solving Generalized Systems of Second-Order Boundary Value Problems using Nonpolynomial Spline Technique

Abstract

In this paper, a nonpolynomial spline technique is used for developing a new algorithm for solving systems of second-order boundary value problems. Convergence analysis of the algorithm has been carried out which shows that the algorithm is second- as well as fourth-order convergent. In addition to that, four numerical problems including linear, nonlinear and singularly perturbed systems are given to prove the effectiveness and applicability of the developed algorithm. The numerical results show that the developed algorithm is better than the existing methods for solving systems of second-order boundary value problems.