Numerical Treatment of General Third Order Boundary Value Problems via B-Spline Method

Abstract

In this paper, the quintic B-spline functions are used to approximate the solution of general third order boundary value problems directly. The convergence analysis of the proposed method is investigated to prove its fourth order of convergence. Four numerical examples are performed to demonstrate the efficiency and accuracy of the proposed technique. The numerical results seem to indicate that the proposed method is more accurate than some accessible methods in the literature in terms of error. The primary strength of the presented method is its simple and rapid implementation.