Table of Contents
International Journal of Computational Mathematics
Volume 2014 (2014), Article ID 527924, 12 pages
Research Article

The Convergence of Geometric Mesh Cubic Spline Finite Difference Scheme for Nonlinear Higher Order Two-Point Boundary Value Problems

1Department of Mathematics, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi 110021, India
2Department of Mathematics, University of Delhi, Delhi 110007, India

Received 31 March 2014; Accepted 10 July 2014; Published 23 July 2014

Academic Editor: Riccardo Dondi

Copyright © 2014 Navnit Jha et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An efficient algorithm for the numerical solution of higher (even) orders two-point nonlinear boundary value problems has been developed. The method is third order accurate and applicable to both singular and nonsingular cases. We have used cubic spline polynomial basis and geometric mesh finite difference technique for the generation of this new scheme. The irreducibility and monotone property of the iteration matrix have been established and the convergence analysis of the proposed method has been discussed. Some numerical experiments have been carried out to demonstrate the computational efficiency in terms of convergence order, maximum absolute errors, and root mean square errors. The numerical results justify the reliability and efficiency of the method in terms of both order and accuracy.