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International Journal of Engineering Mathematics
Volume 2014, Article ID 365209, 8 pages
http://dx.doi.org/10.1155/2014/365209
Research Article

Cubic Hermite Collocation Method for Solving Boundary Value Problems with Dirichlet, Neumann, and Robin Conditions

1Department of Mathematics, SLIET, Longowal, Punjab 148106, India
2Department of Mathematics, Punjabi University, Patiala, Punjab 147002, India

Received 6 August 2013; Revised 15 December 2013; Accepted 29 December 2013; Published 24 February 2014

Academic Editor: Viktor Popov

Copyright © 2014 Ishfaq Ahmad Ganaie 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.

Abstract

Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme.