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Mathematical Problems in Engineering
Volume 2014, Article ID 108560, 10 pages
Research Article

Application of Hybrid Cubic B-Spline Collocation Approach for Solving a Generalized Nonlinear Klien-Gordon Equation

1School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Pulau Pinang, Malaysia
2Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Pauh, Perlis, Malaysia
3Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan

Received 24 June 2014; Accepted 11 December 2014; Published 30 December 2014

Academic Editor: Anuar Ishak

Copyright © 2014 Shazalina Mat Zin 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.


The generalized nonlinear Klien-Gordon equation is important in quantum mechanics and related fields. In this paper, a semi-implicit approach based on hybrid cubic B-spline is presented for the approximate solution of the nonlinear Klien-Gordon equation. The usual finite difference approach is used to discretize the time derivative while hybrid cubic B-spline is applied as an interpolating function in the space dimension. The results of applications to several test problems indicate good agreement with known solutions.