Table of Contents
Journal of Difference Equations
Volume 2014, Article ID 210754, 9 pages
Research Article

Application of Hybrid Functions for Solving Duffing-Harmonic Oscillator

1Department of Mathematics, Yazd University, Yazd, Iran
2Department of Mathematics, Islamic Azad University, Shahrekord Branch, Shahrekord, Iran
3Department of Mathematics, Islamic Azad University, Yazd Branch, Yazd, Iran

Received 9 April 2014; Revised 26 July 2014; Accepted 28 July 2014; Published 14 August 2014

Academic Editor: Athanassios G. Bratsos

Copyright © 2014 Mohammad Heydari 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.


A numerical method for finding the solution of Duffing-harmonic oscillator is proposed. The approach is based on hybrid functions approximation. The properties of hybrid functions that consist of block-pulse and Chebyshev cardinal functions are discussed. The associated operational matrices of integration and product are then utilized to reduce the solution of a strongly nonlinear oscillator to the solution of a system of algebraic equations. The method is easy to implement and computationally very attractive. The results are compared with the exact solution and results from several recently published methods, and the comparisons showed proper accuracy of this method.