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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 317460, 10 pages
http://dx.doi.org/10.1155/2014/317460
Research Article

A Postverification Method for Solving Forced Duffing Oscillator Problems without Prescribed Periods

1Department of Computer Science and Information Engineering, Fu Jen Catholic University, New Taipei City 24205, Taiwan
2Graduate Institute of Applied Science and Engineering, Fu Jen Catholic University, New Taipei City 24205, Taiwan
3Department of Mathematics, Fu Jen Catholic University, New Taipei City 24205, Taiwan
4General Education Center, St. John’s University, New Taipei City 25135, Taiwan

Received 29 March 2014; Revised 17 July 2014; Accepted 20 July 2014; Published 26 August 2014

Academic Editor: Suh-Yuh Yang

Copyright © 2014 Hong-Yen Lin 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

This paper proposes a postverification method (PVM) for solving forced Duffing oscillator problems without prescribed periods. Comprising a postverification procedure and small random perturbation, the proposed PVM improves the sensitivity of the convergence of Newton’s iteration. Numerical simulations revealed that the PVM is more accurate and robust than Kubíček’s approach. We applied the PVM to previous research on bifurcation problems.