A Postverification Method for Solving Forced Duffing Oscillator Problems without Prescribed Periods-Reference-Cited by-同舟云学术

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

Published:2014 Issue: Volume:2014 Page:1-10
ISSN:1110-757X
Container-title:Journal of Applied Mathematics
language:en
Short-container-title:Journal of Applied Mathematics

Author:

Lin Hong-Yen¹²^ORCID,Yen Chien-Chang³^ORCID,Jen Kuo-Ching⁴^ORCID,Jea Kang C.²³^ORCID

Affiliation:

1. Department of Computer Science and Information Engineering, Fu Jen Catholic University, New Taipei City 24205, Taiwan

2. Graduate Institute of Applied Science and Engineering, Fu Jen Catholic University, New Taipei City 24205, Taiwan

3. Department of Mathematics, Fu Jen Catholic University, New Taipei City 24205, Taiwan

4. General Education Center, St. John’s University, New Taipei City 25135, Taiwan

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.

Funder

National Science Council

Publisher

Hindawi Limited

Subject

Applied Mathematics

Link

http://downloads.hindawi.com/journals/jam/2014/317460.pdf

Reference18 articles.

1. Analytical solutions for asymmetric periodic motions to chaos in a hardening Duffing oscillator

2. The Duffing oscillator under combined periodic and random excitations

3. Analytical Approximate Solutions for the Cubic-Quintic Duffing Oscillator in Terms of Elementary Functions