Next Article in Journal
Active Suspension Control of Eight Degrees of Freedom Vehicle Model
Previous Article in Journal
Motor Input Voltage and Rectifier Firing Angle Variation with Load Torque in Constant Current Operated Induction Motors
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
MCA
Volume 13
Issue 1
10.3390/mca13010023
mca-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Previous articles were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence, and they are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Numerical Verification and Comparison of Error of Asymptotic Expansion Solution of the Duffing Equation

by
Jianping Cai
1,2,*,
Shuhui Chen
1 and
Cuihong Yang
3
1
Department of Applied Mechanics and Engineering, Zhongshan University, Guangzhou 510275, China
2
Department of Mathematics, Zhangzhou Teachers College, Zhangzhou 363000, China
3
Department of Mathematics, Central China Normal University, Wuhan 430079, China
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2008, 13(1), 23-29; https://0-doi-org.brum.beds.ac.uk/10.3390/mca13010023
Published: 1 April 2008
Versions Notes

Abstract

A numerical order verification technique is applied to demonstrate that the asymptotic expansions of solutions of the Duffing equation obtained respectively by the Lindstedt-Poincaré(LP) method and the modified Lindstedt-Poincaré(MLP) method are uniformly valid for small parameter values. A numerical comparison of error shows that the MLP method is valid whereas the LP method is invalid for large parameter values.
Keywords: nonlinear oscillation; perturbation method; asymptotic expansion solution;numerical verification nonlinear oscillation; perturbation method; asymptotic expansion solution;numerical verification

Share and Cite

MDPI and ACS Style

Cai, J.; Chen, S.; Yang, C. Numerical Verification and Comparison of Error of Asymptotic Expansion Solution of the Duffing Equation. Math. Comput. Appl. 2008, 13, 23-29. https://0-doi-org.brum.beds.ac.uk/10.3390/mca13010023

AMA Style

Cai J, Chen S, Yang C. Numerical Verification and Comparison of Error of Asymptotic Expansion Solution of the Duffing Equation. Mathematical and Computational Applications. 2008; 13(1):23-29. https://0-doi-org.brum.beds.ac.uk/10.3390/mca13010023

Chicago/Turabian Style

Cai, Jianping, Shuhui Chen, and Cuihong Yang. 2008. "Numerical Verification and Comparison of Error of Asymptotic Expansion Solution of the Duffing Equation" Mathematical and Computational Applications 13, no. 1: 23-29. https://0-doi-org.brum.beds.ac.uk/10.3390/mca13010023

Article Metrics

Back to TopTop