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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 Association for Scientific Research (ASR).
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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://doi.org/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

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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://doi.org/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://doi.org/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://doi.org/10.3390/mca13010023

APA Style

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

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