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Math. Comput. Appl. 2008, 13(1), 23-29; doi:10.3390/mca13010023

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

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.
Published: 1 April 2008
Download PDF [168 KB, uploaded 30 March 2016]

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
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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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.

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