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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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1 April 2008

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

,
and
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
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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.

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