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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 of the Order of the Asymptotic Solutions of a Nonlinear Differential Equation

by
Jianping Cai
Department of Mathematics, Zhangzhou Teachers College, Zhangzhou 363000, China
Math. Comput. Appl. 2006, 11(1), 85-90; https://doi.org/10.3390/mca11010085
Published: 1 April 2006
Versions Notes

Abstract

A perturbation method, the Lindstedt-Poincare method, is used to obtain the asymptotic expansions of the solutions of a nonlinear differential equation arising in general relativity. The asymptotic solutions contain no secular term, which overcomes a defect in Khuri’s paper. A technique of numerical order verification is applied to demonstrate that the asymptotic solutions are uniformly valid for small parameter.
Keywords: perturbation method; asymptotic solution; numerical verification; Lindstedt-Poincare method perturbation method; asymptotic solution; numerical verification; Lindstedt-Poincare method

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MDPI and ACS Style

Cai, J. Numerical Verification of the Order of the Asymptotic Solutions of a Nonlinear Differential Equation. Math. Comput. Appl. 2006, 11, 85-90. https://doi.org/10.3390/mca11010085

AMA Style

Cai J. Numerical Verification of the Order of the Asymptotic Solutions of a Nonlinear Differential Equation. Mathematical and Computational Applications. 2006; 11(1):85-90. https://doi.org/10.3390/mca11010085

Chicago/Turabian Style

Cai, Jianping. 2006. "Numerical Verification of the Order of the Asymptotic Solutions of a Nonlinear Differential Equation" Mathematical and Computational Applications 11, no. 1: 85-90. https://doi.org/10.3390/mca11010085

APA Style

Cai, J. (2006). Numerical Verification of the Order of the Asymptotic Solutions of a Nonlinear Differential Equation. Mathematical and Computational Applications, 11(1), 85-90. https://doi.org/10.3390/mca11010085

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