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

Jianping Cai

doi:10.3390/mca11010085

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Article

1 April 2006

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

Department of Mathematics, Zhangzhou Teachers College, Zhangzhou 363000, China

Math. Comput. Appl.2006, 11(1), 85-90;https://doi.org/10.3390/mca11010085

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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

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