Numerical order verification of the asymptotic expansion of a nonlinear differential equation arising in general relativity

Authors:
S. A. Khuri
Affiliations:
Department of Computer Science, Mathematics and Statistics, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates
Venue:
Applied Mathematics and Computation
Year:
2003

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A technique for the numerical verification of asymptotic expansions

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Abstract

In the present paper, a numerical algorithm is implemented for the order verification of the asymptotic expansion solution of a second-order nonlinear differential equation arising in general relativity. The method is well-adapted and illustrated for a general class of nonlinear perturbation problems. The numerical scheme can be applied to asymptotic problems as long as the numerical solution is also available.