Journal
MISKOLC MATHEMATICAL NOTES
Volume 14, Issue 1, Pages 89-101Publisher
UNIV MISKOLC INST MATH
DOI: 10.18514/MMN.2013.517
Keywords
Perturbation method; nonlinear problems; approximation methods
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In this paper, the perturbation method and Pade transformation are used to provide an approximate solution of elliptic integrals of the second kind and of complete integrals of the first kind. Besides, we used the obtained results to calculate an analytic expression for the period of a simple pendulum. The method has an acceptable accuracy for high values of the initial amplitude, compared to the relative error < 1.7% for initial angles theta <= 70 degrees
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