Using perturbation methods and Laplace-Padé approximation to solve nonlinear problems

Abstract

In this paper, the perturbation method and Pad 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 70 .