An Accurate Analytical Solution to Strongly Nonlinear Differential Equations

Authors

G. M. Ismail, Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, EgyptFollow
M. Abul-Ez, Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, EgyptFollow
N. M. Farea, Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

The study presents an alternative analytical method called Newton Harmonic Balance Method (NHBM) to provide an analytical solution for two nonlinear differential equations that appear in specific dynamics. This method is based on combining Newton’s method and the harmonic balance method. Because the periodic solution is analytically proved, the relation between the natural frequency and the amplitude is obtained in an analytical form. The study compares the present results with the previous ones obtained by other methods to ensure the quality of the NHBM. Comparisons with Runge-Kutta numerical integration solutions are also made and excellent agreement has been observed. The NHBM enables to linearize the governing equations prior to applying the harmonic balance method. Moreover, it can lead to adequately accurate solutions for nonlinear oscillators.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140118

Recommended Citation

M. Ismail, G.; Abul-Ez, M.; and M. Farea, N. (2020) "An Accurate Analytical Solution to Strongly Nonlinear Differential Equations," Applied Mathematics & Information Sciences: Vol. 14: Iss. 1, Article 18.
DOI: http://dx.doi.org/10.18576/amis/140118
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss1/18