A modified global error minimization method for solving nonlinear Duffing-harmonic oscillators

AIMS Mathematics

article

Gamal M. Ismail¹  Maha M. El-Moshneb¹  Mohra Zayed³ 

[1] Department of Mathematics, Faculty of Science, Sohag University;Department of Mathematics, Faculty of Science, Islamic University of Madinah;Mathematics Department, College of Science, King Khalid University

关键词: global error minimization method;    Duffing-harmonic oscillator;    analytical and approximate solutions;    periodic solution;    numerical solution;   

DOI  :  10.3934/math.2023023

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this paper, a third-order approximate solution of strongly nonlinear Duffing-harmonic oscillators is obtained by extending and improving an analytical technique called the global error minimization method (GEMM). We have made a comparison between our results, those obtained from the other analytical methods and the numerical solution. Consequently, we notice a better agreement with the numerical solution than other known analytical methods. The results are valid for both small and large oscillation amplitude. The obtained results demonstrate that the present method can be easily extended to strongly nonlinear problems, as indicated in the presented applications.

【 授权许可】

CC BY