Authors:
Charles Baidya,B M Ikramul Haque,M. M. Ayub Hossain,DOI NO:
https://doi.org/10.26782/jmcms.2026.07.00004Keywords:
Helmholtz Duffing Oscillator,Iteration Method,Extended Iteration Method,Fourier cosine series.,Abstract
The Helmholtz–Duffing oscillator is a type of nonlinear system that frequently occurs in mechanical, electrical, and physical models incorporating nonlinear restoring forces. It combines the features of Helmholtz and Duffing nonlinearities. Due to the presence of the combined quadratic and cubic nonlinear terms, it is still difficult to obtain exact analytical solutions. This paper proposes an Extended Iteration Method (EIM) to provide better analytical solutions for the Helmholtz-Duffing oscillator. The derived analytical solutions are compared with numerical solutions and those found in the literature to verify the accuracy of the method. Numerical solutions and with those available in the literature. The findings show that the suggested EIM outperforms existing analytical methods in terms of accuracy and simplicity, producing outstanding agreement with numerical solutions. The approach may be applied to many additional severely nonlinear models and offers a robust and effective foundation for researching nonlinear oscillatory systems.Refference:
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