Homotopy perturbation method for strongly nonlinear oscillators

JH He, ML Jiao, KA Gepreel, Y Khan - Mathematics and Computers in …, 2023 - Elsevier
This paper reveals the effectiveness of the homotopy perturbation method for strongly
nonlinear oscillators. A generalized Duffing oscillator is adopted to elucidate the solving …

A simple frequency formulation for the tangent oscillator

JH He, Q Yang, CH He, Y Khan - Axioms, 2021 - mdpi.com
The frequency of a nonlinear vibration system is nonlinearly related to its amplitude, and this
relationship is critical in the design of a packaging system and a microelectromechanical …

Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: A review

M Bayat, I Pakar, G Domairry - Latin American Journal of Solids and …, 2012 - SciELO Brasil
This review features a survey of some recent developments in asymptotic techniques and
new developments, which are valid not only for weakly nonlinear equations, but also for …

[BOOK][B] Artificial neural networks for engineers and scientists: solving ordinary differential equations

S Chakraverty, S Mall - 2017 - taylorfrancis.com
Differential equations play a vital role in the fields of engineering and science. Problems in
engineering and science can be modeled using ordinary or partial differential equations …

On the multistage differential transformation method for analyzing dam** Duffing oscillator and its applications to plasma physics

NH Aljahdaly, SA El-Tantawy - Mathematics, 2021 - mdpi.com
The multistage differential transformation method (MSDTM) is used to find an approximate
solution to the forced dam** Duffing equation (FDDE). In this paper, we prove that the …

Hamiltonian approach to nonlinear oscillators

JH He - Physics Letters A, 2010 - Elsevier
A Hamiltonian approach to nonlinear oscillators is suggested. A conservative oscillator
always admits a Hamiltonian invariant, H, which keeps unchanged during oscillation. This …

On the approximate solutions to a damped harmonic oscillator with higher-order nonlinearities and its application to plasma physics: semi-analytical solution and …

AH Salas, SA El-Tantawy - The European Physical Journal Plus, 2020 - Springer
In this paper, a strongly nonlinear oscillator equation with higher-order nonlinear (cubic)
restoring force, namely damped Duffing equation with higher-order nonlinearities, has been …

[HTML][HTML] Approximate solution for nonlinear Duffing oscillator with dam** effect using the modified differential transform method

S Nourazar, A Mirzabeigy - Scientia Iranica, 2013 - Elsevier
The Duffing oscillator is a common model for nonlinear phenomena in science and
engineering. In this paper, we use the modified differential transform method to obtain the …

[HTML][HTML] Exact solution of the cubic-quintic Duffing oscillator

A Elías-Zúñiga - Applied Mathematical Modelling, 2013 - Elsevier
In this paper, we derive the exact solution of the cubic-quintic Duffing oscillator based on the
use of Jacobi elliptic functions. We also showed that the exact angular frequency of this …

[PDF][PDF] Numerical solution of full fractional Duffing equations with Cubic-Quintic-Heptic nonlinearities

P Pirmohabbati, AHR Sheikhani, HS Najafi… - AIMS math, 2020 - researchgate.net
In this article, based on the operational matrix of fractional order integration, we introduce a
method for the numerical solution of fractional strongly nonlinear Duffing oscillators with …