By an Extended Iteration Method to Adequate Solutions of Jerk Oscillator Containing Displacement Times Velocity Time's Acceleration and Velocity
jerk equation; truncated fourier series; newton’s method; angular frequency; extended iteration technique
Abstract
Mathematics has applications in every aspect of real life. So many such type of real-life problems are modeled by differential equations. Therefore, differential equations are used as tools to solve many complex situations. With the help of differential equations, we can find the formula to solve many significant issues in many areas of the Anatomy and Physiology of the human body like physical, mental physical, and medical principles. Differential equations can be linear, nonlinear, autonomous, or non-autonomous. Practically, most of the differential equations involving physical phenomena are nonlinear. Hence nonlinear differential equations play a vital role in case of science and engineering. Nonlinear systems are differently classified, and the 'nonlinear jerk oscillator' is one of the most essential parts of a nonlinear system. Different types of nonlinear jerk oscillators will be analyzed using Extended Iteration Method, and the outcome may leave an impact to be better than the current results.
Downloads
How to Cite
References
M Alquran, K Al-Khaled (2012) Effective approximate methods for strongly nonlinear differential equations with oscillations. 6(1), 32-36.
M Alquran, N Doğan (2010) Variational Iteration method for solving twoparameter singularly perturbed two point boundary value problem. 5(1), 7.
Naveed Anjum, Ji-Huan He, Qura Ain, Dan Tian (2021) LI-HE'S MODIFIED HOMOTOPY PERTURBATION METHOD FOR DOUBLY-CLAMPED ELECTRICALLY ACTUATED MICROBEAMS-BASED MICROELECTROMECHANICAL SYSTEM. 19(4), 601.
A Beléndez, A Hernández, T Beléndez, E Fernández, M Álvarez, C Neipp (2007) Application of He's Homotopy Perturbation Method to the Duffing-Harmonic Oscillator. 8(1), 79-88.
A Elías-Zúñiga, O Martínez-Romero, R Córdoba-Díaz (2012) Approximate solution for the Duffing-harmonic oscillator by the enhanced cubication method.
H Gottlieb (2004) Harmonic balance approach to periodic solutions of non-linear jerk equations. 271(3-5), 671-683.
B Haque (2014) A New Approach of Mickens' Extended Iteration Method for Solving Some Nonlinear Jerk Equations. 4(22), 3146.
B Haque, S Flora (2020) On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method. 6(1), 527-536.
B Haque, M Ikramul, Hossain (2021) An analytical approach for solving the nonlinear jerk oscillator containing velocity times acceleration-squared by an extended iteration method. 16(2), 35-47.
M Hosen, M Chowdhury, M Ali, A Ismail (2016) A comparison study on the harmonic balance method and rational harmonic balance method for the Duffing-harmonic oscillator. 12(3), 2721-2732.
H Hu, J Tang (2006) Solution of a Duffing-harmonic oscillator by the method of harmonic balance. 294(3), 637-639.
H Hu, J Tang (2007) A classical iteration procedure valid for certain strongly nonlinear oscillators. 299(1-2), 397-402.
Gamal Ismail, Hanaa Abu-Zinadah (2021) Analytic approximations to non-linear third order Jerk equations via modified global error minimization method. 33(1), 101219.
M Karahan, Fatih (2017) Approximate solutions for the nonlinear third-order ordinary differential equations. 72(6), 547-557.
Xiaoyan Ma, Liping Wei, Zhongjin Guo (2008) He's homotopy perturbation method to periodic solutions of nonlinear Jerk equations. 314(1-2), 217-227.
R Mickens (1984) Comments on the method of harmonic balance. 94(3), 456-460.
R Mickens (1987) Iteration procedure for determining approximate solutions to non-linear oscillator equations. 116(1), 185-187.
R Mickens (2010) Truly nonlinear oscillations: harmonic balance, parameter expansions, iteration, and averaging methods.
A Nayfeh (1973) Perturbation Methods, Ali Hasan Nayfeh, Chichester. John Wiley & Sons. 1973. 425 pp. £9.00.. 77(751), 360-360.
T Ozis, A Yildirim (2007) Determination of the frequency-amplitude relation for a Duffing-harmonic oscillator by the energy balance method. 54(7), 1184-1187.
J Ramos (2010) Analytical and approximate solutions to autonomous, nonlinear, third-order ordinary differential equations. 11(3), 1613-1626.
Published
2023-08-10
Issue
Section
License
Copyright (c) 2023 Authors and Global Journals Private Limited
This work is licensed under a Creative Commons Attribution 4.0 International License.