Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 23 Issue 4

precise than other existing solution methods and resolution is valid for the large amplitude of oscillation for the jerk system. We have seen that it is not always true that the extended iteration method yields better results than the direct iteration method. It can be accomplished that the adopted modification is steadfast, effectual, and conformable also, it, also present sufficient well-suited solutions to the nonlinear jerk equations arising in mathematical physics, applied mathematics, and different field of engineering, specially in Mechanical, Electrical, and Space engineering. Availability of Data This study was not supported by any data. Conflict of Interest The authors affirm that they are impartial. R eferences R éférences R eferencias 1. Alquran, M. T., & Al-Khaled, K. (2012). Effective approximate methods for strongly nonlinear differential equations with oscillations. Mathematical Sciences , 6(1), 32-6. 2. Alquran, M. T., & Do ğ an, N. (2010). Variational Iteration method for solving two- parameter singularly perturbed two point boundary value problem. Applications and Applied Mathematics: An International Journal (AAM) , 5 (1), 7. 3. Anjum, Naveed, et al. "Li-He ’ s modified homotopy perturbation method for doubly-clamped electrically actuated microbeams-based microelectromechanical system." Facta Universitatis, Series: Mechanical Engineering 19.4 (2021): 601-612. 4. Bel é ndez, A., Hernandez, A., Bel é ndez, T., Fern á ndez, E., Alvarez, M. L., & Neipp, C. (2007). Application of He's homotopy perturbation method to the Duffing- harmonic oscillator. International Journal of Nonlinear Sciences and Numerical Simulation , 8 (1), 79-88. 5. El í as-Z úñ iga, A., Mart í nez-Romero, O., & C ó rdoba-D í az, R. K. (2012). Approximate solution for the Duffing-harmonic oscillator by the enhanced cubication method. Mathematical problems in Engineering , 2012 . 6. Gottlieb, H. P. W. "Harmonic balance approach to periodic solutions of non-linear jerk equations." Journal of Sound and Vibration 271.3-5 (2004): 671-683. 7. Haque, B. I. (2014). A New Approach of Mickens' Extended Iteration Method for Solving Some Nonlinear Jerk Equations. British journal of Mathematics & Computer Science , 4 (22), 3146. 8. Haque, B. I., & Flora, S. A. (2020). On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method. Applied Mathematics and Nonlinear Sciences , 6 (1), 527-536. 9. Haque, BM Ikramul, and M. Iqbal Hossain. “ An analytical approach for solving the nonlinear jerk oscillator containing velocity times acceleration-squared by an extended iteration method." journal of Mechanics of Continua and Mathematical Sciences 16.2 (2021): 35-47. 10. Hosen, M. A., Chowdhury, M. S. H., Ali, M. Y., & Ismail, A. F. (2016).A comparison study on the harmonic balance method and rational harmonic balance method for the Duffing-harmonic oscillator. Global Journal of Pure and Applied Mathematics , 12 (3), 2721-2732. 11. Hu, H., & Tang, J. H. (2006).Solution of a Duffing-harmonic oscillator by the method of harmonic balance. Journal of sound and vibration , 294 (3), 637-639. 1 Year 2023 57 Frontier Research Volume XXIII Issue ersion I V ( F ) Science © 2023 Global Journals Global Journal of By an Extended Iteration Method to Adequate Solutions of Jerk Oscillator Containing Displacement Times Velocity Time’s Acceleration and Velocity N otes IV