Article
On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method
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Abstract
A modified analytical solution of the quadratic non-linear oscillator has been obtained based on an extended iteration method. In this study, truncated Fourier terms have been used in each step of iterations. The frequencies obtained by this technique show good agreement with the exact frequency. The percentage of error between the exact frequency and our third approximate frequency is as low as 0.001%. There is no algebraic complexity in our calculation, which is why this technique is very easy. The results have been compared with the exact and other existing results, which are both convergent and consistent.
Keywords
extended iteration procedure, quadratic oscillator, non-linearity, non-linear oscillations, 34A34, 34B99
Citation
Ikramul Haque, B. M. & Flora, S. A. (2020). On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method. Applied Mathematics and Nonlinear Sciences, 5(2), 527–536. https://doi.org/10.2478/amns.2020.2.00008
B. M. Ikramul Haque and S. A. Flora, “On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method,” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 2, pp. 527–536, 2020, doi: 10.2478/amns.2020.2.00008.
Ikramul Haque BM, Flora SA. On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method. Applied Mathematics and Nonlinear Sciences. 2020;5(2):527–536. doi:10.2478/amns.2020.2.00008.
Ikramul Haque, B. M. and Flora, S. A. (2020), ‘On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method’, Applied Mathematics and Nonlinear Sciences, 5(2), pp. 527–536. Available at: https://doi.org/10.2478/amns.2020.2.00008.
Ikramul Haque, B. M., and Shajia Afrin Flora. “On the Analytical Approximation of the Quadratic Non-linear Oscillator by Modified Extended Iteration Method.” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 2, 2020, pp. 527–536. https://doi.org/10.2478/amns.2020.2.00008.
Ikramul Haque, B. M., and Shajia Afrin Flora. “On the Analytical Approximation of the Quadratic Non-linear Oscillator by Modified Extended Iteration Method.” Applied Mathematics and Nonlinear Sciences 5, no. 2 (2020): 527–536. https://doi.org/10.2478/amns.2020.2.00008.
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Published by: Engineering Journals
