In this paper, the relativistic harmonic oscillator equation which is a nonlinear ordinary differential equation is investigated by Homotopy perturbation method. Selection of a linear operator, which is a part of the main operator, is one of the main steps in HPM. If the aim is to obtain a periodic solution, this choice does not work here. To overcome this lack, a linear operator is imposed, and Fourier series of sines will be used in solving the linear equations arise in the HPM. Comparison of the results, with those of resulted by Differential Transformation and Harmonic Balance Method, shows an excellent agreement.
Biazar, J., & Hosami, M. (2024). An easy trick to a periodic solution of relativistic harmonic oscillator. Journal of the Egyptian Mathematical Society, 22(1), 45-49. doi: 10.1016/j.joems.2013.04.013
MLA
Jafar Biazar; Mohammad Hosami. "An easy trick to a periodic solution of relativistic harmonic oscillator", Journal of the Egyptian Mathematical Society, 22, 1, 2024, 45-49. doi: 10.1016/j.joems.2013.04.013
HARVARD
Biazar, J., Hosami, M. (2024). 'An easy trick to a periodic solution of relativistic harmonic oscillator', Journal of the Egyptian Mathematical Society, 22(1), pp. 45-49. doi: 10.1016/j.joems.2013.04.013
VANCOUVER
Biazar, J., Hosami, M. An easy trick to a periodic solution of relativistic harmonic oscillator. Journal of the Egyptian Mathematical Society, 2024; 22(1): 45-49. doi: 10.1016/j.joems.2013.04.013
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