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Time Dependent Harmonic Oscillator via OM-HPM | ||
| Journal of Computational Applied Mechanics | ||
| دوره 56، شماره 1، فروردین 2025، صفحه 264-275 اصل مقاله (1.17 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jcamech.2024.386177.1304 | ||
| نویسندگان | ||
| Taqwa Alkhader1؛ Dilip K Maiti2؛ Tapas Roy2؛ Olivia Florea3؛ Jihad Asad* 4 | ||
| 1Department of Applied Mathematics, Palestine Technical University- Kadoorie, Tulkarm P 305, Palestine | ||
| 2Department of Applied Mathematics, Vidyasagar University, Midnapure, West Bengal-721102, India | ||
| 3Department of Mathematics and Computer Science, Transilvania University of Brasov, Romania | ||
| 4Department of Physics, Palestine Technical University- Kadoorie, Tulkarm P 305, Palestine | ||
| چکیده | ||
| In this study, we present a semi-analytical technique known as the Optimal and Modified Homotopy Perturbation Method (OM-HPM) for solving nonlinear oscillators with time-dependent mass. The work extends existing approaches, including the standard Homotopy Perturbation Method (HPM), by introducing an auxiliary linear operator that minimizes residual error and enhances the method’s efficiency for both singular and non-singular nonlinear ordinary differential equations. The model of a harmonic oscillator with exponentially decaying mass is investigated using this method, and its equation of motion is derived using the Lagrangian formulation. The OM-HPM technique is applied to solve the resulting second-order nonlinear differential equation, and solutions are presented in series form. The method significantly reduces computational cost through the use of Newton-Cotes quadrature. Analytical illustrations demonstrate that the effectiveness of OM-HPM in solving complex nonlinear oscillatory systems. | ||
| کلیدواژهها | ||
| Harmonic Oscillator؛ Analytical solution؛ Homotopy methods؛ time-dependent mass؛ nonlinear oscillators | ||
| مراجع | ||
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