International Journal of Mathematics and Computational Science

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Approximate Solution of Simple Pendulum Equation for Damped and Undamped Oscillatory Motion by Using Homotopy Perturbation Method

Pages: 24-35 Views: 414 Downloads: 197

[01]
Ahammodullah Hasan, Department of Mathematics, Faculty of Science, Islamic University, Kushtia, Bangladesh.
[02]
Mohammad Masud Rana, Department of Mathematics, Faculty of Science, Islamic University, Kushtia, Bangladesh.

In this article, Homotopy perturbation method (HPM) is applied to find the approximate solution of free oscillation for simple pendulum equation, which is known a well-known nonlinear ordinary differential equation. The Homotopy Perturbation Method deforms a difficult problem into a simple problem which can be easily solved. Firstly, the approximate solution of simple pendulum equation is developed using initial conditions, and then results are compared with the results obtained by numerical solutions. Finally, Homotopy Perturbation Method (HPM) is applied to find the approximate solution of simple pendulum equation with initial conditions. The model absolute error was found below the 5% significance level. The absolute error between homotopy result and numerical result was average 0.0003%. In this study, we have found the Homotopy result and numerical result makes a good agreement. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. Some examples are presented to show the ability of the method for free oscillations of simple Pendulum equation.

Homotopy Perturbation Method (HPM), Simple Pendulum Equation (SPE), Nonlinear Differential Equation, Damped, Undamped, Approximate Solution, Numerical Solution

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