In this paper, we present a reliable algorithm, the homotopy perturbation method, to solve the well-known vibration equation for very large membrane which is given initial conditions. By using initial value, the explicit solutions of the equation for different cases have been derived, which accelerate the rapid convergence of the series solution. Numerical results show that the homotopy perturbation method is easy to implement and accurate when applied to differential equations. Numerical results for different particular cases of the problem are presented graphically.
Yıldırım, Ahmet; Ünlü, Canan; and Mohyud-Din, Syed T.
On the Solution of the Vibration Equation by Means of the Homotopy Perturbation Method,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 5,
3, Article 3.
Available at: https://digitalcommons.pvamu.edu/aam/vol5/iss3/3