Study of strongly nonlinear oscillators using the Aboodh transform and the homotopy perturbation method

A generalized equation is constructed for a class of classical oscillators with strong anharmonicity which are not exactly solvable. The Aboodh transform-based homotopy perturbation method (ATHPM) is applied to get the approximate analytical solution for the generalized equation and hence some physically relevant anharmonic oscillators are studied as the special cases of this solution. ATHPM provides the approximate analytical solution of the generalized equation in a simple way. The solution from this simple method not only shows excellent agreement with the numerical results but is also found to be of better accuracy in comparison to the solutions obtained from other established approximation methods whenever compared for physically relevant special cases.