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

## TL;DR

This paper introduces a simple analytical method combining the Aboodh transform and homotopy perturbation to solve strongly nonlinear oscillators, achieving high accuracy and broad applicability.

## Contribution

It develops a generalized approach for solving strongly nonlinear oscillators using ATHPM, which is simpler and more accurate than existing methods.

## Key findings

- ATHPM provides highly accurate approximate solutions.
- The method outperforms other approximation techniques.
- Solutions show excellent agreement with numerical results.

## Abstract

A generalized equation is constructed for a class of classical oscillators with strong anharmonicity which are not exactly solvable. 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 is very simple and hence provides the approximate analytical solution of the generalized equation without any mathematical rigor. The solution from this simple method not only shows excellent agreement with the exact numerical results but also found to be better accuracy in comparison to the solutions obtained from other established approximation methods whenever compared for physically relevant special cases.