Solution for a rotational pendulum system by the Rach–Adomian–Meyers decomposition method

Abstract

Abstract In this article, we report for the first time the application of a novel and extremely valuable methodology called the Rach–Adomian–Meyers decomposition method (MDM) to obtain numerical solutions to the rotational pendulum equation. MDM is a tool for solving nonlinear differential equations that combines both series solution and the Adomian decomposition method efficiently. We present a simple and highly accurate MDM-based algorithm and its numerical implementation via a one-step recurrence approach for obtaining periodic solutions to the rotational pendulum equation. Finally, numerical simulations are performed to demonstrate the efficiency and accuracy of the proposed technique for both large and small amplitudes of oscillation.