Solving the Nonlinear Charged Particle Oscillation Equation Using the Laplace–Adomian Decomposition Method

Abstract

This manuscript presents a comprehensive exploration of the nonlinear charged particle oscillation equation, employing the Laplace–Adomian decomposition method (LDM) to obtain approximate analytical solutions. The investigation leads to the formulation of five initial equations governing the oscillatory behavior of a charged particle, which are visually represented and analyzed with insightful interpretations. Notably, the existing literature lacks an exact solution to this problem. However, this paper fills this gap by presenting an approximate analytical solution utilizing the LDM. The solution is carefully studied and analyzed, contributing to a deeper understanding of the complex behavior of charged particle oscillation.