HOMOTOPY PERTURBATION METHOD (HPM), ADOMIAN DECOMPOSITION METHOD (ADM) AND COUPLING HPM AND PEM (PARAMETER-EXPANSION METHOD) FOR NONLINEAR OSCILLATOR WITH COORDINATE-DEPENDENT MASS

In this paper, we investigate a nonlinear oscillator with coordinate-dependent mass. We derive approximate solutions for this oscillator using the Homotopy Perturbation Method (HPM), the Adomian Decomposition Method (ADM), and a coupled approach combining HPM with the Parameter-Expansion Method (PEM). The solutions obtained from each method are systematically compared. Additionally, we compute approximate frequency values for the oscillator.