A Novel Isometric–Homotopy Perturbation Technique for Nonlinear Neutrosophic Differential Equations

Abstract

This work deals with the neutrosophic nonlinear Van der Pol oscillator equation (N-VDP) as a model arising in applied dynamics. To obtain approximate analytical solutions, the Homotopy Perturbation Method (HPM) is combined with the One-Dimensional Isometric Transform. The proposed approach provides a systematic framework for the analysis of the N-VDP equation and clarifies some of its fundamental characteristics. The results obtained are compared with those of the classical fourth-order Runge–Kutta method (RK4). The comparison confirms that the present technique gives reliable and accurate results, showing its potential as an effective tool for solving neutrosophic nonlinear differential equations and for further applications in dynamical systems.