Approximate Solution of a Neutrosophic Nonlinear Van der Pol Oscillator Problem by Semi Analytical Method Using Thick Function

                                                    George A. Toma¹*, Fahed Farhood², Taqi A. Alkhatib³

¹Department of fundamental sciences, Higher Institute for Applied Sciences and Technology, Aleppo - Syria

^2,3Department of mathematics, Faculty of Science, Aleppo University, Aleppo -  Syria

Emails: george.toma@hiast.edu.sy¹; fhmath@yahoo.com²;  taaaqimath@gmail.com³

Abstract

In this paper, an analytical method (Homotopy perturbation method HPM) is used for solving the initial value problem represented by a neutrosophic nonlinear Van der Pol oscillator equation (N-VDP) arising in applied dynamics using the thick function. We find the solutions of the (N-VDP) equation by HPM and then compare the numerical results with fourth order Runge-Kutta method (RK4). The results showed that the HPM lead to accurate and efficient results. Furthermore, these results of the HPM scheme and RK4 are implemented in Matlab.

Keywords: Neutrosophic Van der pol oscillator; Neutrosophic thick function; Homotopy perturbation method; Nonlinear initial value problem; Fourth Order Runge-Kutta; Approximate solution.