A new algorithm for solving Van der Pol equation based on piecewise spectral Adomian decomposition ‎method‎

Abstract

‎‎In this article‎, ‎a new method is introduced to give approximate solution to Van der Pol equation‎. ‎The proposed method is based on the combination of two different methods‎, ‎the spectral Adomian decomposition method (SADM) and piecewise method‎, ‎called the piecewise Adomian decomposition method (PSADM)‎. ‎The numerical results obtained from the proposed method show that this method is an effective‎, accurate and powerful tool for solving Van der Pol equation and‎, ‎the comparison show that the proposed technique is in good agreement with the numerical results obtained using Runge-Kutta method‎. ‎The advantage of piecewise spectral Adomian decomposition method over piecewise Adomian decomposition method is that it does not need to calculate complex integrals‎. ‎Another merit of this method is that‎, ‎unlike the spectral method‎, ‎it does not require the solution of any linear or nonlinear system of equations‎. Furthermore‎, ‎the proposed method is easy to implement and computationally very ‎attractive.