a new algorithm for solving van der pol equation based on piecewise spectral adomian decomposition ‎method‎

‎‎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.