A new algorithm for solving Van der Pol equation based on piecewise spectral Adomian decomposition method
الموضوعات : مجله بین المللی ریاضیات صنعتی
S. GH Hosseini
1
(Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.)
E. Babolian
2
(Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.)
S. Abbasbandy
3
(Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.)
الکلمات المفتاحية: Van der Pol equation, Spectral Adomian decomposi, Piecewise method, Runge-Kutta method,
ملخص المقالة :
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.
