An Application of He's Variational Iteration Method for Solving Duffing - Van Der Pol Equation

• Main Authors: Ann Al-Sawoor, Merna Samarchi
• Format: Article
• Language: Arabic
• Published: Mosul University 2013-07-01
• Series: Al-Rafidain Journal of Computer Sciences and Mathematics
• Subjects: he's variational iteration method; adomian decomposition method; duffing-van der pol equation; runge-kutta order four; approximate solution
• Online Access: https://csmj.mosuljournals.com/article_163482_0a6017999bf786fbf9dfe5eaaa28d518.pdf

In this paper, we apply He's variational iteration method (VIM) and the Adomian decomposition method (ADM) to approximate the solution of Duffing-Van Der Pol equation (DVP). In VIM, a correction functional is constructed by a general Lagrange multiplier which can be identified via a variational theory. The VIM yields an approximate solution in the form of a quickly convergent series. Comparisons of the two series solutions with the classical Runge-Kutta order four RK45 method show that the VIM is a powerful method for the solution of nonlinear equations. The convergent of He's variational iteration method to this equation is also considered.