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has been cited by the following article:

• TITLE: Higher-Order Numeric Solutions for Nonlinear Systems Based on the Modified Decomposition Method

  AUTHORS: Junsheng Duan

  KEYWORDS: Adomian Polynomials; Modified Decomposition Method; Adomian-Rach Theorem; Nonlinear Differential Equations; Numeric Solution

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.2 No.1, January 9, 2014

  ABSTRACT: Higher-order numeric solutions for nonlinear differential equations based on the Rach-Adomian-Meyers modified decomposition method are designed in this work. The presented one-step numeric algorithm has a high efficiency due to the new, efficient algorithms of the Adomian polynomials, and it enables us to easily generate a higher-order numeric scheme such as a 10th-order scheme, while for the Runge-Kutta method, there is no general procedure to generate higher-order numeric solutions. Finally, the method is demonstrated by using the Duffing equation and the pendulum equation.