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J. C. Hsu, H. Y. Lai and C. K. Chen, “An Innovative Eigenvalue Problem Solver for Free Vibration of Uniform Timoshenko Beams by Using the Adomian Modified Decomposition Method,” Journal of Sound Vibration, Vol. 325, 2009, pp. 451-470. http://dx.doi.org/10.1016/j.jsv.2009.03.015

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.