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

Junsheng Duan

School of Sciences, Shanghai Institute of Technology, Shanghai, China.

DOI: 10.4236/jamp.2014.21001                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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