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

Higher-Order Numeric Solutions for Nonlinear Systems Based on the Modified Decomposition Method
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摘要 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. 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.
作者 Junsheng Duan
机构地区 School of Sciences
出处 《Journal of Applied Mathematics and Physics》 2014年第1期1-7,共7页 应用数学与应用物理(英文)
关键词 Adomian POLYNOMIALS Modified Decomposition Method Adomian-Rach THEOREM Nonlinear Differential Equations Numeric Solution Adomian Polynomials Modified Decomposition Method Adomian-Rach Theorem Nonlinear Differential Equations Numeric Solution
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