%0 Journal Article %T Higher-Order Numeric Solutions for Nonlinear Systems Based on the Modified Decomposition Method %A Junsheng Duan %J Journal of Applied Mathematics and Physics %P 1-7 %@ 2327-4379 %D 2014 %I Scientific Research Publishing %R 10.4236/jamp.2014.21001 %X

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.

%K Adomian Polynomials %K Modified Decomposition Method %K Adomian-Rach Theorem %K Nonlinear Differential Equations %K Numeric Solution %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=41774