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.