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.
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