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An Aftertreatment Technique for Improving the Accuracy of Adomian's Decomposition Method

Y. C. Jiao
Organization: Xidian University, Xi'an, Shaanxi, China
Y. Yamamoto
Organization: University of Tsukuba, Tsukuba, Japan
C. Dang
Organization: City University of Hong Kong, Kowloon, Hong Kong
Y. Hao
Organization: Xidian University, Xi'an, Shaanxi, China
Journal / Anthology

Computers and Mathematics with Applications
Year: 2002
Volume: 43
Page range: 783-798

Adomian's decomposition method (ADM) is a nonnumerical method which can be edapted for solving nonlinear ordinary differential equations. In this paper, the principle of the decomposition method is described, and its advantages as well as drawbacks are discussed. Then an aftertreatment (AT) is proposed, which yields the analytic approximate solution with fast convergence rate and high accuracy through the application of the Padé approximation to the series solution derived from ADM. Some concrete examples are also studied to show with numerical results how the AT works efficiently.

*Mathematics > Calculus and Analysis > Differential Equations

Adomian's decomposition method, aftertreatment technique, ordinary differential equations, Padé approximant, Mathematica