Recurrence triangle for Adomian polynomials

In this paper a recurrence technique for calculating Adomian polynomials is proposed, the convergence of the series for the Adomian polynomials is discussed, and the dependence of the convergent domain of the solution’s decomposition series ∑ n = 0 ∞ u n on the initial component function u 0 is illu...

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Bibliographic Details
Published in:Applied mathematics and computation 2010-04, Vol.216 (4), p.1235-1241
Main Author: Duan, Jun-Sheng
Format: Article
Language:English
Subjects:
Adomian decomposition method
Adomian polynomials
Computation
Convergence
Decomposition
Iterative methods
Mathematical analysis
Mathematical models
Nonlinear operator
Triangles
Vectors (mathematics)
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Summary:In this paper a recurrence technique for calculating Adomian polynomials is proposed, the convergence of the series for the Adomian polynomials is discussed, and the dependence of the convergent domain of the solution’s decomposition series ∑ n = 0 ∞ u n on the initial component function u 0 is illustrated. By introducing the index vectors of the Adomian polynomials the recurrence relations of the index vectors are discovered and the recurrence triangle is given. The method simplifies the computation of the Adomian polynomials. In order to obtain a solution’s decomposition series with larger domain of convergence, we illustrate by examples that the domain of convergence can be changed by choosing a different u 0 and a modified iteration.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.02.015