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Recurrence triangle for Adomian polynomials. (English) Zbl 1190.65031
Summary: 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 \(\sum_{n=0}^\infty u_n\) 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.

MSC:
65D20 Computation of special functions and constants, construction of tables
33E20 Other functions defined by series and integrals
33F05 Numerical approximation and evaluation of special functions
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