Recurrence triangle for Adomian polynomials

摘要

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∞un on the initial component function u0 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 u0 and a modified iteration.