On the order of convergence of Adomian method E. Babolian a , J. Biazar b, * a University for Teacher Education, Iran b Department of Mathematics, Faculty of Science, Guilan University, P.O. Box 1914, Rasht, Iran Abstract In this paper, we contemplate the order of convergence of the Decomposition method, and we apply the results to some problems. Ó 2002 Elsevier Science Inc. All rights reserved. Keywords: Decomposition method; Adomian’s polynomials 1. Introduction Adomian has developed a numerical technique for solving functional equations [1–3]. In this method he used special kinds of polynomials, called Adomian polynomials, which can be easily derived. The solution is given by a series in which each term is easily obtained. Concrete applications to different func- tional equations are given by Adomian and his collaborators [5–8], and there are some papers considering the convergence of the method applied to special problems [4,10]. Cherruault, proposed a new definition of the technique to prove the con- vergence, of the method, under suitable and reasonable hypotheses [4]. We used Cherruault’s definition and consider the order of convergence of the method. Applied Mathematics and Computation 130 (2002) 383–387 www.elsevier.com/locate/amc * Corresponding author. E-mail address: biazar@cd.gu.ac.ir (J. Biazar). 0096-3003/02/$ - see front matter Ó 2002 Elsevier Science Inc. All rights reserved. PII:S0096-3003(01)00103-5