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Copyright © 2009, Emerald Group Publishing Limited
2009 Awards for Excellence
Article Type: 2009 Awards for Excellence From: Kybernetes, Volume 38, Issue 9
Every year, each journal published by Emerald is invited to select a winner of the “Outstanding Paper” award and up to three “Highly Commended” awards from the previous year's volume. As these are chosen following consultation amongst the journal's editorial team, who are eminent academics or managers, the winning authors will know that their paper was one of the most impressive pieces of work, the team will have seen throughout last year.
The following article was selected for this year's Outstanding Paper Award:
“A new definition of the Adomian polynomials”
Randolph C. RachHartford, Michigan, USA
Purpose –The purpose of this paper is to provide a new proof of convergence of the Adomian decomposition series for solving nonlinear ordinary and partial differential equations based upon a thorough examination of the historical milieu preceding the Adomian decomposition method.
Design/methodology/approach –The paper develops a theoretical background of the Adomian decomposition method under the auspices of the Cauchy-Kovalevskaya Theorem of existence and uniqueness for solution of differential equations. Beginning from the concepts of a parametrized Taylor expansion series as previously introduced in the Murray-Miller Theorem based on analytic parameters, and the Banach-space analog of the Taylor expansion series about a function instead of a constant as briefly discussed by Cherruault et al., the Adomian decompositions series and the series of Adomian polynomials are found to be a uniformly convergent series of analytic functions for the solution u and the nonlinear composite function f(u). To derive the unifying formula for the family of classes of Adomian polynomials, the author develops the novel notion of a sequence of parametrized partial sums as defined by truncation operators, acting upon infinite series, which induce these parametrized sums for simple discard rules and appropriate decomposition parameters. Thus, the defining algorithm of the Adomian polynomials is the difference of these consecutive parametrized partial sums.
Findings –The four classes of Adomian polynomials are shown to belong to a common family of decomposition series, which admit solution by recursion, and are derived from one unifying formula. The series of Adomian polynomials and hence the solution as computed as an Adomian decomposition series are shown to be uniformly convergent. Furthermore, the limiting value of the mth Adomian polynomial approaches zero as the index m approaches infinity for the prerequisites of the Cauchy-Kovalevskaya theorem. The novel truncation operators as governed by discard rules are analogous to an ideal low-pass filter, where the decomposition parameters represent the cut-off frequency for rearranging a uniformly convergent series so as to induce the parametrized partial sums.
Originality/value –This paper unifies the notion of the family of Adomian polynomials for solving nonlinear differential equations. Further, it presents the new notion of parametrized partial sums as a tool for rearranging a uniformly convergent series. It offers a deeper understanding of the elegant and powerful Adomian decomposition method for solving nonlinear ordinary and partial differential equations, which are of paramount importance in modeling natural phenomena and man-made device performance parameters.
Keywords Cybernetics, Differential equations, Polynomial approximation
This article originally appeared in Vol. 37 No. 7, 2008
The following articles was selected for this year's Highly Commended Award:
Kybernetes: The International Journal of Systems and Cybernetics“Explaining institutional change: aspects of an innovation in the new institutional economy”Jon-Arild Johannessen, Vol. 37 No. 1, 2008
“The semantic web: a catalyst for future e-business”Janet K. Durgin and Joseph S. SherifVol. 37 No. 1, 2008
“Toward a formal theory of socioculture: a yin-yang information-based theory of social change”, M. Yolles, B.R. Frieden and G. Kemp, Vol. 37 No. 7, 2008
For the third year running, Emerald has decided to name and reward the outstanding reviewers who contribute to the success of the journals. Peer reviewers are the guardians of the body of knowledge, ensuring that every published paper makes a genuine contribution. They also provide an immensely valuable service to authors – the advice from reviewers is some of the best they will receive on developing as an author and researcher. This new award recognizes that, without the efforts and dedication of our reviewers, Emerald journals would not have the right to be called scholarly. The reviewer mentioned below has been singled out by the editors:
Alex AndrewReading, UK