An extension of the decomposition method for solving nonlinear equations and its convergence

Authors:
Yong-Chang Jiao;Chuangyin Dang;Yoshitsugu Yamamoto
Affiliations:
Institute of Antennas and EM Scattering, Xidian University, Xi'an, Shaanxi 710071, PR China;Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong;Institute of Policy and Planning Sciences, The University of Tsukuba, Tsukuba, Ibaraki 305, Japan
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

In this paper, we propose an extension of the decomposition method for solving nonlinear equations. After a summary of Adomian's decomposition method (ADM), a new kind of decomposition strategy for nonlinear functions in nonlinear equations is proposed, and a generalized decomposition method (GDM) for solving nonlinear equations is presented. Under a rather mild condition, the convergence of the GDM is proved. Also, some concrete examples are studied to illustrate with numerical results how powerful the GDM is. Finally, some general remarks conclude this study.