A note on the local convergence of iterative methods based on Adomian decomposition method and 3-node quadrature rule

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• 作者：D.K.R. Babajee ; M.Z. Dauhoo ; M.T. Darvishi ; A. Barati
• 关键词：Fourth-order methods ; Point of attraction ; Systems of nonlinear equations ; Adomian decomposition method ; 3-Node quadrature rule
• 刊名：Applied Mathematics and Computation
• 出版年：2008
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：15 June 2008
• 卷：200
• 期：1
• 页码：452-458
• 文件大小：149 K

摘要

Darvishi and Barati [M.T. Darvishi, A. Barati, Super cubic iterative methods to solve systems of nonlinear equations, Appl. Math. Comput., 2006, 10.1016/j.amc.2006.11.022] derived a Super cubic method from the Adomian decomposition method to solve systems of nonlinear equations. The authors showed that the method is third-order convergent using classical Taylor expansion but the numerical experiments conducted by them showed that the method exhibits super cubic convergence. In the present work, using Ostrowski’s technique based on point of attraction, we show that their method is in fact fourth-order convergent. We also prove the local convergence of another fourth-order method from 3-node quadrature rule using point of attraction.