Several improvements of the 2-point third order midpoint iterative method using weight functions

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• 作者：Diyashvir Kreetee Rajiv Babajee ^{dbabajee@umail.utm.ac.mu dkrbabajee@gmail.com rajiv.nishi@intnet.mu}
• 关键词：Midpoint method ; Weight functions ; Multi point ; Higher order convergence ; Global convergence ; Kung&ndash ; Traub conjecture
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 出版时间：1 April, 2012
• 年：2012
• 卷：218
• 期：15
• 页码：7958-7966
• 全文大小：309 K

文摘

In this paper, we improve the order of the Midpoint iterative method from three to four with same number of function evaluations using weight functions to obtain a class of 2-point fourth order Jarratt-type methods. Then we prove a general result to further improve the order of the old methods through an additional function evaluation using weight functions. In this way, we develop two 3-point sixth order midpoint methods using different weights. A family of n-point I.F.s of order 2n is proposed. Using weight functions, we further improve the methods to obtain a 5-point sixteenth order midpoint method with same efficiency index as the optimal 2-point fourth order Jarratt-type methods. Two numerical examples using different starting are provided to test the robustness of the methods.