کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4641128 | 1341297 | 2009 | 8 صفحه PDF | دانلود رایگان |
In [YoonMee Ham etal., Some higher-order modifications of Newton’s method for solving nonlinear equations, J. Comput. Appl. Math., 222 (2008) 477–486], some higher-order modifications of Newton’s method for solving nonlinear equations are constructed. But if p=2p=2, then their main theorem did not hold. In this paper, we first give an example to show that YoonMee Ham etal.’s methods are not always correct in the case p=2p=2. Then, we present the condition that H(x,y)H(x,y) should satisfy such that the order of convergence increases three or four or five units. Per iteration they only need two additional function evaluations to increase the order. Based on this and multi-step Newton’s scheme, we give further modifications of the method to obtain higher-order convergent iterative methods. Finally, several examples are given to demonstrate the efficiency and performance of our modified methods and compare them with some other methods.
Journal: Journal of Computational and Applied Mathematics - Volume 228, Issue 1, 1 June 2009, Pages 296–303