کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4626613 | 1631790 | 2015 | 10 صفحه PDF | دانلود رایگان |
By studying the commonness of some fifth order methods modified from third order ones for solving systems of nonlinear equations, we propose a new class of three-step methods of convergence order five by modifying a class of two-step methods with cubic convergence. Next, for a given method of order p ≥ 2 which uses the extended Newton iteration yk = xk − aF′(xk)−1F(xk) as a predictor, a new method of order p + 2 is proposed. For example, we construct a class of m + 2-step methods of convergence order 2m + 3 by introducing only one evaluation of the function to each of the last m steps for any positive integer m. In this paper, we mainly focus on the class of fifth order methods when m = 1. Computational efficiency in the general form is considered. Several examples for numerical tests are given to show the asymptotic behavior and the computational efficiency of these higher order methods.
Journal: Applied Mathematics and Computation - Volume 264, 1 August 2015, Pages 300–309