Solving nonsmooth equations using family of derivative-free optimal methods

Journal of the Egyptian Mathematical Society

M.A. Hafiz¹  Mohamed S.M. Bahgat² 

[1] Department of Mathematics, Faculty of Science and Arts, Najran University, Najran 1988, Saudi Arabia;Department of Mathematics, Faculty of Science, Minia University, Minia 61111, Egypt;

关键词: Nonlinear equations;    Convergence analysis;    Nonsmooth equations;    Iterative methods;    Derivative-free methods;    Optimal order of convergence;   

DOI  :  10.1016/j.joems.2012.10.007

来源: DOAJ

【 摘 要 】

In this paper, a family of derivative-free of third and fourth order convergent methods for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. The efficiency indices of the members of this family are equal to 1.442 and 1.587. The convergence and error analysis are given. Numerical comparisons are made with other existing methods to show the performance of the presented methods.

【 授权许可】

Unknown