Solving nonsmooth equations using family of derivative-free optimal methods
Hafiz, M., Bahgat, M. (2013). Solving nonsmooth equations using family of derivative-free optimal methods. EKB Journal Management System, 21(1), 38-43. doi: 10.1016/j.joems.2012.10.007
M.A. Hafiz; Mohamed S.M. Bahgat. "Solving nonsmooth equations using family of derivative-free optimal methods". EKB Journal Management System, 21, 1, 2013, 38-43. doi: 10.1016/j.joems.2012.10.007
Hafiz, M., Bahgat, M. (2013). 'Solving nonsmooth equations using family of derivative-free optimal methods', EKB Journal Management System, 21(1), pp. 38-43. doi: 10.1016/j.joems.2012.10.007
Hafiz, M., Bahgat, M. Solving nonsmooth equations using family of derivative-free optimal methods. EKB Journal Management System, 2013; 21(1): 38-43. doi: 10.1016/j.joems.2012.10.007

Solving nonsmooth equations using family of derivative-free optimal methods

Journal of the Egyptian Mathematical Society
Volume 21, Issue 1, April 2013, Pages 38-43    PDF (311.33 K)
Document Type: Original Article
DOI: 10.1016/j.joems.2012.10.007
Authors
M.A. Hafiz* 1; Mohamed S.M. Bahgat2
1Department of Mathematics, Faculty of Science and Arts, Najran University, Najran 1988, Saudi Arabia
2Department of Mathematics, Faculty of Science, Minia University, Minia 61111, Egypt
Abstract
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.
Keywords
Nonlinear equations; Convergence analysis; Nonsmooth equations; Iterative methods; Derivative-free methods; Optimal order of convergence
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