Solving nonsmooth equations using family of derivative-free optimal methods
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...
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2013-04-01
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| Series: | Journal of the Egyptian Mathematical Society |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X12000557 |
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doaj-c664bc8e48b04b74a7bbc6d9555d0c972020-11-25T02:12:46ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2013-04-01211384310.1016/j.joems.2012.10.007Solving nonsmooth equations using family of derivative-free optimal methodsM.A. Hafiz0Mohamed S.M. Bahgat1Department of Mathematics, Faculty of Science and Arts, Najran University, Najran 1988, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Minia University, Minia 61111, EgyptIn 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.http://www.sciencedirect.com/science/article/pii/S1110256X12000557Nonlinear equationsConvergence analysisNonsmooth equationsIterative methodsDerivative-free methodsOptimal order of convergence |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M.A. Hafiz Mohamed S.M. Bahgat |
| spellingShingle |
M.A. Hafiz Mohamed S.M. Bahgat Solving nonsmooth equations using family of derivative-free optimal methods Journal of the Egyptian Mathematical Society Nonlinear equations Convergence analysis Nonsmooth equations Iterative methods Derivative-free methods Optimal order of convergence |
| author_facet |
M.A. Hafiz Mohamed S.M. Bahgat |
| author_sort |
M.A. Hafiz |
| title |
Solving nonsmooth equations using family of derivative-free optimal methods |
| title_short |
Solving nonsmooth equations using family of derivative-free optimal methods |
| title_full |
Solving nonsmooth equations using family of derivative-free optimal methods |
| title_fullStr |
Solving nonsmooth equations using family of derivative-free optimal methods |
| title_full_unstemmed |
Solving nonsmooth equations using family of derivative-free optimal methods |
| title_sort |
solving nonsmooth equations using family of derivative-free optimal methods |
| publisher |
SpringerOpen |
| series |
Journal of the Egyptian Mathematical Society |
| issn |
1110-256X |
| publishDate |
2013-04-01 |
| description |
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. |
| topic |
Nonlinear equations Convergence analysis Nonsmooth equations Iterative methods Derivative-free methods Optimal order of convergence |
| url |
http://www.sciencedirect.com/science/article/pii/S1110256X12000557 |
| work_keys_str_mv |
AT mahafiz solvingnonsmoothequationsusingfamilyofderivativefreeoptimalmethods AT mohamedsmbahgat solvingnonsmoothequationsusingfamilyofderivativefreeoptimalmethods |
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1724908344327536640 |