Iteration Methods with an Auxiliary Function for Nonlinear Equations
Various iterative methods have been introduced by involving Taylor’s series on the auxiliary function gx to solve the nonlinear equation fx=0. In this paper, we introduce the expansion of gx with the inclusion of weights wi such that ∑i=1pwi=1 and knots τi∈0,1 in order to develop a new family of ite...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/7356408 |
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| _version_ | 1832551702147891200 |
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| author | Faisal Ali Waqas Aslam Imran Khalid Akbar Nadeem |
| author_facet | Faisal Ali Waqas Aslam Imran Khalid Akbar Nadeem |
| author_sort | Faisal Ali |
| collection | DOAJ |
| description | Various iterative methods have been introduced by involving Taylor’s series on the auxiliary function gx to solve the nonlinear equation fx=0. In this paper, we introduce the expansion of gx with the inclusion of weights wi such that ∑i=1pwi=1 and knots τi∈0,1 in order to develop a new family of iterative methods. The methods proposed in the present paper are applicable for different choices of auxiliary function gx, and some already known methods can be viewed as the special cases of these methods. We consider the diverse scientific/engineering models to demonstrate the efficiency of the proposed methods. |
| format | Article |
| id | doaj-art-cefea82e37a341039fcfb60ce8c9d70c |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-cefea82e37a341039fcfb60ce8c9d70c2025-02-03T06:00:49ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/73564087356408Iteration Methods with an Auxiliary Function for Nonlinear EquationsFaisal Ali0Waqas Aslam1Imran Khalid2Akbar Nadeem3Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, PakistanCentre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, PakistanCentre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, PakistanCentre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, PakistanVarious iterative methods have been introduced by involving Taylor’s series on the auxiliary function gx to solve the nonlinear equation fx=0. In this paper, we introduce the expansion of gx with the inclusion of weights wi such that ∑i=1pwi=1 and knots τi∈0,1 in order to develop a new family of iterative methods. The methods proposed in the present paper are applicable for different choices of auxiliary function gx, and some already known methods can be viewed as the special cases of these methods. We consider the diverse scientific/engineering models to demonstrate the efficiency of the proposed methods.http://dx.doi.org/10.1155/2020/7356408 |
| spellingShingle | Faisal Ali Waqas Aslam Imran Khalid Akbar Nadeem Iteration Methods with an Auxiliary Function for Nonlinear Equations Journal of Mathematics |
| title | Iteration Methods with an Auxiliary Function for Nonlinear Equations |
| title_full | Iteration Methods with an Auxiliary Function for Nonlinear Equations |
| title_fullStr | Iteration Methods with an Auxiliary Function for Nonlinear Equations |
| title_full_unstemmed | Iteration Methods with an Auxiliary Function for Nonlinear Equations |
| title_short | Iteration Methods with an Auxiliary Function for Nonlinear Equations |
| title_sort | iteration methods with an auxiliary function for nonlinear equations |
| url | http://dx.doi.org/10.1155/2020/7356408 |
| work_keys_str_mv | AT faisalali iterationmethodswithanauxiliaryfunctionfornonlinearequations AT waqasaslam iterationmethodswithanauxiliaryfunctionfornonlinearequations AT imrankhalid iterationmethodswithanauxiliaryfunctionfornonlinearequations AT akbarnadeem iterationmethodswithanauxiliaryfunctionfornonlinearequations |