Numerical Algorithms for Finding Zeros of Nonlinear Equations and Their Dynamical Aspects
In this paper, we developed two new numerical algorithms for finding zeros of nonlinear equations in one dimension and one of them is second derivative free which has been removed using the interpolation technique. We derive these algorithms with the help of Taylor’s series expansion and Golbabai an...
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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/10.1155/2020/2816843 |
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| author | Amir Naseem M. A. Rehman Thabet Abdeljawad |
| author_facet | Amir Naseem M. A. Rehman Thabet Abdeljawad |
| author_sort | Amir Naseem |
| collection | DOAJ |
| description | In this paper, we developed two new numerical algorithms for finding zeros of nonlinear equations in one dimension and one of them is second derivative free which has been removed using the interpolation technique. We derive these algorithms with the help of Taylor’s series expansion and Golbabai and Javidi’s method. The convergence analysis of these algorithms is discussed. It is established that the newly developed algorithms have sixth order of convergence. Several numerical examples have been solved which prove the better efficiency of these algorithms as compared to other well-known iterative methods of the same kind. Finally, the comparison of polynomiographs generated by other well-known iterative methods with our developed algorithms has been made which reflects their dynamical aspects. |
| format | Article |
| id | doaj-art-7857974580674978a94a4ba49c356fa3 |
| 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-7857974580674978a94a4ba49c356fa32025-02-03T06:43:59ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/28168432816843Numerical Algorithms for Finding Zeros of Nonlinear Equations and Their Dynamical AspectsAmir Naseem0M. A. Rehman1Thabet Abdeljawad2Department of Mathematics, University of Management and Technology, Lahore, PakistanDepartment of Mathematics, University of Management and Technology, Lahore, PakistanDepartment of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaIn this paper, we developed two new numerical algorithms for finding zeros of nonlinear equations in one dimension and one of them is second derivative free which has been removed using the interpolation technique. We derive these algorithms with the help of Taylor’s series expansion and Golbabai and Javidi’s method. The convergence analysis of these algorithms is discussed. It is established that the newly developed algorithms have sixth order of convergence. Several numerical examples have been solved which prove the better efficiency of these algorithms as compared to other well-known iterative methods of the same kind. Finally, the comparison of polynomiographs generated by other well-known iterative methods with our developed algorithms has been made which reflects their dynamical aspects.http://dx.doi.org/10.1155/2020/2816843 |
| spellingShingle | Amir Naseem M. A. Rehman Thabet Abdeljawad Numerical Algorithms for Finding Zeros of Nonlinear Equations and Their Dynamical Aspects Journal of Mathematics |
| title | Numerical Algorithms for Finding Zeros of Nonlinear Equations and Their Dynamical Aspects |
| title_full | Numerical Algorithms for Finding Zeros of Nonlinear Equations and Their Dynamical Aspects |
| title_fullStr | Numerical Algorithms for Finding Zeros of Nonlinear Equations and Their Dynamical Aspects |
| title_full_unstemmed | Numerical Algorithms for Finding Zeros of Nonlinear Equations and Their Dynamical Aspects |
| title_short | Numerical Algorithms for Finding Zeros of Nonlinear Equations and Their Dynamical Aspects |
| title_sort | numerical algorithms for finding zeros of nonlinear equations and their dynamical aspects |
| url | http://dx.doi.org/10.1155/2020/2816843 |
| work_keys_str_mv | AT amirnaseem numericalalgorithmsforfindingzerosofnonlinearequationsandtheirdynamicalaspects AT marehman numericalalgorithmsforfindingzerosofnonlinearequationsandtheirdynamicalaspects AT thabetabdeljawad numericalalgorithmsforfindingzerosofnonlinearequationsandtheirdynamicalaspects |