Modifikasi metode iterasi berorde tiga dengan orde konvergensi optimal
Weerakoon-Fernando’s and Homeier’s methods are a third-order iterative method to solve nonlinear equations. A new third-order iterative method is constructed by sum of Weerakoon-Fernandon’s and Homeier’s method. This paper discusses the modification of the third-order iterative method using contra...
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| Format: | Article |
| Language: | English |
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Department of Mathematics FMIPA University of Jember
2023-03-01
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| Series: | Majalah Ilmiah Matematika dan Statistika |
| Online Access: | https://jurnal.unej.ac.id/index.php/MIMS/article/view/33940 |
| _version_ | 1797838730204020736 |
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| author | Annisa Agustina Wartono Wartono |
| author_facet | Annisa Agustina Wartono Wartono |
| author_sort | Annisa Agustina |
| collection | DOAJ |
| description | Weerakoon-Fernando’s and Homeier’s methods are a third-order iterative method to solve nonlinear equations. A new third-order iterative method is constructed by sum of Weerakoon-Fernandon’s and Homeier’s method. This paper discusses the modification of the third-order iterative method using contra harmonic mean with involving one real parameter q. The aim of this modification is to improve the convergence order of the method and keep the number of function evaluations. Based on the result of study shows that the method has a third-order of convergence for and a fourth-order of convergence for with three evaluation of functions. Furthermore, numerical simulation is given to exam the perfomance of the methods. The measurement of performance of the methods, such as : number of iterations, number of function evaluations, numerical convergence order, and value of function, are compared with Newton’s, Weerakoon-Fernando’s, and Homeier’s methods. Generally, the result of numerical simulation shows that the new method for has better performance than others.
Keywords: Weerakoon-Fernando’s method, Homeier’smethod, order of convergence, contra harmonic mean, evaluation of function
MSC2020: 41A25, 41A58, 65H05 |
| first_indexed | 2024-04-09T15:46:39Z |
| format | Article |
| id | doaj.art-ba1bfd5ba0d04e57a43b56f3bdb95239 |
| institution | Directory Open Access Journal |
| issn | 1411-6669 2722-9866 |
| language | English |
| last_indexed | 2024-04-09T15:46:39Z |
| publishDate | 2023-03-01 |
| publisher | Department of Mathematics FMIPA University of Jember |
| record_format | Article |
| series | Majalah Ilmiah Matematika dan Statistika |
| spelling | doaj.art-ba1bfd5ba0d04e57a43b56f3bdb952392023-04-27T00:35:35ZengDepartment of Mathematics FMIPA University of JemberMajalah Ilmiah Matematika dan Statistika1411-66692722-98662023-03-01231152610.19184/mims.v23i1.3394033940Modifikasi metode iterasi berorde tiga dengan orde konvergensi optimalAnnisa Agustina0Wartono Wartono1Universitas Islam Negeri Sultan Syarif KasimUniversitas Islam Negeri Sultan Syarif KasimWeerakoon-Fernando’s and Homeier’s methods are a third-order iterative method to solve nonlinear equations. A new third-order iterative method is constructed by sum of Weerakoon-Fernandon’s and Homeier’s method. This paper discusses the modification of the third-order iterative method using contra harmonic mean with involving one real parameter q. The aim of this modification is to improve the convergence order of the method and keep the number of function evaluations. Based on the result of study shows that the method has a third-order of convergence for and a fourth-order of convergence for with three evaluation of functions. Furthermore, numerical simulation is given to exam the perfomance of the methods. The measurement of performance of the methods, such as : number of iterations, number of function evaluations, numerical convergence order, and value of function, are compared with Newton’s, Weerakoon-Fernando’s, and Homeier’s methods. Generally, the result of numerical simulation shows that the new method for has better performance than others. Keywords: Weerakoon-Fernando’s method, Homeier’smethod, order of convergence, contra harmonic mean, evaluation of function MSC2020: 41A25, 41A58, 65H05https://jurnal.unej.ac.id/index.php/MIMS/article/view/33940 |
| spellingShingle | Annisa Agustina Wartono Wartono Modifikasi metode iterasi berorde tiga dengan orde konvergensi optimal Majalah Ilmiah Matematika dan Statistika |
| title | Modifikasi metode iterasi berorde tiga dengan orde konvergensi optimal |
| title_full | Modifikasi metode iterasi berorde tiga dengan orde konvergensi optimal |
| title_fullStr | Modifikasi metode iterasi berorde tiga dengan orde konvergensi optimal |
| title_full_unstemmed | Modifikasi metode iterasi berorde tiga dengan orde konvergensi optimal |
| title_short | Modifikasi metode iterasi berorde tiga dengan orde konvergensi optimal |
| title_sort | modifikasi metode iterasi berorde tiga dengan orde konvergensi optimal |
| url | https://jurnal.unej.ac.id/index.php/MIMS/article/view/33940 |
| work_keys_str_mv | AT annisaagustina modifikasimetodeiterasiberordetigadenganordekonvergensioptimal AT wartonowartono modifikasimetodeiterasiberordetigadenganordekonvergensioptimal |