A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order
A class of three-step eighth-order root solvers is constructed in this study. Our aim is fulfilled by using an interpolatory rational function in the third step of a three-step cycle. Each method of the class reaches the optimal efficiency index according to the Kung-Traub conjecture concerning mult...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/568740 |
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| author | F. Soleymani S. Karimi Vanani M. Jamali Paghaleh |
| author_facet | F. Soleymani S. Karimi Vanani M. Jamali Paghaleh |
| author_sort | F. Soleymani |
| collection | DOAJ |
| description | A class of three-step eighth-order root solvers is constructed in this study. Our aim is fulfilled by using an interpolatory rational function in the third step of a three-step cycle. Each method of the class reaches the optimal efficiency index according to the Kung-Traub conjecture concerning multipoint iterative methods without memory. Moreover, the class is free from derivative calculation per full iteration, which is important in engineering problems. One method of the class is established analytically. To test the derived methods from the class, we apply them to a lot of nonlinear scalar equations. Numerical examples suggest that the novel class of derivative-free methods is better than the existing methods of the same type in the literature. |
| format | Article |
| id | doaj-art-4175491eb84c4d7b8744a7c81fc34cf3 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4175491eb84c4d7b8744a7c81fc34cf32025-02-03T05:59:11ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/568740568740A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence OrderF. Soleymani0S. Karimi Vanani1M. Jamali Paghaleh2Young Researchers Club, Islamic Azad University, Zahedan Branch, Zahedan, IranDepartment of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, IranYoung Researchers Club, Islamic Azad University, Zahedan Branch, Zahedan, IranA class of three-step eighth-order root solvers is constructed in this study. Our aim is fulfilled by using an interpolatory rational function in the third step of a three-step cycle. Each method of the class reaches the optimal efficiency index according to the Kung-Traub conjecture concerning multipoint iterative methods without memory. Moreover, the class is free from derivative calculation per full iteration, which is important in engineering problems. One method of the class is established analytically. To test the derived methods from the class, we apply them to a lot of nonlinear scalar equations. Numerical examples suggest that the novel class of derivative-free methods is better than the existing methods of the same type in the literature.http://dx.doi.org/10.1155/2012/568740 |
| spellingShingle | F. Soleymani S. Karimi Vanani M. Jamali Paghaleh A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order Journal of Applied Mathematics |
| title | A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order |
| title_full | A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order |
| title_fullStr | A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order |
| title_full_unstemmed | A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order |
| title_short | A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order |
| title_sort | class of three step derivative free root solvers with optimal convergence order |
| url | http://dx.doi.org/10.1155/2012/568740 |
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