Iterative methods for solving nonlinear equations with multiple zeros
This thesis discusses the problem of finding the multiple zeros of nonlinear equations. Six two-step methods without memory are developed. Five of them posses third order convergence and an optimal fourth order of convergence. The optimal order of convergence is determined by applying the Kung-Tr...
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| Format: | Thesis |
| Language: | English |
| Published: |
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/76705/1/FS%202018%2056%20-%20IR.pdf |
| _version_ | 1796980142772322304 |
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| author | Jamaludin, Nur Alif Akid |
| author_facet | Jamaludin, Nur Alif Akid |
| author_sort | Jamaludin, Nur Alif Akid |
| collection | UPM |
| description | This thesis discusses the problem of finding the multiple zeros of nonlinear equations.
Six two-step methods without memory are developed. Five of them posses
third order convergence and an optimal fourth order of convergence. The optimal order
of convergence is determined by applying the Kung-Traub conjecture. These
method were constructed by modifying the Victory and Neta’s method, Osada’s
method, Halley’s method and Chebyshev’s method. All these methods are free from
second derivative function. Numerical computation shows that the newly modified
methods performed better in term of error. The multiplicity of roots for the test functions
have been known beforehand. Basin of attraction described that our methods
have bigger choice of initial guess. |
| first_indexed | 2024-03-06T10:18:47Z |
| format | Thesis |
| id | upm.eprints-76705 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T10:18:47Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | upm.eprints-767052020-02-10T00:25:14Z http://psasir.upm.edu.my/id/eprint/76705/ Iterative methods for solving nonlinear equations with multiple zeros Jamaludin, Nur Alif Akid This thesis discusses the problem of finding the multiple zeros of nonlinear equations. Six two-step methods without memory are developed. Five of them posses third order convergence and an optimal fourth order of convergence. The optimal order of convergence is determined by applying the Kung-Traub conjecture. These method were constructed by modifying the Victory and Neta’s method, Osada’s method, Halley’s method and Chebyshev’s method. All these methods are free from second derivative function. Numerical computation shows that the newly modified methods performed better in term of error. The multiplicity of roots for the test functions have been known beforehand. Basin of attraction described that our methods have bigger choice of initial guess. 2018-05 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/76705/1/FS%202018%2056%20-%20IR.pdf Jamaludin, Nur Alif Akid (2018) Iterative methods for solving nonlinear equations with multiple zeros. Masters thesis, Universiti Putra Malaysia. Iterative methods (Mathematics) - Case studies Differential equations, Nonlinear |
| spellingShingle | Iterative methods (Mathematics) - Case studies Differential equations, Nonlinear Jamaludin, Nur Alif Akid Iterative methods for solving nonlinear equations with multiple zeros |
| title | Iterative methods for solving nonlinear equations with multiple zeros |
| title_full | Iterative methods for solving nonlinear equations with multiple zeros |
| title_fullStr | Iterative methods for solving nonlinear equations with multiple zeros |
| title_full_unstemmed | Iterative methods for solving nonlinear equations with multiple zeros |
| title_short | Iterative methods for solving nonlinear equations with multiple zeros |
| title_sort | iterative methods for solving nonlinear equations with multiple zeros |
| topic | Iterative methods (Mathematics) - Case studies Differential equations, Nonlinear |
| url | http://psasir.upm.edu.my/id/eprint/76705/1/FS%202018%2056%20-%20IR.pdf |
| work_keys_str_mv | AT jamaludinnuralifakid iterativemethodsforsolvingnonlinearequationswithmultiplezeros |