A New Sixth Order Method for Nonlinear Equations in R
A new iterative method is described for finding the real roots of nonlinear equations in R. Starting with a suitably chosen x0, the method generates a sequence of iterates converging to the root. The convergence analysis is provided to establish its sixth order of convergence. The number of iteratio...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/890138 |
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| _version_ | 1850168331017912320 |
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| author | Sukhjit Singh D. K. Gupta |
| author_facet | Sukhjit Singh D. K. Gupta |
| author_sort | Sukhjit Singh |
| collection | DOAJ |
| description | A new iterative method is described for finding the real roots of nonlinear equations in R. Starting with a suitably chosen x0, the method generates a sequence of iterates converging to the root. The convergence analysis is provided to establish its sixth order of convergence. The number of iterations and the total number of function evaluations used to get a simple root are taken as performance measure of our method. The efficacy of the method is tested on a number of numerical examples and the results obtained are summarized in tables. It is observed that our method is superior to Newton’s method and other sixth order methods considered. |
| format | Article |
| id | doaj-art-d8953d7a03804cfa8d30babd9f4d2657 |
| institution | OA Journals |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-d8953d7a03804cfa8d30babd9f4d26572025-08-20T02:20:58ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/890138890138A New Sixth Order Method for Nonlinear Equations in RSukhjit Singh0D. K. Gupta1Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, IndiaDepartment of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, IndiaA new iterative method is described for finding the real roots of nonlinear equations in R. Starting with a suitably chosen x0, the method generates a sequence of iterates converging to the root. The convergence analysis is provided to establish its sixth order of convergence. The number of iterations and the total number of function evaluations used to get a simple root are taken as performance measure of our method. The efficacy of the method is tested on a number of numerical examples and the results obtained are summarized in tables. It is observed that our method is superior to Newton’s method and other sixth order methods considered.http://dx.doi.org/10.1155/2014/890138 |
| spellingShingle | Sukhjit Singh D. K. Gupta A New Sixth Order Method for Nonlinear Equations in R The Scientific World Journal |
| title | A New Sixth Order Method for Nonlinear Equations in R |
| title_full | A New Sixth Order Method for Nonlinear Equations in R |
| title_fullStr | A New Sixth Order Method for Nonlinear Equations in R |
| title_full_unstemmed | A New Sixth Order Method for Nonlinear Equations in R |
| title_short | A New Sixth Order Method for Nonlinear Equations in R |
| title_sort | new sixth order method for nonlinear equations in r |
| url | http://dx.doi.org/10.1155/2014/890138 |
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