A New Family of Iterative Methods Based on an Exponential Model for Solving Nonlinear Equations
We present two new families of iterative methods for obtaining simple roots of nonlinear equations. The first family is developed by fitting the model m(x)=epx(Ax2+Bx+C) to the function f(x) and its derivative f′(x), f″(x) at a point xn. In order to remove the second derivative of the first methods,...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/547438 |
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| author | Tianbao Liu Hengyan Li Zaixiang Pang |
| author_facet | Tianbao Liu Hengyan Li Zaixiang Pang |
| author_sort | Tianbao Liu |
| collection | DOAJ |
| description | We present two new families of iterative methods for obtaining simple
roots of nonlinear equations. The first family is developed by fitting the model m(x)=epx(Ax2+Bx+C) to the function f(x) and its derivative f′(x), f″(x) at a point xn. In order to remove the second derivative of the first methods, we construct the second
family of iterative methods by approximating the equation f(x)=0 around the point (xn,f(xn)) by the quadratic equation. Analysis of convergence shows that the new
methods have third-order or higher convergence. Numerical experiments show that
new iterative methods are effective and comparable to those of the well-known existing
methods. |
| format | Article |
| id | doaj-art-8ac67de109a545a09892c8ea8d1ef41c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-8ac67de109a545a09892c8ea8d1ef41c2025-02-03T05:45:15ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/547438547438A New Family of Iterative Methods Based on an Exponential Model for Solving Nonlinear EquationsTianbao Liu0Hengyan Li1Zaixiang Pang2School of Basic Science, Changchun University of Technology, Changchun 130012, ChinaCollege of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, ChinaEngineering Training Center, Changchun University of Technology, Changchun 130012, ChinaWe present two new families of iterative methods for obtaining simple roots of nonlinear equations. The first family is developed by fitting the model m(x)=epx(Ax2+Bx+C) to the function f(x) and its derivative f′(x), f″(x) at a point xn. In order to remove the second derivative of the first methods, we construct the second family of iterative methods by approximating the equation f(x)=0 around the point (xn,f(xn)) by the quadratic equation. Analysis of convergence shows that the new methods have third-order or higher convergence. Numerical experiments show that new iterative methods are effective and comparable to those of the well-known existing methods.http://dx.doi.org/10.1155/2013/547438 |
| spellingShingle | Tianbao Liu Hengyan Li Zaixiang Pang A New Family of Iterative Methods Based on an Exponential Model for Solving Nonlinear Equations Journal of Applied Mathematics |
| title | A New Family of Iterative Methods Based on an Exponential Model for Solving Nonlinear Equations |
| title_full | A New Family of Iterative Methods Based on an Exponential Model for Solving Nonlinear Equations |
| title_fullStr | A New Family of Iterative Methods Based on an Exponential Model for Solving Nonlinear Equations |
| title_full_unstemmed | A New Family of Iterative Methods Based on an Exponential Model for Solving Nonlinear Equations |
| title_short | A New Family of Iterative Methods Based on an Exponential Model for Solving Nonlinear Equations |
| title_sort | new family of iterative methods based on an exponential model for solving nonlinear equations |
| url | http://dx.doi.org/10.1155/2013/547438 |
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