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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |