International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.1, No.3, Jun. 2015, Pub. Date: May 16, 2015
New Efficient Optimal Derivative-Free Method for Solving Nonlinear Equations
[01] Q. W. Guo, Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, China.
[02] Y. H. Qian, Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, China.
In this paper, we suggest a new technique which uses Lagrange polynomials to get derivative-free iterative methods for solving nonlinear equations. With the use of the proposed technique and Steffens on-like methods, a new optimal fourth-order method is derived. By using three-degree Lagrange polynomials with other two-step methods which are efficient optimal methods, eighth-order methods can be achieved. Besides, we can get sixteenth-order methods if we use other three-step methods and higher-order degree Lagrange polynomials. The error equations and asymptotic convergence constants are obtained for the proposed methods. Some numerical examples are illustrated to verify the accuracy of the proposed computational scheme.
Lagrange Polynomials, Steffens on-Like Method, Derivative-Free, Convergence Order, Efficiency Index
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