A fourth-order derivative-free algorithm for nonlinear equations

Authors:
Yehui Peng;Heying Feng;Qiyong Li;Xiaoqing Zhang
Affiliations:
School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, PR China;School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China;Department of Mathematics, Huaihua College, Huaihua, Hunan 418008, PR China;School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

A two-step derivative-free iterative algorithm is presented for solving nonlinear equations. Error analysis shows that the algorithm is fourth-order with efficiency index equal to 1.5874. A lot of numerical results show that the algorithm is effective and is preferable to some existing derivative-free methods in terms of computation cost.