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A Steffensen-like method and its higher-order variants
Authors:Quan Zheng  Jing Wang  Peng Zhao  Li Zhang
Institution:College of Sciences, North China University of Technology, Beijing 100144, China
Abstract:For solving nonlinear equations, we suggest a second-order parametric Steffensen-like method, which is derivative free and only uses two evaluations of the function in one step. We also suggest a variant of the Steffensen-like method which is still derivative free and uses four evaluations of the function to achieve cubic convergence. Moreover, a fast Steffensen-like method with super quadratic convergence and a fast variant of the Steffensen-like method with super cubic convergence are proposed by using a parameter estimation. The error equations and asymptotic convergence constants are obtained for the discussed methods. The numerical results and the basins of attraction support the proposed methods.
Keywords:Nonlinear equation  Newton&rsquo  s method  Steffensen method  Convergence order  Error equation  Asymptotic convergence constant  Basin of attraction
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