New predictor-corrector methods for solving nonlinear equations |
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Authors: | Kun Wang Xinlong Feng |
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Affiliation: | 1. Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, P.R. China 2. College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, P.R. China
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Abstract: | In this paper, we present a new one-step iterative method for solving nonlinear equations, which inherits the advantages of both Newton’s and Steffensen’s methods. Moreover, two two-step methods of second-order are proposed by combining it with the regula falsi method. These new two-step methods present attractive features such as being independent of the initial values in the iterative interval, or being adaptive for the iterative formulas. The convergence of the iterative sequences is deduced. Finally, numerical experiments verify their merits. |
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