Eighth-order methods with high efficiency index for solving nonlinear equations |
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| Authors: | Liping Liu Xia Wang |
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| Affiliation: | a Department of Mathematics, North Carolina Agricultural and Technical State University, Greensboro, NC 27411, USA
b Department of Mathematics and Information Science, Zheng Zhou University of Light Industry, Zheng Zhou 450002, China |
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| Abstract: | In this paper, we derive a new family of eighth-order methods for solving simple roots of nonlinear equations by using weight function methods. Per iteration these methods require three evaluations of the function and one evaluation of its first derivative, which implies that the efficiency indexes are 1.682. Numerical comparisons are made to show the performance of the derived methods, as shown in the illustration examples. |
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| Keywords: | Eighth-order convergence Nonlinear equations Weight function methods Convergence order Efficiency index |
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