Unifying fourth-order family of iterative methods |
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Authors: | SK Khattri MA Noor E Al-Said |
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Institution: | 1. Department of Engineering, Stord Haugesund University College, Norway;2. Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan;3. Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia |
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Abstract: | In this work, we develop a new two-parameter family of iterative methods for solving nonlinear scalar equations. One of the parameters is defined through an infinite power series consisting of real coefficients while the other parameter is a real number. The methods of the family are fourth-order convergent and require only three evaluations during each iteration. It is shown that various fourth-order iterative methods in the published literature are special cases of the developed family. Convergence analysis shows that the methods of the family are fourth-order convergent which is also verified through the numerical work. Computations are performed to explore the efficiency of various methods of the family. |
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