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Modified Householder iterative method free from second derivatives for nonlinear equations |
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| Authors: | Muhammad Aslam Noor Vijay Gupta |
| Institution: | aMathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan bSchool of Applied Sciences, Netaji Subhas Institute of Technology, New Delhi 110075, India |
| Abstract: | In this paper, we suggest and analyze a new two-step predictor–corrector type iterative method free from second derivatives for solving nonlinear equations of the type f(x)=0. This new method includes the two-step Newton method as a special case. We prove that the new iterative method is of fourth-order. Several examples are given to illustrate the efficiency of this new method and its comparison with other iterative methods. This method can be considered as a significant improvement of the Newton method and its variant forms. |
| Keywords: | Iterative method Convergence Newton method Taylor series Examples |
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