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Mathematical Computation

Mathematical Computation (Yearly) is an international comprehensive professional academic journal of Ivy Publisher, concerning the development of mathematical theory and computing application on the combination of mathematical theory and modern industrial technology. The main focus of the journal is the academic papers and comments of latest theoretical and apolitical mathematics improvement in the fields of nature science, engineering technology... [More] Mathematical Computation (Yearly) is an international comprehensive professional academic journal of Ivy Publisher, concerning the development of mathematical theory and computing application on the combination of mathematical theory and modern industrial technology. The main focus of the journal is the academic papers and comments of latest theoretical and apolitical mathematics improvement in the fields of nature science, engineering technology, economy and science, report of latest research result, aiming at providing a good communication platform to transfer, share and discuss the theoretical and technical development of mathematics theory development for professionals, scholars and researchers in this field, reflecting the academic front level, promote academic change and foster the rapid expansion of mathematics theory and application technology.

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ISSN Print:2327-0519

ISSN Online:2327-0527

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Paper Infomation

Three Modified Efficient Iterative Methods for Non-linear Equations

Full Text(PDF, 551KB)

Author: Liang Fang, Lili Ni, Rui Chen

Abstract: In this paper, we present three modified iterative methods for solving non-linear equations. Firstly, we give a fourth-order convergent iterative method. Then based on the fourth-order method we propose two modified three step Newton-type iterative methods with order of convergence six for solving non-linear equations. All of the methods are free from second derivatives. The efficiency index of Algorithm 1 is equal to that of classical Newton's method 1.414, while the efficiency index of Algorithm 2 and Algorithm 3 is 1.431 which is better than that of classical Newton's method. Several numerical results demonstrate that the proposed methods are more efficient and perform better than classical Newton's method and some other methods.

Keywords: Iterative Method,Non-linear Equation,Order of Convergence,Newton's Method,Efficiency Index

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