Three Modified Efficient Iterative Methods for Non-linear Equations

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.
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