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In this paper, we present two new three-step predictor-corrector methods for solving nonlinear equations. This two algorithms are free from second derivative and per iteration they only require three evaluations of the given function and one evaluation of its first derivative. Convergence analysis shows that they are fifth-order convergent. Numerical tests demonstrate that both of the two new methods...
In this paper, we present a seventh-order convergent Newton-type method for solving nonlinear equations which is free from second derivative. At each iteration it requires three evaluations of the given function and two evaluation of its first derivative. Therefore its efficiency index is equal to equation which is better than that of Newton's method √2. Several examples demonstrate that the algorithm...
We present some modified Newton-type methods for solving nonlinear equations. These algorithms are free from second derivatives and permit f'(x) = 0 in some iteration points. The convergent analysis demonstrates that the order of convergence and the efficiency index of the present methods are better than that of the classical Newton's method. Some numerical examples are given to illustrate their efficiency...
Under weak conditions, we present an iteration formula to improve Newton's method for solving nonlinear equations. The method is free from second derivatives, permitting f′(x)=0 in some points and per iteration it requires two evaluations of the given function and one evaluation of its derivative. Analysis of convergence demonstrates that the new method is cubically convergent. Some numerical examples...
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