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ABSTRACT:In this paper, we suggest and discuss an iterative method for solving nonlinear equations of the type f(x) = 0 having eighteenth order convergence. This new technique based on Newton's method and extrapolated Newton's method. This method is compared with the existing ones through some numerical examples to exhibit its superiority.

In this paper, the Eighteenth Order Convergent Method (EOCM) developed by Vatti et.al is considered and this method is further studied without the presence of second derivative. It is shown that this method has same efficiency index as that of EOCM. Several numerical examples are given to illustrate the efficiency and performance of the new method. AMS Subject Classification: 41A25, 65K05, 65H05.

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