Some Fifth and Sixth Order Iterative Methods for Solving Nonlinear Equations

In this paper, we derive multipoint iterative methods of fifth and sixth order for finding simple zeros of nonlinear equations. The methods are based on the composition of two steps – the first step consists of Jarratt fourth order method and the second is weighted Newton step to which correction term is applied. Per iteration each method requires two evaluations of the given function and two evaluations of its derivative. Numerical examples are presented to support that the methods thus obtained are competitive with Jarratt method. Moreover, it is shown that these methods are very useful in the applications requiring high precision in computations.