An improvement of the Jarratt method

In this paper, we present a variant of Jarratt method for solving non-linear equations. Per iteration the new method adds the evaluation of the function at another point in the procedure iterated by Jarratt method. As a consequence, the local order of convergence is improved from four for Jarratt method to six for the new method. The new multistep iteration scheme, based on the new method, is developed and numerical tests verifying the theory are also given.