Efficient Jarratt-like methods for solving systems of nonlinear equations

Abstract

We present the iterative methods of fourth and sixth order convergence for solving systems of nonlinear equations. Fourth order method is composed of two Jarratt-like steps and requires the evaluations of one function, two first derivatives and one matrix inversion in each iteration. Sixth order method is the composition of three Jarratt-like steps of which the first two steps are that of the proposed fourth order scheme and requires one extra function evaluation in addition to the evaluations of fourth order method. Computational efficiency in its general form is discussed. A comparison between the efficiencies of proposed techniques with existing methods of similar nature is made. The performance is tested through numerical examples. Moreover, theoretical results concerning order of convergence and computational efficiency are confirmed in the examples. It is shown that the present methods are more efficient than their existing counterparts, particularly when applied to the large systems of equations.