An improvement to double-step Newton method and its multi-step version for solving system of nonlinear equations and its applications (Q509651)

The two-step fifth-order method, which is an improvement to the double-step Newton method as well as to the multi-step version of the two-step fifth-order method are proposed. The main advantages of the proposed schemes are the following: (i) they do not use second-order Fréchet derivatives and (ii) evaluate only one inverse of first-order Fréchet derivatives. It is verified that the root \(\alpha\) is a point of attraction for the proposed schemes in the sense of Ostrowski. The performances of the new methods are compared with Newton's method and some existing methods.