A Family of Fourth-order Convergence Variant Newton′s Methods

A family of fourth-order convergence methods of solving roots for nonlinear equation,which are variant Newton′s method,are given.Their convergence properties are proved.They are at least fourth-order convergence near simple root and one order convergence near multiple roots.In the end,numerical tests are given and compared with other known Newton-like methods.The results show that the proposed methods have some more advantages than others.They enrich the methods to find the roots of nonlinear equation and they are important in both theory and application.