A Third-order Variant of Newton′s Method

Based on inverse function′s integral equation and Simpson scheme,a new method for solving roots of non-linear equations is obtained,which is a variant of Newton′s method.The present method is proved to be at least third-order convergence near simple root and it improves convergence order and efficiency index compared with Newton′s method.In the end,numerical tests are given and compared with Newton′s method and Newton-like methods.The results show that the present method has some more advantages than others.It enriches the methods for solving the roots of non-linear equations.