Abstract: A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton’s method, are given. Their convergence properties are proved. They are at least third 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’s methods. The results show that the proposed methods have some more advantages than others. They enrich the methods to find the roots of non-linear equations and they are important in both theory and application. 

Key words: variant Newton’s methods, third-order convergence, numerical test