New family of Chebyshev's Method for Finding Simple Roots of Nonlinear Equations

摘要

In this paper, we present a new family of Chebyshev’s method for finding simple roots of nonlinear equations. The proposed schema is represented by a simple and original expression, which depends on a natural integer parameter , thus generating infinity of methods. The convergence analysis shows that the order of convergence of all methods of the proposed scheme is three. A first study on the global convergence of these methods will performed. The peculiarity and strength of the proposed family lies in the fact that, under certain conditions, the convergence speed of its methods improves by increasing . In order to show the power of this new family and to support the theory developed in this paper, some numerical tests will performed and some comparisons will make with several other existing third order and higher order methods.