Study On Two Iterative Methods For Solving Nonlinear Equations

Solving nonlinear equations is one of the most important problems in numerical analysis. In this thesis, we study two classes of iterative methods for solving nonlinear equations.(1) By using the multipoint iterative techniques for single variable nonlinear equations, we develop a multipoint iterative methods which do not require the use of second or higher derivatives of the function. The order of convergence of the proposed methods are three. In order to verify the efficiency, a comparison of the numerical results for the proposed methods and the classical Newton’s method have been given.(2) A new family of iterative methods without derivatives for solving nonlinear equation is also proposed. According to the quadrature rules, the new iterative formulas without derivatives are obtained, and the convergence is proved. This thesis also generalize the results of the recent papers. The numerical experiments show that our methods derived without derivatives are effective and comparable to the well-known Newton method.