A Family Of Multi-point Methods With Memory For Solving Nonlinear Equations

When we use mathematical tools to study the social, natural and engineering prob-lems, many of them are considered as solving the nonlinear equations f(x)=0. There-fore, the methods for solving nonlinear equations play an important role in both theoretical research and practical applications. The iterative method is the common and important algorithm to solve the equationf(x)=0, and the choices of iterative method have in-fluence on the solution of a nonlinear equation. So looking for new iterative methods with high convergence order is of great scientific and practical importance. This article present an efficient family of multi-point derivative free method based on two-pointed iterative scheme, and we also prove that the convergence order is increased from8to at least10、11、11.35、12, In our new methods, the increase of convergence order does not add any additional functions. Therefore, our new algorithms are more efficient than the existed methods. Numerical examples are included to testify the efficiency of our schemes.