A High-Order Derivative Free Iteration Method For Solving Nonlinear Equations

In this thesis, we study high-order derivative free iteration methods for solving nonlinear equations.Through the research of Newton method and some three-steps iter-ation methods for solving nonlinear equations,we find they all require the first derivative exist and not equal to zero.But the actual situation is not so and solving of derivatives will increase the complexity of the calculation.So based on the eighth-order conver-gent iteration method been proposed by R.Thukral and M.S.Petkovic in [45],we develop a seventh-order convergent iteration method for solving nonliner equations using central difference quotient instead of the first derivative.This method is totally free of derivatives. Convergence analysis shows this method is seventh-order conver-gent. Finally,numerical experiments show that this new method is right and effective by comparing with some existing methods.