Modifications Of Chebyshev Method For Solving Nonlinear Equation

Nonlinear problem play a great role in modern scientific computing disciplines. Many equations derived from practical problem are always the nonlinear forms.So how to solve these nonlinear Problem appropriately become more and more hot in research disciplines.The main content of the article is constructing iterative methods for solving nonlinear equations.The whole article contains of foure hapters.In the first chapter, the background and history of nonlinear problem and iterative methods are presented. The concept which occur in many places of the article is introduced.In the second chapter, some classical iterative methods are presented.In the third chapter, a family of one-point formulas for solving systems of nonlinear equations are presented by introducing a parameter into the Chebyshev iterative formula and their convergent order are found to be at least three and they only require the evaluation of one order derivative, and the methods contant some classical iterative methods and some methods given by others,at last the given methods are extended to n-dimensional case and some examples are given to demonstrate their efficiency and performance in one-dimensional and n-dimensional.In the last chapter, based on the Chebyshev-Halley iterative formula ,a family of multi-point iterative methods based on two parameters for solving nonlinear equation is obtained ,its convergent order is found to be at least three and can reach four under some conditions and it only requires the evaluation of one order derivative,it also can be extended to n-dimensional case, at last,numerical examples are given to illustrate its advantages in one-dimensional.