The Research On High-order Iterative Methods For Solving Nonlinear Equations

In this paper,we mainly discuss the high-order iteration methods for solving nonlinear equations.The main contents of this paper are to construct two five order methods and two six order methods.The effectiveness of the new iteration methods are verified by numerical experiments.The whole paper is divided into five chapters.Chapter 1:we mainly introduce the background,basic knowledge and re-search status of solving nonlinear equation problems.Chapter 2:we mainly introduce several classical iteration methods for solving nonlinear equations,including Newton iteration method,Euler iteration method,Halley iteration method,Chebyshev iteration method and several deformed New-ton methods.Chapter 3:On the basis of two existing third order iteration methods,we use interpolation method to estimate derivatives,add only one function value to calculate,and raise the convergence order of two third order iteration methods to the fifth order.Finally,numerical experiments verify the effectiveness and superiority of the new iteration methods.Chapter 4:On the basis of two third order Newton iteration methods,we use interpolation method to improve the convergence order of the two third order Newton iteration methods.The convergence order of the two third order New-ton iteration methods is raised to the sixth order.Compared with the method proposed by A.Cordero,the new Newton iteration method has higher efficiency.Finally,numerical experiments verify the effectiveness and superiority of the new Newton iteration methods.Chapter 5:we summarize the whole paper,analyze the unsolved problems in the research process,and discuss the areas to be improved in the future research.