The Modified Iterative Methods To Solve Nonlinear Equation (Equations)

This paper mainly studies some improved iterative methods for solving nonlinear equations,which include a family of third-order Newton-Type iterative methods with parameters,three kinds of fifth-order predictor-corrector Newton-Type iterative methods and a sixth-order Newton-Type iterative method.There are five chapters in this paper:In the first chapter,we introduce the background of nonlinear equations,recall the development and research status of iterative methods and improved iterative methods,introduce the theorems and the conceptions.In the second chapter,we construct a family of third-order Newton-Type iterative methods with several parameters by using the method of undetermined coefficients.The construction process of the scheme is discussed,and its convergence analysis is given.In the numerical examples,we discuss the influence of parameters on the number of iterations for the six nonlinear equations.Compared with the Newton method and the other three kinds of the same order algorithms,the new algorithm has better advantages.In the third chapter,we construct three new kinds of fifth-order Newton-Type iterative methods based on the Newton iterative and the difference coefficient methods to solve nonlinear equations.Then,we analyze its convergence.By the numerical examples,we verify that the new constructed methods are effective.In the fourth chapter,we construct a sixth-order Newton-Type iterative method by using the method of the Newton-Cotes the quadrature's open formula and then we analyze its convergence.In the numerical examples,the results of this paper are compared with the other kinds of the algorithms,from which we conclude that the new algorithm has the better advantages.In the fifth chapter,we make simple summary of this thesis and point out the deficiency of this thesis as prospects for future research direction.