Higher-order Iterative Methods And Applications In Differential Equations

Solving nonlinear equations or systems of nonlinear equations is one ofthe most important problems in numerical analysis. However, It is difcultto fnd the exact roots of these equations. Therefore, fnding the approximatesolutions of such equations becomes very important. In this paper, we discussthe problems of nonlinear equations or systems of nonlinear equations usingone-dimensional and higher-dimensional iterative methods. Firstly, a generaliterative method which contains many special methods is developed, and nu-merical analysis is given to illustrate the efciency of this method. Secondly,based on the third-order accelerated Newton’s method, a new fourth-step iter-ative method is presented and the order of convergence is at least nine. Numer-ical results also show that this method is better than other existing methods.Lastly, a new iterative method of fnding roots of nonlinear equations in Ba-nach Space is presented and the applications in diferential equations are alsogiven.