A New Iterative Method for Non-linear Equations and Its Application

Newton’s iterative method, which is quadratically convergent, is often used to calculate water surface profile of a river. But when the river is long, it will be spent much of time on calculating. In this paper, a new fourth-order iterative method for non-linear equations is proposed. Analysis of convergence shows that the method has at least third-order convergence, and if the parameter φ of the method is equal to 3, it will have fourth-order convergence. Several numerical examples are given to illustrate the efficiency and performance of the proposed method. In the end, the new method is used in water surface profile computing, which performs better than Newton’s iterative method and Potra’s method