• 论文 •

### 两类五阶解非线性方程组的迭代算法

1. 合肥工业大学 数学学院, 合肥 230009
• 收稿日期:2016-01-21 出版日期:2017-05-15 发布日期:2017-07-18
• 通讯作者: 刘植,E-mail:liuzhi314@126.com
• 基金资助:

国家自然科学基金（11471093）.

Yu Jingjing, Jiang Ping, Liu Zhi. THE TWO KIND OF ITERATIVE METHODS WITH FIFTH-ORDER FOR SOLVING THE SYSTEM OF NONLINEAR EQUATIONS[J]. Mathematica Numerica Sinica, 2017, 39(2): 151-166.

### THE TWO KIND OF ITERATIVE METHODS WITH FIFTH-ORDER FOR SOLVING THE SYSTEM OF NONLINEAR EQUATIONS

Yu Jingjing, Jiang Ping, Liu Zhi

1. School of Mathematics, Hefei University of Technology, Hefei 230009, China
• Received:2016-01-21 Online:2017-05-15 Published:2017-07-18

In this paper,for solving system of nonlinear equations,we use the Runge-Kutta method to achieve a family of iterative methods with parameters,which are based on Newton s method.And the other iterative method is built up which is based on the King s method for solving the nonlinear equation.And then,we prove that these two methods are convergent with fifth order.These two iterative method s efficiency indexes and some other recently published method s efficiency indexes are given.Compared with other methods,the two methods have higher computational efficiency.Finally,four numerical examples are given to show that our methods are effective.

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