摘要
本文首先根据Runge-Kutta方法的思想,结合Newton迭代法,提出了一类带参数的解非线性方程组F(x)=0的迭代算法,然后基于解非线性方程f(x)=0的King算法,给出第二类解非线性方程组的迭代算法,收敛性分析表明这两类算法都是五阶收敛的.其次给出了本文两类算法的效率指数,以及一些已知算法的效率指数,并且将本文算法的效率指数与其它方法进行详细的比较,通过效率比率R_(i,j)可知本文算法具有较高的计算效率.最后给出了四个数值实例,将本文两类算法与现有的几种算法进行比较,实验结果说明本文算法收敛速度快,迭代次数少,有明显的优势.
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.
出处
《计算数学》
CSCD
北大核心
2017年第2期151-166,共16页
Mathematica Numerica Sinica
基金
国家自然科学基金(11471093)
