改进的两步高阶Euler-Chebyshev方法

Improved Two-Step High Order Euler-Chebyshev Methods

给出非线性方程求根的Euler-Chebyshev方法的改进方法,证明了方法的收敛性,它们七次和九次收敛到单根.给出数值试验,且与牛顿法及其它较高阶的方程求根方法做了比较.结果表明方法具有很好的优越性,它丰富了非线性方程求根的方法,在理论上和应用上都有一定的价值.

Improvments of Euler-Chebyshev methods for solving roots of nonlinear equation are given.Their convergence properties are proved.They are at least seventh-order convergence and nineth-order convergence near simple root.In the end,numerical tests are given and compared with other known high order root-finding methods.The results show that the proposed methods have some more advantages than others.They enrich the methods to find the roots of nonlinear equation and they are important in both theory and application.