求解非线性方程的一个新的预测-校正方法

A New Forecast-Correction for Solving Nonlinear Equations

关键词:  非线性方程  牛顿迭代  收敛阶

Key words:  nonlinear equaton  Newton's iteration  convergence order

摘要:

将一种基于数值积分公式的隐式迭代格式与一种改进的牛顿迭代法结合,得到一种新的求解非线性方程的预测-校正方法,并用数值实例来验证该方法.新方法比一些已知的方法收敛阶、收敛精度更高,适合函数类的范围更宽,是一种较优的方法.

Abstract:

An implicit iteration formula for solving nonlinear equations is presented, then by the implicit iteration scheme and the improved Newton iterative method, a new forecast correction method is given, and use numerical examples to verify the method.The new method is better than the known methods on the high covergence order and convergence precision.The method is superior in range of function class to the other methods.