Abstract

We present a family of fifth-order iterative methods for finding multiple roots of nonlinear equations. Numerical examples are considered to check the validity of the theoretical results. It is shown that the new methods are competitive with other methods for finding multiple roots. Basins of attraction for the new methods and some existing methods to observe the dynamics in the complex plane are drawn.

中文翻译：

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求解非线性方程多重根的一系列五阶迭代方法

摘要

我们提出了一系列用于寻找非线性方程的多个根的五阶迭代方法。数值例子被认为是检查理论结果的有效性。结果表明，新方法与其他寻找多根的方法相比具有竞争力。绘制了新方法和一些现有方法在复平面中观察动力学的吸引力盆地。