一类求解非线性方程的五阶迭代法

Ali Zein
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引用次数: 0

摘要

提出了一组利用权函数技术求解非线性方程的五阶迭代方法。该系列通过其结构和权重函数的选择提供了灵活性,从而产生了广泛的新的特定方案。结果表明,作为特例,该家族包含了几种已知的和最新的方法。此外,还设计了几种新的特殊方法,以获得比现有同类方法更好的结果。对该族中的几种具体方案进行了收敛性分析,并给出了实域和复域的数值算例。将这个家族中的现有方法与新引入的方法进行比较,通常表明新成员的性能有所提高。值得注意的是,对复杂动力学和引力盆地的研究表明,我们的新具体方案具有更广泛的初始点集,这些初始点集导致收敛。
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A General Family of Fifth-order Iterative Methods for Solving Nonlinear Equations
A family of fifth-order iterative methods is proposed for solving nonlinear equations using the weight function technique. This family offers flexibility through its structure and the choice of weight functions, resulting in a wide range of new specific schemes. It is demonstrated that this proposed family includes several well-known and recent methods as special cases. In addition, several new particular methods are designed to achieve better results than existing methods of the same type. Convergence analysis is conducted, and numerical examples in both real and complex domains are provided for several specific schemes within the proposed family. Comparisons between the existing methods within this family and the newly introduced methods generally indicate improved performance among the new members. Notably, the study of complex dynamics and basins of attraction reveals that our new specific schemes have broader sets of initial points that lead to convergence.
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CiteScore
1.30
自引率
28.60%
发文量
156
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