拓宽满足Lipschitz和赫尔德条件的七阶方法的收敛域
Broadening the convergence domain of Seventh-order method satisfying Lipschitz and Hölder conditions
摘要：
本文在一阶Fréchet导数属于Lipschitz类的条件下，给出了求解非线性方程的多步七阶方法的局部收敛分析.我们工作的意义在于避免了泰勒展开的标准做法，从而通过应用仅基于一阶导数的技术扩展了格式的适用性。此外，这项研究提供了半径球的收敛，误差界的距离，除了唯一的解决方案。此外，由于该分析比Lipschitz连续条件更宽松，因此提供了满足Hölder连续条件的分析的推广。我们考虑了一些数值例子，并计算了收敛球的半径。
英文摘要：
In this paper, the local convergence analysis of the multi-step seventh order method is presented for solving nonlinear equations assuming that the first-order Fréchet derivative belongs to the Lipschitz class. The significance of our work is that it avoids the standard practice of Taylor expansion thereby, extends the applicability of the scheme by applying the technique based on the first-order derivative only. Also, this study provides radii of balls of convergence, the error bounds in terms of distances in addition to the uniqueness of the solution. Furthermore, generalization of this analysis satisfying Hölder continuity condition is provided since it is more relaxed than Lipschitz continuity condition. We have considered some numerical examples and computed the radii of the convergence balls.
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