扩大了满足lipschitz和holder条件的七阶方法的收敛范围

Q1 Mathematics Results in Nonlinear Analysis Pub Date : 2022-12-30 DOI:10.53006/rna.1146027

A. Saxena, J. P. Jai̇swal, Kamal Raj Paradasani̇

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引用次数: 0

摘要

在当前的讨论中，通过假设？一阶Fréchet导数属于Lipschitz类。该方法给出了收敛球半径、误差界和解的唯一性。此外，通过考虑Hölder连续性条件，对研究进行了推广。最后，我们使用各种数值例子，包括非线性Hammerstein方程，估计了会聚球的半径。

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BROADENING THE CONVERGENCE DOMAIN OF SEVENTH-ORDER METHOD SATISFYING LIPSCHITZ AND HOLDER CONDITIONS

The local convergence analysis of a seventh order algorithm for solving nonlinear equations is presented inthe current discussion by assuming that the ?rst-order Fréchet derivative belongs to the Lipschitz class. Thisapproach yields radii of convergence ball, error bound and uniqueness of the solution. Further, generalizationof the study extended by considering Hölder continuity condition. At last, we estimated the radii of theconvergence balls using a variety of numerical examples, including a nonlinear Hammerstein equation.

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