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

Year 2022, Volume: 5 Issue: 4, 473 - 486, 30.12.2022

Akanksha Saxena , J. P. Jaiswal , Kamal Raj Paradasani

https://doi.org/10.53006/rna.1146027

Cited By: 1

Abstract

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

Keywords

Nonlinear equation, Banach space, local convergence, Lipschitz continuity condition, Holder continuity condition.

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