Iterative process of order 2 without inverting the derivative

TL;DR

This paper establishes convergence conditions for a second-order iterative method solving nonlinear equations without derivative inversion, with theoretical proofs, system translation, and numerical validation.

Contribution

It introduces a novel second-order iterative process that avoids derivative inversion and provides rigorous convergence criteria.

Findings

Proved sufficient convergence conditions for the method.

Applied the method to nonlinear systems with numerical examples.

Demonstrated effectiveness without derivative inversion.

Abstract

We prove the sufficient conditions for convergence of a certain iterative process of order 2 for solving nonlinear functional equations, which does not require inverting the derivative. We translate and detail our results for a system of nonlinear equations, and apply it for some numerical example which illustrates our theorems.