# On Extending the Applicability of two-Step Secant Method for non-differentiable operators

## TL;DR

This paper extends the two-step Secant method's applicability to non-differentiable operators in Banach spaces, providing convergence analysis and numerical validation for such cases.

## Contribution

It introduces a semi-local convergence analysis for the two-step Secant method applied to non-differentiable operators, which was not previously addressed.

## Key findings

- Convergence is established for non-differentiable operators.
- Numerical examples confirm the theoretical results.
- The method fails for non-differentiable functions without the extended analysis.

## Abstract

The semi-local convergence analysis of a well defined and efficient two-step Secant method in Banach spaces is presented in this study. The recurrence relation technique is used under some weak assumptions. The pertinency of the assumed method is extended for nonlinear non-differentiable operators. The convergence theorem is also established to show the existence and uniqueness of the approximate solution. A numerical illustration is quoted to certify the theoretical part which shows that the earlier study will fail if the function is non-differentiable.