Design and Applicability of Two-Step Fractional Newton–Raphson Method

Abstract

Developing two-step fractional numerical methods for finding the solution of nonlinear equations is the main objective of this research article. In addition, we present a detailed study of convergence analysis for the methods that have been proposed. By comparing numerically, we can see that the proposed methods significantly improve convergence rate and accuracy. Additionally, we demonstrate how our main results can be applied to basins of attraction.

Keywords

• fractional Newton method
• two-step schemes
• nonlinear equations
• convergence analysis
• numerical analysis