Newton Like Iterative Method without Derivative for Solving Nonlinear Equations Based on Dynamical Systems

TL;DR

This paper introduces a derivative-free Newton-like iterative method based on dynamical systems theory, which uses difference quotients for higher accuracy and broader initial value applicability.

Contribution

A novel derivative-free iterative method with adjustable parameters, improving accuracy and initial value range over existing methods.

Findings

Higher accuracy of the difference quotient scheme

Broader initial value applicability

Numerical examples confirm effectiveness

Abstract

The iterative problem of solving nonlinear equations is studied. A new Newton like iterative method with adjustable parameters is designed based on the dynamic system theory. In order to avoid the derivative function in the iterative scheme, the difference quotient is used instead of the derivative. Different from the existing methods, the difference quotient scheme in this paper has higher accuracy. Thus, the new iterative method is suitable for a wider range of initial values. Finally, several numerical examples are given to verify the practicability and superiority of the method.