A New Modified Newton Method use of Haar wavelet for solving Nonlinear equations

TL;DR

This paper introduces a modified Newton method utilizing Haar wavelets for solving nonlinear equations, achieving third-order convergence without second derivatives, supported by numerical experiments confirming theoretical results.

Contribution

The paper presents a novel Haar wavelet-based modified Newton method that does not require second derivatives and demonstrates third-order convergence.

Findings

Method achieves third-order convergence.

Numerical experiments confirm theoretical convergence order.

No second derivatives needed in the new method.

Abstract

In this paper, we present a new modified Newton method a use of Haar wavelet formula for solving non-linear equations. This new method do not require the use of the second-order derivative. It is shown that the new method has third-order of convergent. Furthermore, some numerical experiments are conducted which confirm our theoretical findings.