Interval Methods with Fifth Order of Convergence for Solving Nonlinear Scalar Equations

Ivan Ivanov,Tonya Mateva

doi:10.3390/axioms8010015

Abstract

In this paper, based on Kou’s classical iterative methods with fifth-order of convergence, we propose new interval iterative methods for computing a real root of the nonlinear scalar equations. Some numerical experiments have executed with the program INTLAB in order to confirm the theoretical results. The computational results have described and compared with Newton’s interval method, Ostrowski’s interval method and Ostrowski’s modified interval method. We conclude that the proposed interval schemes are effective and they are comparable to the classical interval methods.

Highlights

Several iterative methods are used to solve nonlinear equations, the most famous being Newton’s method
In article [14], the authors have described iterative formulas proposed by Ostrowski [15] and based on Newton’s interval method and offer interval modifications of these iterative patterns
We look at three iterative schemes that we modify in the interval form and with them we explore selected functions to find the number of iterations needed to find their roots at a pre-selected interval

Summary

Introduction

Several iterative methods are used to solve nonlinear equations, the most famous being Newton’s method. In addition to the classic iteration schemes, interval methods are used to solve nonlinear equations. In article [14], the authors have described iterative formulas proposed by Ostrowski [15] and based on Newton’s interval method and offer interval modifications of these iterative patterns. We discuss some modifications of Newton’s method and we present them in an interval form. We use the methodology for the research, analysis and comparison of iterative schemes applied by authors in articles [14,16] and others.

Methods

Results

Conclusion