Interval Root Finding with Extended Lagrange Interpolation

Year 2025, Volume: 13 Issue: 2, 100 - 108, 29.12.2025

Yasemin Demirel , Oya Mert , Gülay Karakaya

https://doi.org/10.51354/mjen.1660028

Abstract

Finding the root is one of the most common problems in scientific disciplines. Due to their increasing importance in a wide variety of practical applications, nonlinear functions are utilized across the entire spectrum of various areas within mathematics, science, and engineering. Using computers to solve these functions is very important, especially in today's world. The most important things to think about when working out the roots of non-linear equations are how well the method works and how much it costs to do it. A better method is more effective and less expensive. Considering these facts, the main aim of this paper is to present a new method that doesn't involve derivatives and is more efficient. This paper presents an approach to solving nonlinear equations by extending the Lagrange method to find roots of polynomial curves. These equations can be solved using various iterative techniques, including the Secant, Newton-Raphson, Bisection, Regula Falsi, and others. The objective is to find the roots of such equations without considering any derivative operations. This is achieved by considering polynomial curves produced using Lagrange interpolation under specific initial circumstances. The effectiveness of the proposed approach is demonstrated by examining well-documented cases from the literature. It could also be used in mathematical modeling, optimization, and computational science, making it useful for solving many practical problems.

Keywords

Lagrange approximation , nonlinear equation , root finding

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