Work

Derivative-Free Families of With- and Without-Memory Iterative Methods for Solving Nonlinear Equations and Their Engineering Applications

Year: 2023

Type: article

Abstract: In this paper, we propose a new fifth-order family of derivative-free iterative methods for solving nonlinear equations. Numerous iterative schemes found in the existing literature either exhibit divergence or fail to work when the function derivative is zero. However, the proposed family of methods successfully works even in such scenarios. We extended this idea to memory-based iterative methods by utilizing self-accelerating parameters derived from the current and previous approximations. As a result, we increased the convergence order from five to ten without requiring additional function evaluations. Analytical proofs of the proposed family of derivative-free methods, both with and without memory, are provided. Furthermore, numerical experimentation on diverse problems reveals the effectiveness and good performance of the proposed methods when compared with well-known existing methods.

Source: Mathematics

DOI: 10.3390/math11214512

Authors: Ekta Sharma, Sunil Panday, Shubham Kumar Mittal, Dan-Marian Joița, Lavinia Lorena Pruteanu, Lorentz Jäntschi

Institutions: National Institute of Technology Manipur, Technical University of Cluj-Napoca, Babeș-Bolyai University

Language: English

Topic: Iterative Methods for Nonlinear Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,336

Funder: Universitatea Tehnică din Cluj-Napoca