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

Ekta Sharma (), Sunil Panday, Shubham Kumar Mittal (), Dan-Marian Joița, Lavinia Lorena Pruteanu and Lorentz Jäntschi
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Ekta Sharma: Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, Manipur, India
Sunil Panday: Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, Manipur, India
Shubham Kumar Mittal: Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, Manipur, India
Dan-Marian Joița: Chemistry Doctoral School, Babeş-Bolyai University, 400084 Cluj, Romania
Lavinia Lorena Pruteanu: Department of Chemistry and Biology, North University Center at Baia Mare, Technical University of Cluj-Napoca, 430122 Baia Mare, Romania
Lorentz Jäntschi: Department of Physics and Chemistry, Technical University of Cluj-Napoca, B.-dul Muncii nr. 103-105, 400641 Cluj-Napoca, Romania

Mathematics, 2023, vol. 11, issue 21, 1-13

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.

Keywords: nonlinear equation; roots; efficiency index; iterative method; with-memory methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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