Title

Memory Based Approaches to One-Dimensional Nonlinear Models.

Authors

Naseem, Amir; Argyros, Ioannis K.; Qureshi, Sania; Aziz ur Rehman, Muhammad; Soomro, Amanullah; Gdawiec, Krzysztof; Iyanda Abdulganiy, Ridwanulahi

Abstract

Algorithms that locate roots are used to analyze nonlinear equations in computer science, mathematics, and physical sciences. In order to speed up convergence and increase computational efficiency, memory-based root-seeking algorithms may look for the previous iterations. Three memory-based methods with a convergence order of about 2.4142 and one method without memory with third-order convergence are devised using both Taylor's expansion and the backward difference operator. We provide an extensive analysis of local and semilocal convergence. We also use polynomiography to analyze the methods visually. Finally, the proposed iterative approaches outperform a number of existing memory-based methods when applied to one-dimensional nonlinear models taken from different fields of science and engineering.

Subjects

ARTIFICIAL intelligence; DIFFERENCE operators; PHYSICAL sciences; COMPUTER science; NONLINEAR equations

Publication

Acta Applicandae Mathematicae, 2024, Vol 195, Issue 1, p1

ISSN

0167-8019

Publication type

Academic Journal

DOI

10.1007/s10440-024-00703-9