Enhanced Ninth-Order Memory-Based Iterative Technique for Efficiently Solving Nonlinear Equations

Shubham Kumar Mittal, Sunil Panday () and Lorentz Jäntschi
Additional contact information
Shubham Kumar Mittal: 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
Lorentz Jäntschi: Department of Physics and Chemistry, Technical University of Cluj-Napoca, 103-105 Muncii Blvd., 400641 Cluj-Napoca, Romania

Mathematics, 2024, vol. 12, issue 22, 1-15

Abstract: In this article, we present a novel three-step with-memory iterative method for solving nonlinear equations. We have improved the convergence order of a well-known optimal eighth-order iterative method by converting it into a with-memory version. The Hermite interpolating polynomial is utilized to compute a self-accelerating parameter that improves the convergence order. The proposed uni-parametric with-memory iterative method improves its R-order of convergence from 8 to 8.8989 . Additionally, no more function evaluations are required to achieve this improvement in convergence order. Furthermore, the efficiency index has increased from 1.6818 to 1.7272 . The proposed method is shown to be more effective than some well-known existing methods, as shown by extensive numerical testing on a variety of problems.

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: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/22/3490/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/22/3490/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:22:p:3490-:d:1516596

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().