A New Adaptive Eleventh-Order Memory Algorithm for Solving Nonlinear Equations

Sunil Panday, Shubham Kumar Mittal (), Carmen Elena Stoenoiu and Lorentz Jäntschi
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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
Carmen Elena Stoenoiu: Department of Electric Machines and Drives, Technical University of Cluj-Napoca, 26-28 Baritiu Str., 400027 Cluj-Napoca, Romania
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 12, 1-14

Abstract: In this article, we introduce a novel three-step iterative algorithm with memory for finding the roots of nonlinear equations. The convergence order of an established eighth-order iterative method is elevated by transforming it into a with-memory variant. The improvement in the convergence order is achieved by introducing two self-accelerating parameters, calculated using the Hermite interpolating polynomial. As a result, the R-order of convergence for the proposed bi-parametric with-memory iterative algorithm is enhanced from 8 to 10.5208 . Notably, this enhancement in the convergence order is accomplished without the need for extra function evaluations. Moreover, the efficiency index of the newly proposed with-memory iterative algorithm improves from 1.5157 to 1.6011 . Extensive numerical testing across various problems confirms the usefulness and superior performance of the presented algorithm relative to some well-known existing algorithms.

Keywords: nonlinear equation; iterative method; efficiency index; with-memory algorithms; R-order convergence; self-accelerating (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: View citations in EconPapers (1)

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