Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 1, pp. 32 – 41
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0121
A class of power series based modified newton method with high precision for solving nonlinear models
Oghovese Ogbereyivwe\(^{1},*\), Salisu Shehu Umar\(^{2}\)
\(^{1}\) Department of Mathematics, Delta State University of Science and Tech., Ozoro, Delta State, Nigeria
\(^{2}\) Department of Statistics, Federal Polytechnic Auchi, Edo State, Nigeria
Copyright © 2023 Oghovese Ogbereyivwe and Salisu Shehu Umar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: August 07, 2022 – Accepted: December 26, 2022 – Published: June 30, 2023
Abstract
This manuscript proposed high-precision methods for obtaining solutions for nonlinear models. The method uses the Newton method as its predictor and an iterative function that involves the perturbed Newton method with the quotient of two power series as the corrector function. The theoretical analysis of convergence indicates that the methods class is of convergence order four, requiring three functions evaluation per cycle. The computation performance comparison with some existing methods shows that the developed methods class has perfect precision.
Keywords:
nonlinear models; iterative method; Newton method; power series