High-level convergence order accelerators of iterative methods for nonlinear problems
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Date
2025
Subject
Métodos iterativos (Matemáticas)
Sistemas no lineales
Análisis numérico
Ecuaciones integrales no lineales
Sistemas no lineales
Análisis numérico
Ecuaciones integrales no lineales
Language:
Inglés
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier B.V.
Description
We present an efficient strategy to increase, under certain conditions, the order of convergence of iterative methods to solve nonlinear systems of equations. We analytically compare the new accelerator with others and establish the conditions under which this technique is more efficient. We perform an analysis of the efficiency of some one-step accelerators that increase the convergence order by two units. New concepts about efficiency are introduced which allow us to compare different iterative schemes from other points of view. We demonstrate that our proposal is a good alternative to the existing ones. As a consequence, we propose two new maximally efficient, damped Newton-Traub type schemes of order 5 and 6. These are an improvement of two other maximally efficient methods. Their numerical performance is better than that of known methods of the same order, and we find that it is a very economical way to achieve high order. Some numerical examples confirm the theoretical results.
Type
Artículo