Efficient high-order iterative methods for solving nonlinear systems and their application on heat conduction problems
type: Item
instance of: scholarly article
title: Efficient high-order iterative methods for solving nonlinear systems and their application on heat conduction problems
zbMATH Open document ID: 1367.65117
DOI: 10.1155/2017/6457532
author: Esther Gómez
author: Alicia Cordero
author: Juan Ramón Torregrosa Sánchez
published in: Complexity
publication date: 2017-08-03T00:00:00Z
review text: Summary: For solving nonlinear systems of big size, such as those obtained by applying finite differences for approximating the solution of diffusion problem and heat conduction equations, three-step iterative methods with eighth-order local convergence are presented. The computational efficiency of the new methods is compared with those of some known ones, obtaining good conclusions, due to the particular structure of the iterative expression of the proposed methods. Numerical comparisons are made with the same existing methods, on standard nonlinear systems and a nonlinear one-dimensional heat conduction equation by transforming it in a nonlinear system by using finite differences. From these numerical examples, we confirm the theoretical results and show the performance of the presented schemes.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 6755990
zbMATH Keywords: nonlinear systems of big size
zbMATH Keywords: diffusion
zbMATH Keywords: heat conduction
Wikidata QID: Q59142933
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/6457532
OpenAlex ID: W2580309451
cites work: On new iterative method for solving systems of nonlinear equations
cites work: A modified Newton-Jarratt's composition
cites work: Convergence, efficiency and dynamics of new fourth and sixth order families of iterative methods for nonlinear systems
cites work: On a new method for computing the numerical solution of systems of nonlinear equations
cites work: Efficient Jarratt-like methods for solving systems of nonlinear equations
cites work: A multi-step class of iterative methods for nonlinear systems
cites work: Increasing the order of convergence for iterative methods to solve nonlinear systems
cites work: Seventh-order derivative-free iterative method for solving nonlinear systems
cites work: On Approximation of Equations by Algebraic Equations
cites work: Numerical investigation of the nonlinear heat diffusion equation with high nonlinearity on the boundary
cites work: Variants of Newton's method using fifth-order quadrature formulas
description: scientific article; zbMATH DE number 6755990