A new approach for solving nonlinear system of equations using Newton method and HAM

A new approach for solving nonlinear system of equations using Newton method and HAM

A new approach utilizing Newton Method and Homotopy Analysis Method (HAM) is proposed for solving nonlinear system of equations. Accelerating the rate of convergence of HAM, and obtaining a global quadratic rate of convergence are the main purposes of this approach. The numerical results demonstrate...

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Bibliographic Details
Main Authors: Jalal Izadian, Reza Abrishami, Maryam Jalili
Format: Article
Language:English
Published: Ferdowsi University of Mashhad 2014-11-01
Series:Iranian Journal of Numerical Analysis and Optimization
Subjects:
homotopy analysis method
zero order deformation equations
control convergence parameter
newton's method
iterative method
multi-step iterative method
order of convergence
Online Access:https://ijnao.um.ac.ir/article_24435_a799b8bc98a0f6bcfbb86bf286ec9ca8.pdf
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spelling doaj-0fc11ff0df904276b2d639f89d3758d32021-06-02T06:40:52ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692014-11-0142577210.22067/ijnao.v4i2.3255524435A new approach for solving nonlinear system of equations using Newton method and HAMJalal Izadian0Reza Abrishami1Maryam Jalili2Islamic Azad UniversityIslamic Azad UniversityIslamic Azad UniversityA new approach utilizing Newton Method and Homotopy Analysis Method (HAM) is proposed for solving nonlinear system of equations. Accelerating the rate of convergence of HAM, and obtaining a global quadratic rate of convergence are the main purposes of this approach. The numerical results demonstrate the efficiency and the performance of proposed approach. The comparison with conventional homotopy method, Newton Method and HAM shows the great freedom of selecting the initial guess, in this approach.https://ijnao.um.ac.ir/article_24435_a799b8bc98a0f6bcfbb86bf286ec9ca8.pdfhomotopy analysis methodzero order deformation equationscontrol convergence parameternewton's methoditerative methodmulti-step iterative methodorder of convergence
collection DOAJ
language English
format Article
sources DOAJ
author Jalal Izadian
Reza Abrishami
Maryam Jalili
spellingShingle Jalal Izadian
Reza Abrishami
Maryam Jalili
A new approach for solving nonlinear system of equations using Newton method and HAM
Iranian Journal of Numerical Analysis and Optimization
homotopy analysis method
zero order deformation equations
control convergence parameter
newton's method
iterative method
multi-step iterative method
order of convergence
author_facet Jalal Izadian
Reza Abrishami
Maryam Jalili
author_sort Jalal Izadian
title A new approach for solving nonlinear system of equations using Newton method and HAM
title_short A new approach for solving nonlinear system of equations using Newton method and HAM
title_full A new approach for solving nonlinear system of equations using Newton method and HAM
title_fullStr A new approach for solving nonlinear system of equations using Newton method and HAM
title_full_unstemmed A new approach for solving nonlinear system of equations using Newton method and HAM
title_sort new approach for solving nonlinear system of equations using newton method and ham
publisher Ferdowsi University of Mashhad
series Iranian Journal of Numerical Analysis and Optimization
issn 2423-6977
2423-6969
publishDate 2014-11-01
description A new approach utilizing Newton Method and Homotopy Analysis Method (HAM) is proposed for solving nonlinear system of equations. Accelerating the rate of convergence of HAM, and obtaining a global quadratic rate of convergence are the main purposes of this approach. The numerical results demonstrate the efficiency and the performance of proposed approach. The comparison with conventional homotopy method, Newton Method and HAM shows the great freedom of selecting the initial guess, in this approach.
topic homotopy analysis method
zero order deformation equations
control convergence parameter
newton's method
iterative method
multi-step iterative method
order of convergence
url https://ijnao.um.ac.ir/article_24435_a799b8bc98a0f6bcfbb86bf286ec9ca8.pdf
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AT maryamjalili anewapproachforsolvingnonlinearsystemofequationsusingnewtonmethodandham
AT jalalizadian newapproachforsolvingnonlinearsystemofequationsusingnewtonmethodandham
AT rezaabrishami newapproachforsolvingnonlinearsystemofequationsusingnewtonmethodandham
AT maryamjalili newapproachforsolvingnonlinearsystemofequationsusingnewtonmethodandham
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