Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy method
type: Item
instance of: scholarly article
title: Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy method
zbMATH Open document ID: 1461.65094
author: Uswah Qasim
author: Zulifqar Ali
author: Fayyaz Ahmad
author: Malik Zaka Ullah
author: Mir Asma
author: Stefano Serra Capizzano
published in: Algorithms
publication date: 2019-03-26T00:00:00Z
review text: Summary: A homotopy method is presented for the construction of frozen Jacobian iterative methods. The frozen Jacobian iterative methods are attractive because the inversion of the Jacobian is performed in terms of LUfactorization only once, for a single instance of the iterative method. We embedded parameters in the iterative methods with the help of the homotopy method: the values of the parameters are determined in such a way that a better convergence rate is achieved. The proposed homotopy technique is general and has the ability to construct different families of iterative methods, for solving weakly nonlinear systems of equations. Further iterative methods are also proposed for solving general systems of nonlinear equations.
Mathematics Subject Classification ID: 65H20
zbMATH DE Number: 7042327
zbMATH Keywords: systems of nonlinear equations
zbMATH Keywords: frozen Jacobian
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: partial differential equations
zbMATH Keywords: homotopy method
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a9010018
OpenAlex ID: W2294488377
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DOI: 10.3390/A9010018
description: scientific article; zbMATH DE number 7042327