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Solving Nonlinear Algebraic Problem Using Newton Homotopy Differential Equation

This paper presents an efficient algorithm for solving a nonlinear equation. In our algorithm, the nonlinear system f (x) = 0 is solved by a homotopy method, in which a homotopy H (x,t) = f (x)-(1-t) f (x0) is introduced and the solution path of H(x, t) = 0 is followed from an obvious solution (x0,0...

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Main Authors: Hasan, Talib Hashim, Chowdhury, Md. Sazzad Hossien, Prayoto, .
Format: Article
Language:English
Published: INSI Publications 2011
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/143/1/56-59.pdf
http://irep.iium.edu.my/143/
http://www.insipub.com/ajbas/2011/56-59.pdf
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spelling my.iium.irep.1432011-07-12T01:02:52Z http://irep.iium.edu.my/143/ Solving Nonlinear Algebraic Problem Using Newton Homotopy Differential Equation Hasan, Talib Hashim Chowdhury, Md. Sazzad Hossien Prayoto, . QA Mathematics This paper presents an efficient algorithm for solving a nonlinear equation. In our algorithm, the nonlinear system f (x) = 0 is solved by a homotopy method, in which a homotopy H (x,t) = f (x)-(1-t) f (x0) is introduced and the solution path of H(x, t) = 0 is followed from an obvious solution (x0,0)to the solution (x*,1) which we seek. An ordinary differential equation based on Newton homotopy is used for following the solution path. Our homotop algorithm is much more efficient than the conventional iterations type algorithms. Some numerical examples are given in order to demonstrate the effectiveness. INSI Publications 2011 Article REM application/pdf en http://irep.iium.edu.my/143/1/56-59.pdf Hasan, Talib Hashim and Chowdhury, Md. Sazzad Hossien and Prayoto, . (2011) Solving Nonlinear Algebraic Problem Using Newton Homotopy Differential Equation. Australian Journal of Basic and Applied Sciences, 5 (4). pp. 56-59. ISSN 1991-8178 http://www.insipub.com/ajbas/2011/56-59.pdf
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Hasan, Talib Hashim
Chowdhury, Md. Sazzad Hossien
Prayoto, .
Solving Nonlinear Algebraic Problem Using Newton Homotopy Differential Equation
description This paper presents an efficient algorithm for solving a nonlinear equation. In our algorithm, the nonlinear system f (x) = 0 is solved by a homotopy method, in which a homotopy H (x,t) = f (x)-(1-t) f (x0) is introduced and the solution path of H(x, t) = 0 is followed from an obvious solution (x0,0)to the solution (x*,1) which we seek. An ordinary differential equation based on Newton homotopy is used for following the solution path. Our homotop algorithm is much more efficient than the conventional iterations type algorithms. Some numerical examples are given in order to demonstrate the effectiveness.
format Article
author Hasan, Talib Hashim
Chowdhury, Md. Sazzad Hossien
Prayoto, .
author_facet Hasan, Talib Hashim
Chowdhury, Md. Sazzad Hossien
Prayoto, .
author_sort Hasan, Talib Hashim
title Solving Nonlinear Algebraic Problem Using Newton Homotopy Differential Equation
title_short Solving Nonlinear Algebraic Problem Using Newton Homotopy Differential Equation
title_full Solving Nonlinear Algebraic Problem Using Newton Homotopy Differential Equation
title_fullStr Solving Nonlinear Algebraic Problem Using Newton Homotopy Differential Equation
title_full_unstemmed Solving Nonlinear Algebraic Problem Using Newton Homotopy Differential Equation
title_sort solving nonlinear algebraic problem using newton homotopy differential equation
publisher INSI Publications
publishDate 2011
url http://irep.iium.edu.my/143/1/56-59.pdf
http://irep.iium.edu.my/143/
http://www.insipub.com/ajbas/2011/56-59.pdf
_version_ 1643604544205094912
score 13.211869

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