Solving Nonlinear Algebraic Problem Using Newton Homotopy Differential Equation

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

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	5604/143
Uncontrolled Keywords:	Newton Homotopy, Homotopy Differential Equation, HOMMAT
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Engineering
Depositing User:	Dr. Md Sazzad Hossien Chowdhury
Date Deposited:	28 Apr 2011 11:50
Last Modified:	12 Jul 2011 09:02
URI:	http://irep.iium.edu.my/id/eprint/143

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