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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
INSI Publications
2011
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/143/ http://irep.iium.edu.my/143/1/56-59.pdf |
| _version_ | 1848775665757716480 |
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| author | Hasan, Talib Hashim Chowdhury, Md. Sazzad Hossien Prayoto, . |
| author_facet | Hasan, Talib Hashim Chowdhury, Md. Sazzad Hossien Prayoto, . |
| author_sort | Hasan, Talib Hashim |
| building | IIUM Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T14:17:49Z |
| format | Article |
| id | iium-143 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:17:49Z |
| publishDate | 2011 |
| publisher | INSI Publications |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-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 PeerReviewed 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 |
| spellingShingle | QA Mathematics Hasan, Talib Hashim Chowdhury, Md. Sazzad Hossien Prayoto, . Solving Nonlinear Algebraic Problem Using Newton Homotopy Differential Equation |
| title | 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_short | Solving Nonlinear Algebraic Problem Using Newton Homotopy Differential Equation |
| title_sort | solving nonlinear algebraic problem using newton homotopy differential equation |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/143/ http://irep.iium.edu.my/143/ http://irep.iium.edu.my/143/1/56-59.pdf |