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Solving directly two point non-linear boundary value problems using direct Adams Moulton method.

Problem statement: In this study, a direct method of Adams Moulton type was developed for solving non linear two point Boundary Value Problems (BVPs) directly. Most of the existence researches involving BVPs will reduced the problem to a system of first order Ordinary Differential Equations (ODEs)....

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Main Authors: Abdul Majid, Zanariah, Phang, Pei See, Suleiman, Mohamed
Format: Article
Language:English
English
Published: Science Publications 2011
Online Access:http://psasir.upm.edu.my/id/eprint/24816/1/Solving%20directly%20two%20point%20non.pdf
http://psasir.upm.edu.my/id/eprint/24816/
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spelling my.upm.eprints.248162015-10-21T03:10:25Z http://psasir.upm.edu.my/id/eprint/24816/ Solving directly two point non-linear boundary value problems using direct Adams Moulton method. Abdul Majid, Zanariah Phang, Pei See Suleiman, Mohamed Problem statement: In this study, a direct method of Adams Moulton type was developed for solving non linear two point Boundary Value Problems (BVPs) directly. Most of the existence researches involving BVPs will reduced the problem to a system of first order Ordinary Differential Equations (ODEs). This approach is very well established but it obviously will enlarge the systems of first order equations. However, the direct method in this research will solved the second order BVPs directly without reducing it to first order ODEs. Approach: Lagrange interpolation polynomial was applied in the derivation of the proposed method. The method was implemented using constant step size via shooting technique in order to determine the approximated solutions. The shooting technique will employ the Newton’s method for checking the convergent of the guessing values for the next iteration. Results: Numerical results confirmed that the direct method gave better accuracy and converged faster compared to the existing method. Conclusion: The proposed direct method is suitable for solving two point non linear boundary value problems. Science Publications 2011 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/24816/1/Solving%20directly%20two%20point%20non.pdf Abdul Majid, Zanariah and Phang, Pei See and Suleiman, Mohamed (2011) Solving directly two point non-linear boundary value problems using direct Adams Moulton method. Journal of Mathematics and Statistics, 7 (2). pp. 124-128. ISSN 1549-3644 http://www.thescipub.com/ English
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
English
description Problem statement: In this study, a direct method of Adams Moulton type was developed for solving non linear two point Boundary Value Problems (BVPs) directly. Most of the existence researches involving BVPs will reduced the problem to a system of first order Ordinary Differential Equations (ODEs). This approach is very well established but it obviously will enlarge the systems of first order equations. However, the direct method in this research will solved the second order BVPs directly without reducing it to first order ODEs. Approach: Lagrange interpolation polynomial was applied in the derivation of the proposed method. The method was implemented using constant step size via shooting technique in order to determine the approximated solutions. The shooting technique will employ the Newton’s method for checking the convergent of the guessing values for the next iteration. Results: Numerical results confirmed that the direct method gave better accuracy and converged faster compared to the existing method. Conclusion: The proposed direct method is suitable for solving two point non linear boundary value problems.
format Article
author Abdul Majid, Zanariah
Phang, Pei See
Suleiman, Mohamed
spellingShingle Abdul Majid, Zanariah
Phang, Pei See
Suleiman, Mohamed
Solving directly two point non-linear boundary value problems using direct Adams Moulton method.
author_facet Abdul Majid, Zanariah
Phang, Pei See
Suleiman, Mohamed
author_sort Abdul Majid, Zanariah
title Solving directly two point non-linear boundary value problems using direct Adams Moulton method.
title_short Solving directly two point non-linear boundary value problems using direct Adams Moulton method.
title_full Solving directly two point non-linear boundary value problems using direct Adams Moulton method.
title_fullStr Solving directly two point non-linear boundary value problems using direct Adams Moulton method.
title_full_unstemmed Solving directly two point non-linear boundary value problems using direct Adams Moulton method.
title_sort solving directly two point non-linear boundary value problems using direct adams moulton method.
publisher Science Publications
publishDate 2011
url http://psasir.upm.edu.my/id/eprint/24816/1/Solving%20directly%20two%20point%20non.pdf
http://psasir.upm.edu.my/id/eprint/24816/
http://www.thescipub.com/
_version_ 1643828474060734464
score 13.211869

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