Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration

In previous studies, the effectiveness of the second-order quarter-sweep finite difference approximation equations has been shown in solving singularly perturbed boundary value problems. In this paper, however, we investigate the application of the fourth-order quarter-sweep finite difference approx...

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Main Authors:	Sulaiman, Jumat, Hasan, Mohammad Khatim, Othman, Mohamed, Abdul Karim, Samsul Ariffin
Format:	Conference or Workshop Item
Language:	English
Published:	AIP Publishing LLC 2012
Online Access:	http://psasir.upm.edu.my/id/eprint/57617/ http://psasir.upm.edu.my/id/eprint/57617/ http://psasir.upm.edu.my/id/eprint/57617/1/Fourth%20order%20solutions%20of%20singularly%20perturbed%20boundary%20value%20problems%20by%20quarter-sweep%20iteration.pdf

id	upm-57617
recordtype	eprints
spelling	upm-576172017-10-24T07:50:01Z http://psasir.upm.edu.my/id/eprint/57617/ Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration Sulaiman, Jumat Hasan, Mohammad Khatim Othman, Mohamed Abdul Karim, Samsul Ariffin In previous studies, the effectiveness of the second-order quarter-sweep finite difference approximation equations has been shown in solving singularly perturbed boundary value problems. In this paper, however, we investigate the application of the fourth-order quarter-sweep finite difference approximation equation based on the fourth-order standard central difference scheme. To solve the problems numerically, discretization of the singularly perturbed problems via second-order and fourth-order finite difference schemes is proposed to form the corresponding system of linear algebraic equations. For comparison purpose, we also discuss on how to derive the basic formulation and implementation for the family of Successive Over-Relaxation (SOR) iterative methods such as FSSOR, HSSOR and QSSOR in solving the corresponding linear systems generated from the fourth-order discretization schemes based on full, half- and quarter-sweep cases. Some numerical tests were conducted to show that the accuracy of fourth-order finite difference schemes via the corresponding GS methods is more accurate than second-order schemes. AIP Publishing LLC 2012 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57617/1/Fourth%20order%20solutions%20of%20singularly%20perturbed%20boundary%20value%20problems%20by%20quarter-sweep%20iteration.pdf Sulaiman, Jumat and Hasan, Mohammad Khatim and Othman, Mohamed and Abdul Karim, Samsul Ariffin (2012) Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration. In: 20th National Symposium on Mathematical Sciences (SKSM20), 18-20 Dec. 2012, Palm Garden Hotel, Putrajaya, Malaysia. (pp. 275-284). 10.1063/1.4801134
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Putra Malaysia
building	UPM Institutional Repository
collection	Online Access
language	English
description	In previous studies, the effectiveness of the second-order quarter-sweep finite difference approximation equations has been shown in solving singularly perturbed boundary value problems. In this paper, however, we investigate the application of the fourth-order quarter-sweep finite difference approximation equation based on the fourth-order standard central difference scheme. To solve the problems numerically, discretization of the singularly perturbed problems via second-order and fourth-order finite difference schemes is proposed to form the corresponding system of linear algebraic equations. For comparison purpose, we also discuss on how to derive the basic formulation and implementation for the family of Successive Over-Relaxation (SOR) iterative methods such as FSSOR, HSSOR and QSSOR in solving the corresponding linear systems generated from the fourth-order discretization schemes based on full, half- and quarter-sweep cases. Some numerical tests were conducted to show that the accuracy of fourth-order finite difference schemes via the corresponding GS methods is more accurate than second-order schemes.
format	Conference or Workshop Item
author	Sulaiman, Jumat Hasan, Mohammad Khatim Othman, Mohamed Abdul Karim, Samsul Ariffin
spellingShingle	Sulaiman, Jumat Hasan, Mohammad Khatim Othman, Mohamed Abdul Karim, Samsul Ariffin Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration
author_facet	Sulaiman, Jumat Hasan, Mohammad Khatim Othman, Mohamed Abdul Karim, Samsul Ariffin
author_sort	Sulaiman, Jumat
title	Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration
title_short	Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration
title_full	Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration
title_fullStr	Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration
title_full_unstemmed	Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration
title_sort	fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration
publisher	AIP Publishing LLC
publishDate	2012
url	http://psasir.upm.edu.my/id/eprint/57617/ http://psasir.upm.edu.my/id/eprint/57617/ http://psasir.upm.edu.my/id/eprint/57617/1/Fourth%20order%20solutions%20of%20singularly%20perturbed%20boundary%20value%20problems%20by%20quarter-sweep%20iteration.pdf
first_indexed	2018-09-07T18:55:52Z
last_indexed	2018-09-07T18:55:52Z
_version_	1610976123251851264

Fourth order solutions of singularly perturbed boundary value problems by quarter-sweep iteration

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