Numerical study of self-adjoint singularly perturbed two-point boundary value problems using collocation method with error estimation

Numerical study of self-adjoint singularly perturbed two-point boundary value problems using collocation method with error estimation

A numerical treatment for self-adjoint singularly perturbed second-order two-point boundary value problems using trigonometric quintic B-splines is presented, which depend on different engineering applications. The method is found to have a truncation error of O(h6) and converges to the exact soluti...

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Main Authors: Khalid K. Ali, A.R. Hadhoud, M.A. Shaalan
Format: Article
Language:English
Published: Elsevier 2018-09-01
Series:Journal of Ocean Engineering and Science
Online Access:http://www.sciencedirect.com/science/article/pii/S2468013318300652
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spelling doaj-d41a1bad433941e3946485c7c99914652020-11-24T23:39:28ZengElsevierJournal of Ocean Engineering and Science2468-01332018-09-0133237243Numerical study of self-adjoint singularly perturbed two-point boundary value problems using collocation method with error estimationKhalid K. Ali0A.R. Hadhoud1M.A. Shaalan2Faculty of Science, Al-Azhar University, Cairo, EgyptFaculty of Science, Menoufia University, Shebeen El-Koom, EgyptCorresponding author.; Higher Technological Institute, 10th of Ramadan City, EgyptA numerical treatment for self-adjoint singularly perturbed second-order two-point boundary value problems using trigonometric quintic B-splines is presented, which depend on different engineering applications. The method is found to have a truncation error of O(h6) and converges to the exact solution at O(h4). The numerical examples show that our method is very effective and the maximum absolute error is acceptable. Keywords: Self-adjoint singularly-perturbation problems, Two-point boundary value problems, Trigonometric quintic B-spline collocation method, MSC: 41A15, 65M70, 65M12, 65L11http://www.sciencedirect.com/science/article/pii/S2468013318300652
collection DOAJ
language English
format Article
sources DOAJ
author Khalid K. Ali
A.R. Hadhoud
M.A. Shaalan
spellingShingle Khalid K. Ali
A.R. Hadhoud
M.A. Shaalan
Numerical study of self-adjoint singularly perturbed two-point boundary value problems using collocation method with error estimation
Journal of Ocean Engineering and Science
author_facet Khalid K. Ali
A.R. Hadhoud
M.A. Shaalan
author_sort Khalid K. Ali
title Numerical study of self-adjoint singularly perturbed two-point boundary value problems using collocation method with error estimation
title_short Numerical study of self-adjoint singularly perturbed two-point boundary value problems using collocation method with error estimation
title_full Numerical study of self-adjoint singularly perturbed two-point boundary value problems using collocation method with error estimation
title_fullStr Numerical study of self-adjoint singularly perturbed two-point boundary value problems using collocation method with error estimation
title_full_unstemmed Numerical study of self-adjoint singularly perturbed two-point boundary value problems using collocation method with error estimation
title_sort numerical study of self-adjoint singularly perturbed two-point boundary value problems using collocation method with error estimation
publisher Elsevier
series Journal of Ocean Engineering and Science
issn 2468-0133
publishDate 2018-09-01
description A numerical treatment for self-adjoint singularly perturbed second-order two-point boundary value problems using trigonometric quintic B-splines is presented, which depend on different engineering applications. The method is found to have a truncation error of O(h6) and converges to the exact solution at O(h4). The numerical examples show that our method is very effective and the maximum absolute error is acceptable. Keywords: Self-adjoint singularly-perturbation problems, Two-point boundary value problems, Trigonometric quintic B-spline collocation method, MSC: 41A15, 65M70, 65M12, 65L11
url http://www.sciencedirect.com/science/article/pii/S2468013318300652
work_keys_str_mv AT khalidkali numericalstudyofselfadjointsingularlyperturbedtwopointboundaryvalueproblemsusingcollocationmethodwitherrorestimation
AT arhadhoud numericalstudyofselfadjointsingularlyperturbedtwopointboundaryvalueproblemsusingcollocationmethodwitherrorestimation
AT mashaalan numericalstudyofselfadjointsingularlyperturbedtwopointboundaryvalueproblemsusingcollocationmethodwitherrorestimation
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