(6)Numerical study of self-adjoint singularly perturbed two-point boundary value problems using collocation method with error estimation
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Khalid K. Alia, A.R. Hadhoudb, M.A. Shaalanc,*
a Faculty of Science, Al-Azhar University, Cairo, Egypt
b Faculty of Science, Menoufia University, Shebeen El-Koom, Egypt
c Higher Technological Institute, 10th of Ramadan City, Egypt
Received 1 May 2018; received in revised form 26 July 2018; accepted 27 July 2018
Available online 1 August 2018
Abstract
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.
© 2018 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. ( http://creativecommons.org/licenses/by-nc-nd/4.0/)
Keywords: Self-adjoint singularly-perturbation problems; Two-point boundary value problems; Trigonometric quintic B-spline collocation method.