QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems

Two-point boundary value problems are commonly used as a numerical test in developing an efficient numerical method. Several researchers studied the application of a cubic non-polynomial spline method to solve the two-point boundary value problems. A preliminary study found that a cubic non-polynomi...

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Main Authors: A Sunarto, P Agarwal, Jackel Vui Lung Chew, H Justine, Jumat Sulaiman
Format: Proceedings
Language:English
English
Published: IOP Publishing Ltd. 2021
Subjects:
Online Access:https://eprints.ums.edu.my/id/eprint/32519/1/QSSOR%20and%20cubic%20non-polynomial%20spline%20method%20for%20the%20solution%20of%20two-point%20boundary%20value%20problems.ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/32519/2/QSSOR%20and%20cubic%20non-polynomial%20spline%20method%20for%20the%20solution%20of%20two-point%20boundary%20value%20problems.pdf
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author A Sunarto
P Agarwal
Jackel Vui Lung Chew
H Justine
Jumat Sulaiman
author_facet A Sunarto
P Agarwal
Jackel Vui Lung Chew
H Justine
Jumat Sulaiman
author_sort A Sunarto
collection UMS
description Two-point boundary value problems are commonly used as a numerical test in developing an efficient numerical method. Several researchers studied the application of a cubic non-polynomial spline method to solve the two-point boundary value problems. A preliminary study found that a cubic non-polynomial spline method is better than a standard finite difference method in terms of the accuracy of the solution. Therefore, this paper aims to examine the performance of a cubic non-polynomial spline method through the combination with the full-, half-, and quarter-sweep iterations. The performance was evaluated in terms of the number of iterations, the execution time and the maximum absolute error by varying the iterations from full-, half- to quarter-sweep. A successive over-relaxation iterative method was implemented to solve the large and sparse linear system. The numerical result showed that the newly derived QSSOR method, based on a cubic non-polynomial spline, performed better than the tested FSSOR and HSSOR methods.
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spelling ums.eprints-325192022-05-03T13:14:55Z https://eprints.ums.edu.my/id/eprint/32519/ QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems A Sunarto P Agarwal Jackel Vui Lung Chew H Justine Jumat Sulaiman QA101-(145) Elementary mathematics. Arithmetic Two-point boundary value problems are commonly used as a numerical test in developing an efficient numerical method. Several researchers studied the application of a cubic non-polynomial spline method to solve the two-point boundary value problems. A preliminary study found that a cubic non-polynomial spline method is better than a standard finite difference method in terms of the accuracy of the solution. Therefore, this paper aims to examine the performance of a cubic non-polynomial spline method through the combination with the full-, half-, and quarter-sweep iterations. The performance was evaluated in terms of the number of iterations, the execution time and the maximum absolute error by varying the iterations from full-, half- to quarter-sweep. A successive over-relaxation iterative method was implemented to solve the large and sparse linear system. The numerical result showed that the newly derived QSSOR method, based on a cubic non-polynomial spline, performed better than the tested FSSOR and HSSOR methods. IOP Publishing Ltd. 2021 Proceedings PeerReviewed text en https://eprints.ums.edu.my/id/eprint/32519/1/QSSOR%20and%20cubic%20non-polynomial%20spline%20method%20for%20the%20solution%20of%20two-point%20boundary%20value%20problems.ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/32519/2/QSSOR%20and%20cubic%20non-polynomial%20spline%20method%20for%20the%20solution%20of%20two-point%20boundary%20value%20problems.pdf A Sunarto and P Agarwal and Jackel Vui Lung Chew and H Justine and Jumat Sulaiman (2021) QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems. https://iopscience.iop.org/article/10.1088/1742-6596/2000/1/012007
spellingShingle QA101-(145) Elementary mathematics. Arithmetic
A Sunarto
P Agarwal
Jackel Vui Lung Chew
H Justine
Jumat Sulaiman
QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems
title QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems
title_full QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems
title_fullStr QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems
title_full_unstemmed QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems
title_short QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems
title_sort qssor and cubic non polynomial spline method for the solution of two point boundary value problems
topic QA101-(145) Elementary mathematics. Arithmetic
url https://eprints.ums.edu.my/id/eprint/32519/1/QSSOR%20and%20cubic%20non-polynomial%20spline%20method%20for%20the%20solution%20of%20two-point%20boundary%20value%20problems.ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/32519/2/QSSOR%20and%20cubic%20non-polynomial%20spline%20method%20for%20the%20solution%20of%20two-point%20boundary%20value%20problems.pdf
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AT jackelvuilungchew qssorandcubicnonpolynomialsplinemethodforthesolutionoftwopointboundaryvalueproblems
AT hjustine qssorandcubicnonpolynomialsplinemethodforthesolutionoftwopointboundaryvalueproblems
AT jumatsulaiman qssorandcubicnonpolynomialsplinemethodforthesolutionoftwopointboundaryvalueproblems