Application of conjugate gradient method with cubic non-polynomial spline scheme for solving two-point boundary value problems

Objective - Conjugate Gradient (CG) method is used to solve two-point boundary value problems together with non-polynomial spline approach at cubic degree. Methodology/Technique - To develop a system of linear equations in a matrix form, cubic non-polynomial splines are used to descretize the two...

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Main Authors: H. Justine, Jumat Sulaiman
Format: Article
Language:English
Published: Global Academy of Training & Research (GATR) Enterprise. 2016
Subjects:
Online Access:https://eprints.ums.edu.my/id/eprint/19010/1/Application%20of%20conjugate%20gradient%20method%20with%20cubic%20non.pdf
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author H. Justine
Jumat Sulaiman
author_facet H. Justine
Jumat Sulaiman
author_sort H. Justine
collection UMS
description Objective - Conjugate Gradient (CG) method is used to solve two-point boundary value problems together with non-polynomial spline approach at cubic degree. Methodology/Technique - To develop a system of linear equations in a matrix form, cubic non-polynomial splines are used to descretize the two-point boundary value problems so that the approximation can be computed using CG method. Since many previous researchers attempt to obtain the approximate solution for the two-point boundary value-problems at different degree of non-polynomial splines only, then the present paper aims to look into method which is best used with the cubic non-polynomial splines in order to approximate the solution of these problem Findings - According to the performance analysis results in term of iterations number, execution time and maximum absolute error at different grid sizes, the application of CG method together with the cubic non-polynomial spline give the best approximation to the solution of two-point boundary value problems compared to the approximation shown by Successive Over Relaxation (SOR) method and Gauss-Seidel (GS) method. Novelty - the performance of CG iterative method is found to be superior in respect of iterations number, execution time and maximum absolute error on various grid sizes.
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spelling ums.eprints-190102018-02-28T06:50:08Z https://eprints.ums.edu.my/id/eprint/19010/ Application of conjugate gradient method with cubic non-polynomial spline scheme for solving two-point boundary value problems H. Justine Jumat Sulaiman QA Mathematics Objective - Conjugate Gradient (CG) method is used to solve two-point boundary value problems together with non-polynomial spline approach at cubic degree. Methodology/Technique - To develop a system of linear equations in a matrix form, cubic non-polynomial splines are used to descretize the two-point boundary value problems so that the approximation can be computed using CG method. Since many previous researchers attempt to obtain the approximate solution for the two-point boundary value-problems at different degree of non-polynomial splines only, then the present paper aims to look into method which is best used with the cubic non-polynomial splines in order to approximate the solution of these problem Findings - According to the performance analysis results in term of iterations number, execution time and maximum absolute error at different grid sizes, the application of CG method together with the cubic non-polynomial spline give the best approximation to the solution of two-point boundary value problems compared to the approximation shown by Successive Over Relaxation (SOR) method and Gauss-Seidel (GS) method. Novelty - the performance of CG iterative method is found to be superior in respect of iterations number, execution time and maximum absolute error on various grid sizes. Global Academy of Training & Research (GATR) Enterprise. 2016 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/19010/1/Application%20of%20conjugate%20gradient%20method%20with%20cubic%20non.pdf H. Justine and Jumat Sulaiman (2016) Application of conjugate gradient method with cubic non-polynomial spline scheme for solving two-point boundary value problems. Global Journal of Engineering and Technology Review, 1 (1). pp. 85-92. ISSN 0128-2905 http://www.gjetr.org/pdf/PDF-GJETR%201(1)%20Dec.%202016/12.%20H.%20Justine-GJETR%201(1)%202016.pdf
spellingShingle QA Mathematics
H. Justine
Jumat Sulaiman
Application of conjugate gradient method with cubic non-polynomial spline scheme for solving two-point boundary value problems
title Application of conjugate gradient method with cubic non-polynomial spline scheme for solving two-point boundary value problems
title_full Application of conjugate gradient method with cubic non-polynomial spline scheme for solving two-point boundary value problems
title_fullStr Application of conjugate gradient method with cubic non-polynomial spline scheme for solving two-point boundary value problems
title_full_unstemmed Application of conjugate gradient method with cubic non-polynomial spline scheme for solving two-point boundary value problems
title_short Application of conjugate gradient method with cubic non-polynomial spline scheme for solving two-point boundary value problems
title_sort application of conjugate gradient method with cubic non polynomial spline scheme for solving two point boundary value problems
topic QA Mathematics
url https://eprints.ums.edu.my/id/eprint/19010/1/Application%20of%20conjugate%20gradient%20method%20with%20cubic%20non.pdf
work_keys_str_mv AT hjustine applicationofconjugategradientmethodwithcubicnonpolynomialsplineschemeforsolvingtwopointboundaryvalueproblems
AT jumatsulaiman applicationofconjugategradientmethodwithcubicnonpolynomialsplineschemeforsolvingtwopointboundaryvalueproblems