H. Justine and Jumat Sulaiman (2016) Application of conjugate gradient method with cubic nonpolynomial spline scheme for solving twopoint boundary value problems. Global Journal of Engineering and Technology Review, 1 (1). pp. 8592. ISSN 01282905

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Abstract
Objective  Conjugate Gradient (CG) method is used to solve twopoint boundary value problems together with nonpolynomial spline approach at cubic degree. Methodology/Technique  To develop a system of linear equations in a matrix form, cubic nonpolynomial splines are used to descretize the twopoint 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 twopoint boundary valueproblems at different degree of nonpolynomial splines only, then the present paper aims to look into method which is best used with the cubic nonpolynomial 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 nonpolynomial spline give the best approximation to the solution of twopoint boundary value problems compared to the approximation shown by Successive Over Relaxation (SOR) method and GaussSeidel (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.
Item Type:  Article 

Keyword:  Cubic NonPolynomial Solution, TwoPoint Boundary Value Problems, Conjugate Gradient, Successive Over Relaxation, GaussSeidel 
Subjects:  Q Science > QA Mathematics 
Department:  FACULTY > Faculty of Science and Natural Resources 
Depositing User:  MUNIRA BINTI MARASAN  
Date Deposited:  28 Feb 2018 14:50 
Last Modified:  28 Feb 2018 14:50 
URI:  https://eprints.ums.edu.my/id/eprint/19010 
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