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An Improved Symmetric Numerical Approach for Systems of Second-Order Two-Point BVPs

This study deals with the numerical solution of a class of linear systems of second-order boundary value problems (BVPs) using a new symmetric cubic B-spline method (NCBM). This is a typical cubic B-spline collocation method powered by new approximations for second-order derivatives. The flexibility...

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Main Authors: Busyra Latif, Md Yushalify Misro, Samsul Ariffin Abdul Karim, Ishak Hashim
Format: Article
Language:English
English
Published: MDPI 2023
Subjects:
QA1-939 Mathematics
Online Access:https://eprints.ums.edu.my/id/eprint/38395/1/ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/38395/2/FULL%20TEXT.pdf
https://eprints.ums.edu.my/id/eprint/38395/
https://www.mdpi.com/2073-8994/15/6/1166
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spelling my.ums.eprints.383952024-02-29T00:51:08Z https://eprints.ums.edu.my/id/eprint/38395/ An Improved Symmetric Numerical Approach for Systems of Second-Order Two-Point BVPs Busyra Latif Md Yushalify Misro Samsul Ariffin Abdul Karim Ishak Hashim QA1-939 Mathematics This study deals with the numerical solution of a class of linear systems of second-order boundary value problems (BVPs) using a new symmetric cubic B-spline method (NCBM). This is a typical cubic B-spline collocation method powered by new approximations for second-order derivatives. The flexibility and high order precision of B-spline functions allow them to approximate the answers. These functions have a symmetrical property. The new second-order approximation plays an important role in producing more accurate results up to a fifth-order accuracy. To verify the proposed method’s accuracy, it is tested on three linear systems of ordinary differential equations with multiple step sizes. The numerical findings by the present method are quite similar to the exact solutions available in the literature. We discovered that when the step size decreased, the computational errors decreased, resulting in better precision. In addition, details of maximum errors are investigated. Moreover, simple implementation and straightforward computations are the main advantages of the offered method. This method yields improved results, even if it does not require using free parameters. Thus, it can be concluded that the offered scheme is reliable and efficient. MDPI 2023 Article NonPeerReviewed text en https://eprints.ums.edu.my/id/eprint/38395/1/ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/38395/2/FULL%20TEXT.pdf Busyra Latif and Md Yushalify Misro and Samsul Ariffin Abdul Karim and Ishak Hashim (2023) An Improved Symmetric Numerical Approach for Systems of Second-Order Two-Point BVPs. Symmetry, 15. pp. 1-18. https://www.mdpi.com/2073-8994/15/6/1166
institution Universiti Malaysia Sabah
building UMS Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Sabah
content_source UMS Institutional Repository
url_provider http://eprints.ums.edu.my/
language English
English
topic QA1-939 Mathematics
spellingShingle QA1-939 Mathematics
Busyra Latif
Md Yushalify Misro
Samsul Ariffin Abdul Karim
Ishak Hashim
An Improved Symmetric Numerical Approach for Systems of Second-Order Two-Point BVPs
description This study deals with the numerical solution of a class of linear systems of second-order boundary value problems (BVPs) using a new symmetric cubic B-spline method (NCBM). This is a typical cubic B-spline collocation method powered by new approximations for second-order derivatives. The flexibility and high order precision of B-spline functions allow them to approximate the answers. These functions have a symmetrical property. The new second-order approximation plays an important role in producing more accurate results up to a fifth-order accuracy. To verify the proposed method’s accuracy, it is tested on three linear systems of ordinary differential equations with multiple step sizes. The numerical findings by the present method are quite similar to the exact solutions available in the literature. We discovered that when the step size decreased, the computational errors decreased, resulting in better precision. In addition, details of maximum errors are investigated. Moreover, simple implementation and straightforward computations are the main advantages of the offered method. This method yields improved results, even if it does not require using free parameters. Thus, it can be concluded that the offered scheme is reliable and efficient.
format Article
author Busyra Latif
Md Yushalify Misro
Samsul Ariffin Abdul Karim
Ishak Hashim
author_facet Busyra Latif
Md Yushalify Misro
Samsul Ariffin Abdul Karim
Ishak Hashim
author_sort Busyra Latif
title An Improved Symmetric Numerical Approach for Systems of Second-Order Two-Point BVPs
title_short An Improved Symmetric Numerical Approach for Systems of Second-Order Two-Point BVPs
title_full An Improved Symmetric Numerical Approach for Systems of Second-Order Two-Point BVPs
title_fullStr An Improved Symmetric Numerical Approach for Systems of Second-Order Two-Point BVPs
title_full_unstemmed An Improved Symmetric Numerical Approach for Systems of Second-Order Two-Point BVPs
title_sort improved symmetric numerical approach for systems of second-order two-point bvps
publisher MDPI
publishDate 2023
url https://eprints.ums.edu.my/id/eprint/38395/1/ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/38395/2/FULL%20TEXT.pdf
https://eprints.ums.edu.my/id/eprint/38395/
https://www.mdpi.com/2073-8994/15/6/1166
_version_ 1793154678042656768
score 13.244745

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