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

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.

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URL: https://www.mdpi.com/2073-8994/15/6/1166

Abstract

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.

Item Type:	Article
Keyword:	Cubic B-spline, Two-point boundary value problems, Ordinary differential equation, Linear system, Error analysis
Subjects:	Q Science > QA Mathematics > QA1-939 Mathematics
Department:	FACULTY > Faculty of Computing and Informatics
Depositing User:	SITI AZIZAH BINTI IDRIS -
Date Deposited:	29 Feb 2024 08:51
Last Modified:	29 Feb 2024 08:51
URI:	https://eprints.ums.edu.my/id/eprint/38395

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