Symmetric Bernstein Polynomial Approach for the System of Volterra Integral Equations on Arbitrary Interval and Its Convergence Analysis

Samsul Ariffin Abdul Karim and Faheem Khan and Muhammad Basit (2022) Symmetric Bernstein Polynomial Approach for the System of Volterra Integral Equations on Arbitrary Interval and Its Convergence Analysis. Symmetry, 14. pp. 1-14. ISSN 2073-8994

	Text Abstract.pdf Download (39kB)
	Text Full text.pdf Restricted to Registered users only Download (340kB) \| Request a copy

URL: https://www.mdpi.com/2073-8994/14/7/1343?type=chec...

Abstract

In this paper, a new numerical technique is introduced to find the solution of the system of Volterra integral equations based on symmetric Bernstein polynomials. The use of Bernstein polynomials to find the numerical solutions of differential and integral equations increased due to its fast convergence. Here, the numerical solution of the system of Volterra integral equations on any finite interval [m, n] is obtained by replacing the unknown functions with the generalized Bernstein basis functions. The proposed technique converts the given system of equations into the system of algebraic equations which can be solved by using any standard rule. Further, Hyers–Ulam stability criteria are used to check the stability of the given technique. The comparison between exact and numerical solution for the distinct nodes is demonstrated to show its fast convergence.

Item Type:	Article
Keyword:	Bernstein basis function , Discretization , Convergence analysis , Physical model , Stability analysis
Subjects:	Q Science > QA Mathematics > QA1-939 Mathematics
Department:	FACULTY > Faculty of Computing and Informatics
Depositing User:	SITI AZIZAH BINTI IDRIS -
Date Deposited:	27 Sep 2022 11:53
Last Modified:	27 Sep 2022 11:53
URI:	https://eprints.ums.edu.my/id/eprint/34323

Actions (login required)

View Item