Symmetric Bernstein Polynomial Approach for the System of Volterra Integral Equations on Arbitrary Interval and Its Convergence Analysis
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 converg...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English English |
| Published: |
MDPI AG
2022
|
| Subjects: | |
| Online Access: | https://eprints.ums.edu.my/id/eprint/34323/1/Abstract.pdf https://eprints.ums.edu.my/id/eprint/34323/2/Full%20text.pdf |
| _version_ | 1796911574068232192 |
|---|---|
| author | Samsul Ariffin Abdul Karim Faheem Khan Muhammad Basit |
| author_facet | Samsul Ariffin Abdul Karim Faheem Khan Muhammad Basit |
| author_sort | Samsul Ariffin Abdul Karim |
| collection | UMS |
| description | 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. |
| first_indexed | 2024-03-06T03:20:40Z |
| format | Article |
| id | ums.eprints-34323 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:20:40Z |
| publishDate | 2022 |
| publisher | MDPI AG |
| record_format | dspace |
| spelling | ums.eprints-343232022-09-27T03:53:39Z https://eprints.ums.edu.my/id/eprint/34323/ Symmetric Bernstein Polynomial Approach for the System of Volterra Integral Equations on Arbitrary Interval and Its Convergence Analysis Samsul Ariffin Abdul Karim Faheem Khan Muhammad Basit QA1-939 Mathematics 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. MDPI AG 2022 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/34323/1/Abstract.pdf text en https://eprints.ums.edu.my/id/eprint/34323/2/Full%20text.pdf 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 https://www.mdpi.com/2073-8994/14/7/1343?type=check_update&version=1 https://doi.org/10.3390/sym14071343 https://doi.org/10.3390/sym14071343 |
| spellingShingle | QA1-939 Mathematics Samsul Ariffin Abdul Karim Faheem Khan Muhammad Basit Symmetric Bernstein Polynomial Approach for the System of Volterra Integral Equations on Arbitrary Interval and Its Convergence Analysis |
| title | Symmetric Bernstein Polynomial Approach for the System of Volterra Integral Equations on Arbitrary Interval and Its Convergence Analysis |
| title_full | Symmetric Bernstein Polynomial Approach for the System of Volterra Integral Equations on Arbitrary Interval and Its Convergence Analysis |
| title_fullStr | Symmetric Bernstein Polynomial Approach for the System of Volterra Integral Equations on Arbitrary Interval and Its Convergence Analysis |
| title_full_unstemmed | Symmetric Bernstein Polynomial Approach for the System of Volterra Integral Equations on Arbitrary Interval and Its Convergence Analysis |
| title_short | Symmetric Bernstein Polynomial Approach for the System of Volterra Integral Equations on Arbitrary Interval and Its Convergence Analysis |
| title_sort | symmetric bernstein polynomial approach for the system of volterra integral equations on arbitrary interval and its convergence analysis |
| topic | QA1-939 Mathematics |
| url | https://eprints.ums.edu.my/id/eprint/34323/1/Abstract.pdf https://eprints.ums.edu.my/id/eprint/34323/2/Full%20text.pdf |
| work_keys_str_mv | AT samsulariffinabdulkarim symmetricbernsteinpolynomialapproachforthesystemofvolterraintegralequationsonarbitraryintervalanditsconvergenceanalysis AT faheemkhan symmetricbernsteinpolynomialapproachforthesystemofvolterraintegralequationsonarbitraryintervalanditsconvergenceanalysis AT muhammadbasit symmetricbernsteinpolynomialapproachforthesystemofvolterraintegralequationsonarbitraryintervalanditsconvergenceanalysis |