A Comparison of Three Methods Based on the Bernstein Operational Matrix for Solving Differential and Integral Equations
GAZI UNIVERSITY JOURNAL OF SCIENCE, cilt.38, sa.4, ss.2046-2063, 2025 (ESCI, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 38 Sayı: 4
- Basım Tarihi: 2025
- Doi Numarası: 10.35378/gujs.1619802
- Dergi Adı: GAZI UNIVERSITY JOURNAL OF SCIENCE
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.2046-2063
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Gazi Üniversitesi Adresli: Evet
Özet
This article investigates combining traditional methods for solving differential equations with Aboodh integral transformation and the Bernstein method. This approach offers a new perspective in solving various differential and integral equations. The solution approach obtained from the combination of Bernstein polynomials and integral transformations stands out in terms of theoretical and practical implications. This method can be applied to various examples of differential equations, and its practical applicability can be evaluated through studies conducted using programming languages. The error between the exact solution and the proposed method's approximate solution has been calculated. We compare the numerical results of the Aboodh-Bernstein, Laplace-Bernstein, and Sumudu-Bernstein methods.