KaydedilenlerDerginizi ekleyin

Dergiler / Mathematical Sciences and Applications E-Notes / 2021 / Cilt: 9 - Sayı: 1

Bernstein Operator Approach for Solving Linear Differential Equations

Neşe İŞLER ACAR
Sayfa
28–35
Yayın Tarihi
2021-03-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Some applications are also revealed to show how the procedure can be performed for the problems.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this study, an alternative numerical method having regard to the Bernstein operator is generated for approximate solutions of linear differential equations in the most general form under the initial and boundary conditions.
📊
Temel Bulgular & Veri:In this study, an alternative numerical method having regard to the Bernstein operator is generated for approximate solutions of linear differential equations in the most general form under the initial and boundary conditions.
💡
Sonuç & Katkı:Some applications are also revealed to show how the procedure can be performed for the problems.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Bernstein polynomials · Linear differential equations · Operator numerical method

Abstract

In this study, an alternative numerical method having regard to the Bernstein operator is generated for approximate solutions of linear differential equations in the most general form under the initial and boundary conditions. Some applications are also revealed to show how the procedure can be performed for the problems.

🔖

Bu Makaleye Atıf Yap

ACAR, N. İ. (2021). Bernstein Operator Approach for Solving Linear Differential Equations. Mathematical Sciences and Applications E-Notes, Cilt: 9 - Sayı: 1, 28–35. https://ajindex.com/articles/690686

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (15)

  1. Akyüz-Daşcıoğlu, A., Işler, N.: Bernstein Collocation Method for Solving Nonlinear Differential Equations. Mathematical and Computational Applications. 18 (3), 293-300 (2013)
  2. Akyüz-Daşcıoğlu, A., Acar Işler, N.: Bernstein Collocation Method for Solving Linear Differential Equations. Gazi University Journal of Science. 26 (4), 527-534 (2013)
  3. Bataineh, A., Isik, O., Aloushoush, N., Shawagfeh, N.: Bernstein Operational Matrix with Error Analysis for Solving High Order Delay Differential Equations. Int. J. Appl. Comput. Math. 3, 1749-1762 (2017)
  4. Bhatta, D.D., Bhatti, M.I.: Numerical Solution of KdV equation using modified Bernstein polynomials. Applied Mathematics and Computation. 174 (2), 1255-1268 (2006)
  5. Bhattacharya, S., Mandal, B.N.: Use of Bernstein polynomials in numerical solutions of Volterra integral equations. Applied Mathematical Sciences. 2, 1773-1787 (2008)
  6. Bhattacharya, S., Mandal, B.N.: Numerical solution of a singular integro-differential equation. Applied Mathematics and Computation. 195, 346-350 (2008)
  7. Bhatti, M.I., Bracken, P.: Solutions of differential equations in a Bernstein polynomial basis. Journal of Computational and Applied Mathematics. 205 (2), 172-280 (2007)
  8. Bernstein, S.: Démonstration du théorème de Weierstrass Fondeé sur le calcul des probabilités. Commun. Soc. Math. Kharkow. 13 (2), 1-2 (1912)
  9. Büyükyazıcı, İ: Approximation by Stancu-Chlodowsky polynomials. Computers and Mathematics with Applications. 59 (1), 274-282 (2010)
  10. Doha, E.H., Bhrawy, A.H., Saker, M.A.: On the derivatives of Bernstein polynomials: An application for the solution of high even-order differential equations. Boundary Value Problems. 2011, 1-16 (2011)
  11. Doha, E.H., Bhrawy, A.H., Saker, M.A.: Integrals of Bernstein polynomials: An application for the solution of high even-order differential equations. Applied Mathematics Letters. 24, 559-565 (2011)
  12. El-Gamel, M.: A comparison between the Sinc-Galerkin and the modified decomposition methods for solving two-point boundary-value problems. Journal of Computational Pysics. 223 (1), 369-383 (2007)
  13. Faheem, K., Ghulam, M., Muhammad, O., Haziqa, K.: Numerical approach based on Bernstein polynomials for solving mixed Volterra-Fredholm integral equations. AIP Advances. 7, 1-14 (2017).
  14. Farouki, R.T., Rajan, V.T.: Algorithms for polynomials in Bernstein form. Computer Aided Geometric Design. 5, 1-26 (1988)
  15. Framma