Academic Journal
A numerical approach based on Bernstein collocation method: Application to differential Lyapunov and Sylvester matrix equations
| العنوان: | A numerical approach based on Bernstein collocation method: Application to differential Lyapunov and Sylvester matrix equations |
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| المؤلفون: | Sadek, Lakhlifa, Bataineh, Ahmad Sami, Işık, Osman Raşit, Alaoui, Hamad Talibi, Hashim, Ishak |
| المساهمون: | MÜ, Eğitim Fakültesi, Matematik ve Fen Bilimleri Eğitimi Bölümü, orcid:0000-0003-1401-4553, Işık, Osman Raşit |
| بيانات النشر: | Elsevier B.V. |
| سنة النشر: | 2023 |
| مصطلحات موضوعية: | Bernstein polynomials (BP), Sylvester matrix differential equation (Sy-MDE), Operational matrix of derivative, Ly-MSE, Bernstein collocation (BC) method |
| الوصف: | In this paper, we apply the Bernstein collocation method to construct the solution set of the Sylvester matrix differential equation (Sy-MDE) which involves the Lyapunov matrix differential equation. The method depends on the collocation method and Bernstein polynomials. The main advantage of the proposed method is that by using this method Sy-MDE reduces to a linear system of algebraic equations which can be solved by using an appropriate iterative method. We analyze the error and give a theorem that bounds the error. We also give the residual correction procedure to estimate the error. By using the procedure, we obtain a new approximate solution, namely a corrected Bernstein collocation solution. To illustrate how the proposed method is applied, several examples are given. Numerical experiments show the effectiveness and accuracy of the method for solving such types of Sy-MDE. |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 03784754 |
| Relation: | Mathematics and Computers in Simulation; Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı; Sadek, L., Bataineh, A. S., Isik, O. R., Alaoui, H. T., & Hashim, I. (2023). A numerical approach based on bernstein collocation method: Application to differential lyapunov and sylvester matrix equations. Mathematics and Computers in Simulation, 212, 475-488. doi:10.1016/j.matcom.2023.05.011; https://doi.org/10.1016/j.matcom.2023.05.011; https://hdl.handle.net/20.500.12809/10759; 212; 475; 488 |
| DOI: | 10.1016/j.matcom.2023.05.011 |
| الاتاحة: | https://hdl.handle.net/20.500.12809/10759 https://doi.org/10.1016/j.matcom.2023.05.011 |
| Rights: | info:eu-repo/semantics/closedAccess |
| رقم الانضمام: | edsbas.9DD0C2CD |
| قاعدة البيانات: | BASE |
| تدمد: | 03784754 |
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| DOI: | 10.1016/j.matcom.2023.05.011 |