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A numerical approach based on Bernstein collocation method: Application to differential Lyapunov and Sylvester matrix equations

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Date

2023

Author

Sadek, Lakhlifa
Bataineh, Ahmad Sami
Işık, Osman Raşit
Alaoui, Hamad Talibi
Hashim, Ishak

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Citation

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

Abstract

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.

Source

Mathematics and Computers in Simulation

Volume

212

URI

https://doi.org/10.1016/j.matcom.2023.05.011
https://hdl.handle.net/20.500.12809/10759

Collections

  • Matematik ve Fen Bilimleri Eğitimi Bölümü Koleksiyonu [131]
  • Scopus İndeksli Yayınlar Koleksiyonu [6219]
  • WoS İndeksli Yayınlar Koleksiyonu [6466]



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