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

Lakhlifa Sadek, Ahmad Sami Bataineh, Osman Rasit Isik, Hamad Talibi Alaoui and Ishak Hashim

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 212, issue C, 475-488

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.

Keywords: Bernstein polynomials (BP); Sylvester matrix differential equation (Sy-MDE); Operational matrix of derivative; Ly-MSE; Bernstein collocation (BC) method (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:212:y:2023:i:c:p:475-488

DOI: 10.1016/j.matcom.2023.05.011

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