An iterative algorithm for robust simulation of the Sylvester matrix differential equations

Advances in Difference Equations

article

Nouri, Kazem¹  Beik, Samaneh Panjeh Ali²  Torkzadeh, Leila¹  Baleanu, Dumitru³ 

[1] Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University;National Center for Medical Education Assessment;Department of Mathematics, Faculty of Arts and Sciences, Cankaya University;Institute of Space Sciences

关键词: Sylvester matrix differential equations;    Iterative algorithm;    Chebyshev polynomials;    Coupled linear matrix equations;    Collocation method;   

DOI  :  10.1186/s13662-020-02757-z

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This paper proposes a new effective pseudo-spectral approximation to solve the Sylvester and Lyapunov matrix differential equations. The properties of the Chebyshev basis operational matrix of derivative are applied to convert the main equation to the matrix equations. Afterwards, an iterative algorithm is examined for solving the obtained equations. Also, the error analysis of the propounded method is presented, which reveals the spectral rate of convergence. To illustrate the effectiveness of the proposed framework, several numerical examples are given.

【 授权许可】

CC BY