Journal
ADVANCES IN DIFFERENCE EQUATIONS
Volume 2020, Issue 1, Pages -Publisher
SPRINGER
DOI: 10.1186/s13662-020-02757-z
Keywords
Sylvester matrix differential equations; Iterative algorithm; Chebyshev polynomials; Coupled linear matrix equations; Collocation method
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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.
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