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.

中文翻译：

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Sylvester矩阵微分方程鲁棒仿真的迭代算法

本文提出了一种新的有效伪谱逼近来求解Sylvester和Lyapunov矩阵微分方程。使用Chebyshev基导数运算矩阵的性质将主方程式转换为矩阵方程式。之后，检查迭代算法以求解所获得的方程。同时，对提出的方法进行了误差分析，揭示了收敛的频谱速率。为了说明所提出框架的有效性，给出了几个数值示例。