The resolution of the differential Sylvester matrix equations usin gbackward differentiation formula method

The resolution of the differential Sylvester matrix equations

\(\begin{equation}\label{1} \left\{ \begin{array}{ll} \dot{X}(t)=AX(t)+X(t)B+C,& \hbox{} \\ X(t_{0})=X_{0}, & t\in[t_{0},T_{f}], \end{array} \right. \end{equation}\) où    \(A\in\mathbb{R}^{n\times n}, B\in\mathbb{R}^{p\times p}, C\in\mathbb{R}^{n\times p},\)

usin gbackward differentiation formula method

 Author                 :  LAKHLIFA SADEK.

  E-mail: lakhlifasdek@gmail.com; sadek.l@ucd.ac.ma