The resolution of the systems of differential equations using backward differentiation formula method

The resolution of the systems of differential equations

\(\begin{equation}\label{PC} \left\{ \begin{array}{ll} \dot{\mathscr{Y}}(t)=\mathscr{A}\mathscr{Y}(t)+\mathscr{B}, \ \ \ t\in[t_{0},t_f], & \hbox{} \\ \mathscr{Y}(t_0)=\mathscr{Y}_0.& \hbox{} \end{array} \right. \end{equation}\)

using backward differentiation formula method.

 Inputs :     \(\mathscr{A}\)          : size matrix  (n,n).
                  \(\mathscr{B}\)          : size matrix  (n,s).

                  \(\mathscr{Y}_0\)          : size matrix  (n,s).
                  \(t_0, t_f\)      : temps.

 Output:     Y(1,:)    : solution \(\mathscr{Y}_{1,1}(t)\) of the systems of differential equation.

   Author                 :  LAKHLIFA SADEK.

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

  Last modification     :  10/08/2019.

From the test, this method was found to be faster than the normal method known in Matlab (ode23s) in terms of time to calculate the approximate solution.