The resolution of the systems of differential equations using backward differentiation formula method dY(t)/dt = AY + B (*) Y(t0) = Y0. Input: : A : size matrix (n,n). B : size matrix (n,s). Y0 : size matrix (n,s). tf , t0 : temps. Output: Y(1,:) : solution Y_{1,1}(t) of (*) . Author : LAKHLIFA SADEK. Last modification : 10/08/2019 E-mail: lakhlifasdek@gmail.com; sadek.l@ucd.ac.ma 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. test close all clear all clc n=16; s=2; t0=0;tf=1; A=randn(n); B=randn(n,s); B=B/norm(B,'fro'); Y0=randn(n,s); disp('BDF method') tic [t2,Y] = BDFSDE(A,B,Y0,t0,tf); toc odefun = @(t,y) fonction(t,y,A,B); disp('ode23s') tic [T,y1] = ode23s(odefun,[t0 tf],Y0); toc hold on plot(t2,Y(1,:)) plot(T,y1(:,1)) xlabel('Temps') ylabel('The solution Y_{1,1}') title(['n=',num2str(n),', s=',num2str(s)]) legend('BDF method','ode23s') hold off