  In the present paper, we consider large-scale continuous-time differential
matrix Riccati equations having low rank right-hand sides. These equations are
generally solved by Backward Differentiation Formula (BDF) or Rosenbrock
methods leading to a large scale algebraic Riccati equation which has to be
solved for each timestep. We propose a new approach, based on the reduction of
the problem dimension prior to integration. We project the initial problem onto
an extended block Krylov subspace and obtain a low-dimentional differential
algebraic Riccati equation. The latter matrix differential problem is then
solved by Backward Differentiation Formula (BDF) method and the obtained
solution is used to reconstruct an approximate solution of the original
problem. We give some theoretical results and a simple expression of the
residual allowing the implementation of a stop test in order to limit the
dimension of the projection space. Some numerical experiments will be given.
