Before revision: We are interested in approximating the numerical solution {\bf U}(t) of the large dimensional nonlinear matrix differential equation \bf U(t) = A { \bf  \bf U}(t) + {\bf U}(t) B { \bf  + {\cal F}({\bf U},t) + G , with appropriate starting and boundary conditions, and t \in [0, T_f].
After revision: We are interested in approximating the numerical solution {\bf U}(t) of the large dimensional semilinear matrix differential equation \bf U(t) = A { \bf \bf U}(t) + {\bf U}(t) B { \bf + {\cal F}({\bf U},t) + G , with appropriate starting and boundary conditions, and t \in [0, T_f].