u(t)

Define the function, $f_r:=(1-e^{-\kappa_r^\star\,t})/\kappa_r^\star, f_x=\dots, f_y=\dots$ Then the multiplications $u=Q(e^{tD}-1)D^-Q^-e_1$ can be carried out to yield

$$u= \left( \begin{array}{c} f_r \\ (f_r-f_x) q_{rr}^- \\... ..._x) + q_{xx}^-(f_r-f_x)\right) \end{array} \right) \quad .$$ (61)