  We propose a time-exact Krylov-subspace-based method for solving linear ODE
(ordinary differential equation) systems of the form $y'=-Ay + g(t)$, where
$y(t)$ is the unknown function. The method consists of two stages. The first
stage is an accurate polynomial approximation of the source term $g(t)$,
constructed with the help of the truncated SVD (singular value decomposition).
The second stage is a special residual-based block Krylov subspace method.
  The accuracy of the method is only restricted by the accuracy of the
polynomial approximation and by the error of the block Krylov process. Since
both errors can, in principle, be made arbitrarily small, this yields, at some
costs, a time-exact method.
