  A numerical method is developed for calculating the real time Green's
functions of very large sparse Hamiltonian matrices, which exploits the
numerical solution of the inhomogeneous time-dependent Schroedinger equation.
The method has a clear-cut structure reflecting the most naive definition of
the Green's functions, and is very suitable to parallel and vector
supercomputers. The effectiveness of the method is illustrated by applying it
to simple lattice models. An application of this method to condensed matter
physics will be found in H. Tanaka, Phys. PRB 57, 2168 (1998).
