We report a method to efficiently describe wavepacket evolution in an unbound system for arbitrary large times. The problem is difficult using current methods due to the spatial expansion of wavepacket with time. Our approach circumvents this difficulty by solving the time development operator in a small interaction region outside of which the wavepacket evolution is described analytically. The formulation is illustrated by comparing numerical results of wavepacket propagation in a Morse potential with results using the pseudo-spectral Chebyshev expansion method.