Local artifical boundary condition in time domain is based on concept of travelingwave. It cannot simulate zero-frequency component(evanescent motion) generally.

To reach the ground state, physicists had to cool their beams to nearly absolute zero. They also had to make the quanta as large as possible by making a beam stiffer to increase its frequency.

For discrete convolution equation set, generally, people use Fourier transform method to solve. But in some positions, zero frequency will lose.