Abstract: In the paper, based on the Modified PDE of finite difference schemes, a general and systematical research and analysis on the remainder effects of finite difference schemes are advanced. The dissipasion relationship and the dispersion relationship are defined. By the use of the two relationships, the stability, the dissipation, the dispersion and the group velocity of finite difference schemes are all disccused.

Key words: finite difference scheme, Modified PDE, remainder effect, group velocity