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.

In the paper, an improvement λ-type scheme is proposed based on characteristics idea in order to overcome the strong dispersive effect or nonlinear instability of the original λ-scheme. Furthermore, the numerical simulations of two models of ID computational fluid dynamics problems by using the improvement scheme are given, and the numerical results are satisfactory.