A new group explicit scheme for solving Burgers equation is constructed by the conservative Samarskii scheme. The linear stability of this method is discussed. Some numerical examples are given which illustrated that the present method is more suitable than Evans's method for solving Burgers equation with a large Reynolds number.

In this paper, Four classes of three level semi-explieit difference Schemes for solving the dispersive equation u₁=au_xxx are developed. The orders of the local truncation error are all O(τ²+h²+(τ²)/(h³)) or O(τ²+h⁴+((τ)/(h))²+τh). The schemes of Ⅰ,Ⅱ and when paramater α≤1, the schemes of Ⅲ. Ⅳ are all shown to be unconditionally stable by the Von Neumann criterion for stability. And thev can be calculated explicitly when necessary boundary value are given.