Abstract: 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.

Key words: semi-explicit difference scheme, unconditional stability dispersive equation