A kind of three level explicit difference scheme with two parameters m and θ,including four knots in the middle level is presented, for the dispersion equation u_r=au_xxx.When the m and θ satisfy a certain ralation, the stability condition is |γ|≤(m+1)/(4(m-1))(|m|>1).Thus, as m goes sufficiently neer to 1, an arbitrary stability condition can be obtained, and the order of the truncation error is not changed. The numerical example verifies the results of the theoretical analysis.

A kind of the methods with high accurate of the generalized Galerkin method-inteprotation corrective method and error corrctive method are proposed in this paper.