Abstract: 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.

Key words: dispersion equation, explicit correction scheme with two parameters, arbitrary stability