Abstract: When the convection-dominated Burgers equation is solved by use of the difference method, the computational accuracy of many usual difference schemes will lower.The designre-quirements of difference scheme of the non-linear convection term are presented, and some new difference schemes, which is known as follow-flow schemes, are obtained in this paper, in order to raise the computational accuracy of convection-dominated equation. The advantages of the follow-flow schemes are shown by means of some examples in this paper.

Key words: convection-dominated, Burgers equation, follow-flow scheme