Abstract: A class of characteristic difference method with moving mesh is presented for one-dimensional nonlinear convection-dominated diffusion equations.This method can adaptively adjust the computational mesh according to the gradient of the solutions.Compared with the uniform mesh method,the method in this paper has higher computational efficiency for convection-dominated diffusion equations.

Key words: one-dimensional nonlinear convection-dominated diffusion equation, characteristic difference scheme with moving mesh, maximum norm error estimate