In this paper a fourth-oder dissipation exponent-type scheme of one-sided approximation for solving convective diffusion equations is derived. The theoretical results on the stability and the properties of one-sided approximation and fourth-oder dissipation of this scheme have been presented. The relations of this scheme and finite analytic method is also obtained. Some numerical examples are qiven.

In this paper a kind of Finite Analytic Methods is derived and applied on convection-diffusion equations. These qualities proved are existence, uniqueness, absolute stability and convergence of solutions of finite analytic scheme of linear equations, so are existence, uniqueness and generalized weak stabability of solutions of finite analytic scheme of Burger's equation. Numerical experiments show that the finite analytic scheme is very effective, especially numerical solutions arc not oscillating.