Abstract: 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.

Key words: Convection, Difiusion, Analytics, Stability