Abstract: A two-level implicit scheme for Burgers equations is shown,whose truncation error is O(τ²+h²) (where τ is time step and h is space step).An alternating segment method is proposed and its unconditional linear stability is proved.The new method is free from nonphysical oscillations and suitable for parallel computers.A numerical example shows that the method has good applicability and high accuracy, in particular, it is more accurate when diffusion coefficient is small.

Key words: Burgers equation, parallel computing, alternating segment method, stabilty