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.

A new finite difference scheme is proposed for radial symmetric nonlinear Schrödinger equation. This is a scheme of three levels which needn't to iterate. Thus, the new scheme requires less CPU time. Convergence and stability of the new scheme are proved. By means of numerical computation, it is followed that the new scheme is efficient.