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.

SCM finite difference method for solving inviscid subsonic, transonic and supersonic flow over spherical cone is presented. This method is based on the mathematical theory of characteristics.In the SCM approach these coefficients are split according to the sign of the chara-oteristic slopes. The split coefficients are multiplied by appropriate one-sided. F orwardiffe-rences are associated with negative characteristic stopes, while baokward diflerchces are associated with positive slope values.In the SCM technique the governing Euler equations are solved by a secondorder accurate finit difference elgori thm in a predictor-corrector sequence. To maintain Secondorder spatial accuracy for the one-sided derivatives associated with the split coefficients the discretization formulas alternate between two-point and three -point approximation.The numerical example of the blunt spherecones have been worked in this paper and compared with Conventional finite difference to demonstrate good accuracy of SCM in rate mesh.