In this paper, an essentially conservative scheme is constructed. The scheme can not be written in the usual conservative form but it can be proven that the limit solutions of this scheme are the weak solutions of hyperbolic conservation laws. It is shown that the scheme is second order accuracy, total variation bounded, stable in L¹ norm and in L^∞ norm, and satisfies the entropy condition.

In this paper, a high resolution finite difference scheme based on artificial viscosity is introduced. The scheme can obtain almost as good results as total variation diminishing schemes can obtain, but the time consuming of the scheme is much less than that of total variation diminishing schemes.

In this paper, an universial program for the simulation of elastic waves were developed by adding some treatment routines of artificial boundary conditions to the famous program of SAP5 and its micro-computer version SAP5P. The numerical results presented show that the program simulated the propagation of elastic waves in the uniformly elastic media quite well.

In the paper,a improved form of the fully conservative finite difference schemes, established by Samarski and Popov(2), for gas dynamics equations in Lagrangian form is presented. To check the quality of the improved scheme, two problems are computed. The first test problem is the typical shock tube problem used by Sod(3). Then the flow fields in a large Shock tube of variable cross sectional ares(4) is computed. The numerical results show that the improved scheme is more efficient than Samarski and Popov's schemes. Meanwhile the nonphysical oscillation and the numerical dissipation also are reduced.