Two High-precision Methods Of Hyperbolic Conservation Laws Equations Comparative Study

WENO methods is based on the ENO methods by Liu, Osher, who in 1994 proposed a new type of high-precision, high-resolution format. WENO format not only inherits the good features of ENO format, that is interrupted in the vicinity to maintain good resolution capability, but also through the introduction of changes in the weighting factors to form a smooth solution of the truncation error of areas the number had further increased, the format stability, there has been further strengthened.The research of the discontinuous Galerkin methods has been an important issue of numerical computation. Due to the development of scientists, the discontinuous Galerkin method shows its unprecedented efficiency in many aspects and plays an important part in solving those problems that contain discontinuities. It has widely applied to hydrodynamics, gas dynamics and wave propagation. In mathematics, it is effective in solving elliptic equations, hyperbolic conservation laws and also diffusion equations.In this paper,we discuss in detail for solving hyperbolic conservation laws equations of two high-precision numerical methods, namely, WENO methods and discontinuous Galerkin methods, and show a number of typical problems numerical comparative tests, by accuracy, computing speed and the resolution of such exotic in comparison, we can get a more detailed understanding of these two methods and obtain some useful conclusions.