本文主要对于高精度加权本质无震荡（WENO）格式进行了研究，其中主要包括了两个部分。第一部分是对于WENO格式相关的基础知识进行了一定的介绍，主要涵盖了一维的双曲守恒律方程，黎曼问题，拉格朗日插值，有限体积法，迎风格式以及Godunov方法。第二部分是对于高阶的WENO格式进行了比较。首先是对经典的WENO五阶格式进行了介绍并对其进行扩展进而引入了七阶WENO和九阶WENO格式。同时，在高阶WENO格式中加入了对WENO-JS非线性权的运用。其次，运用以WENO-JS加权的高阶WENO格式分别对不同初值的黎曼问题以及黎曼问题的变式进行了刻画，并由此得出更高阶的WENO格式对于问题解的贴合程度特别是间断点的描述精确程度要高于低阶的WENO格式的结论。

In this thesis, we study the high-order weighted essentially non-oscillatory (WENO) schemes and it mainly contains two parts. For the first part, we introduce some basic background of the WENO schemes which includes: one-dimensional hyperbolic conservation equation, Riemann problem, Lagrange-interpolation, finite volume method, upwind schemes and Godunov method. In the second part, we compare the different kinds of high-order WENO schemes. To begin with, we introduce the classical fifth-order WENO scheme and then the seventh-order WENO scheme and ninth-order WENO scheme with the use of the same order WENO-JS scheme. Furthermore, we use the WENO schemes mentioned above to solve the Riemann problems having different initial condition and their variant. Finally, we come to the conclusion that the higher order the WENO scheme is, the more precisely and more accurately we can tell about the solution and its discontinuities.