在此篇論文中，我們主要探討 2x2 的退化雙曲方程對於黎曼問題的數值計算。此方程源自於愛因斯坦場方程的原型，我們將以一維非線性守恆態去建構簡易的退化雙曲方程，並用數值計算找出近似解。本研究中所使用的數值方法有Godunov's Method和Euler's Method，藉由不同的初始值來觀測我們的數值結果發散與否。最後歸納出來的結果及數據都可幫助我們在退化雙曲方程的問題上有更多的了解。 In this thesis, we study the numerical computation for the Riemann problem of the 2x2 degenerate hyperbolic system of conservation laws. The equations we consider is an one-dimensional nonlinear balance laws, which can be considered as a warm-up system of shock wave model for the Einstein's field equations in spherical symmetric space-time. We will give a numerical method, which is called the Godunov method, to construct the approximate solutions for the Riemann problem. By giving several initial conditions for our numerical computation, we observer the consequences of existence or blow-up of solutions for Cauchy problem to the degenerate hyperbolic system.
