在本文中，我們考慮球對稱空間時間可壓縮歐拉方程泊松。方程，代表品質和重力吸引潛在的物理量動量守恆，可以寫成一個混合型的3x3部分迪系統的差動或平衡法與全球源2X2雙曲系統。我們展示的方程為品質守恆，歐拉 - 泊松下方程可以轉化為平衡定律與本地源純3x3的雙曲系統。歐拉 - 泊松方程黎曼問題，這是在初始邊值問題廣義Glimm方案的構建塊的通用解決方案，提供不嚴的類型相關聯的同質守恆定律弱解和擾動項解決了疊加通過與些線性雙曲系統與這種鬆懈的解決方案。最後，我們提供LAX-Wendroff無限迪方法和辛普森的數值積分為某些初始邊值問題全球資源。提供了幾種類型的初始和邊界資料的數值類比。;In this thesis, we consider the compressible Euler-Poisson equations in spherically symmetric space-times. The equations, which represent the conservation of mass and momentum of physical quantity with attracting gravity potential, can be written as a mixed-type $3\times 3$ partial differential systems or an $2\times 2$ hyperbolic systems of balance laws with $global$ source. We show under the equation for the conservation of mass, Euler-Poisson equations can be transformed into a pure $3\times 3$ hyperbolic system of balance laws with $local$ source. The generalized solutions to the Riemann problem of Euler-Poisson equations, which is the building block of generalized Glimm scheme for the initial-boundary value problem, are provided as the superposition of Lax′s type weak solutions of associated homogeneous conservation laws and the perturbation terms solved by some linearized hyperbolic system with coefficients related to such Lax′s solution. Finally, we provide Lax-Wendroff finite difference method and Simpson′s numerical integration to the global sources for some initial-boundary value problems. Numerical simulations are provided for several types of initial and boundary data.
