基于有限差分法的一维输运方程定解问题

The fixed solutions of one-dimensional transport equation based on the finite difference method

许多物理方程的定解问题,如波动方程、输运方程等,或由于其泛定方程比较复杂,或由于边界形状比较复杂,或由于其它原因,往往不具有解析解,或者其解析解不易计算,所以要采用可行的数值解法。有限差分方法就是一种数值解法,它把表示变量连续变化关系的偏微分方程离散为有限个代数方程,然后利用电子计算机求解此线性代数方程组。

Many fixed solutions of physical equations,such as the wave equation,transport equation,etc.,because of its complex pan-setting equation,or complex boundary shape,or due to other reasons,often do not have analytical solutions,or its analytical solution is not easy to calculate,so we must use the feasible solution.Finite difference method is a numerical method,it put partial differential equations discretized into a finite number of algebraic equations,and then use the computer to solve the linear algebraic equations.