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本文给出一种用有限差分法求解高空大气成分数密度的方法。基本方程是二阶非线性偏微分方程组,采用隐式差分格式,为了节省存贮量和避免求解大型非线性方程组的复杂性,对于每一积分时间步,采用分组线化Gauss—Seidel迭代法,以其迭代过程的收敛值来近似非线性和隐式差分式。在本文给定的边界条件下,将边界条件的差分式联立于内点的差分方程组中,构造了一种三对角线矩阵的追赶算法。以本算法编制的计算程序对于五种大气成分,在几种不同状态条件下进行试算,和现有的观测资料比较,结果是令人满意的。
In this paper, a method for solving the compositional density of the upper atmosphere using finite difference method is given. The underlying equations are second-order nonlinear partial differential equations, using an implicit difference scheme. To save storage and avoid the complexity of solving large-scale nonlinear equations, for each integration time step, a Gaussian-Seidel iteration Method approximates the nonlinear and implicit difference equations based on the convergence of the iterative process. Under the boundary conditions given in this paper, the differential equation of the boundary conditions is set in the system of difference equations of the interior point, and a catch-up algorithm of tridiagonal matrices is constructed. The calculation program compiled by this algorithm is satisfactory for five kinds of atmospheric components under several different conditions and compared with the existing observation data.