对差分法时程积分的反思

Rethinking to Finite Difference Time-Step Integrations

以往偏微分方程时间步的数值积分主要由有限差分法来执行，然而当时间步长较大时会引起数值不稳定性。本文给出的单点精细积分法导出的显式积分格式可证明是无条件稳定的。就扩散方程与对流─扩散方程作出了本文方法与差分法导出的格式之间的对比。数值例题也表明了单点积分法的优越性。

The numerical time step integrations of PDEs are mainly carried out by the finite difference method to date. However,when the step becomes longer,it causes the problem of numerical instability.The explieit integration schemes derived by the single point precise intcgration method given in this paper are proved unconditionally stable.Compaxisons between the schemes derived by the finite difference method and the schemes by the method imployed in the present paper are made for diffusion and conveetive-diffusion equations.Numerical exam- ples show the superiority of the single point integration method.