非定态对流扩散方程的二层显式差分格式研究

Study of two level explicit difference schemes for unsteady convection-diffusion problems

综合分析了十多种一维非定态线性和拟线性对流扩散方程的二层显式差分格式，指出它们的包含关系和等价关系。简便地给出了全部差分格式的局部截断误差，稳定性条件和正性条件。指出这些格式均属局部指数格式的局部近似格式，其中部分格式近似较好，此外，本文构造了指数分段逼近格式。

More than ten explicit two level difference schemes for one dimensional unsteady linear and quasi -- linear convection -- diffusion problems are synthetically analysed. Their involving relation and equivalence relation are revealed. The local truncation error,stable conditions and positivity condition,for all these difference schemes areeasily given. It is shown that these schemes are approximate schemes to local exponential scheme. Some of them are effective. In addition,a piecewise approximate scheme forlocal exponential scheme is presented.