讨论了一维常系数对流扩散方程的一种数值解法.对于对流占优和扩散占优的情况,分别构造了相应的隐式差分格式,分析了截断误差、收敛和稳定性.理论分析和数值实验结果表明,该隐式差分格式有效地消除了对流主导所引起的数值振荡,控制了扩散主导引起的耗散问题,并且可以在保持差分格式的所有优点的基础上直接推广到二维问题.最后在此基础上给出了一种隐式分裂中心差分算法.“,”A numerical method of constant coefficient convection diffusion equation is studied.An implicit difference scheme is established for convective dominance and diffusion dominance respectively.The truncation error,convergence and stability of this scheme are discussed.Theoretical analysis and experimental results show that when the grid ratio is properly selected,the difference scheme is quite stable.It can be extended directly to the two-dimensional problem,and all the advantages of the difference scheme can be maintained.On this basis,an implicit split center difference algorithm is presented.