关键词: 对流, 扩散, 差分, 高精度, 稳定性

Abstract: Convection-diffusion equation mainly contains two terms—convection and diffusion. In the numerical calculation，
central difference scheme，with excellent physical properties and high accuracy is often employed to discretize the diffusion
term，which has been fully able to meet the requirements for most practical problems，but somewhat difficult to handle convective
term. If handled improperly，it will produce numerical oscillation or numerical dispersion，which will bring difficulties
to the numerical calculation. To avoid handling the convection term directly，we change the convection-diffusion equation into
a diffusion equation with an exponential transformation. According to fourth-order compact difference scheme，three types
of special high-precision differential equation schemes are established firstly，then the process of the establishment of onedimensional
unsteady convection diffusion equation with source term is derived with stability analysis. The scheme has high
precision and absolute stability. In the end，the numerical result shows the effectiveness of the scheme.

Key words: convection, diffusion, difference scheme, high-precision, stability