一维非定常对流扩散方程的新型差分方法

his paper is intended to construct a new kind of finite difference method to solve one dimensional unsteady convection-diffusion equation. First of all, by the base transformation, the unsteady convection-diffusion equation is converted into unsteady reaction-diffusion equation; Secondly, the difference scheme on the spatial direction is obtained by combining the reaction diffusion equation and Taylor expansion; Finally, a new finite difference method with simple form is obtained in this paper by combining vector transform, Taylor expansion and (1,1) Padé approximant. Numerical results of the two examples show that, spatial convergence order in this paper is 2-order higher than the traditional Crank-Nicolson method, and can even reach 4-order convergence with the decrease of space step; Time convergence order is 2 order, it's also better than Crank Nicolson method with the decrease of time step. The numerical results also verify that the difference scheme proposed in this paper has higher accuracy, more effective and reliable results and faster convergence speed.