含源项非定常对流扩散方程的高精度紧致隐式差分方法

A high-order compact implicit difference method for the unsteady convection-diffusion equation with source term

提出了数值求解含源项非定常对流扩散方程的一种高精度紧致隐式差分方法,其空间为四阶精度,时间为二阶精度。由于每一时间层上只用到了三个网格点,所以差分方程为三对角型的,可采用追赶法进行求解。数值实验结果验证了本文方法的精确性和可靠性。

A High-Order compact implicit difference method is proposed for solving the one-dimensional unsteady convection-diffusion equation with source term. The method is fourth order in space and second order in time. Because only three points are used at each time level, the difference equation can be solved by the method of forward elimination and backward substitution. Numerical results prove the efficiency and dependability.