2维带色散4阶扩散方程的高精度紧致格式OA北大核心CSTPCD

In this paper,a high-order compact scheme for one-dimensional and two-dimensional fourth-order diffusion equation with dispersion was proposed.Firstly,the two-dimensional problem was transformed into two one-dimensional fourth-order diffusion equations with dispersion in the x and y directions by using the local one-dimensional method.Secondly,the third-order and fourth-order spatial derivatives were discretized by the sixth-order compact scheme respectively,and the fourth-order diffusion equation with dispersion was transformed into a system of ordinary differential equations,then the L-stable Simpson method for solving ordinary differential equations was used to construct the numerical scheme with third-order accuracy in time and sixth-order accuracy in space,and it was proved that the scheme was absolutely stable.Numerical experiments and comparisons verified the effectiveness of the proposed scheme.