A High Accuracy Compact Difference on Non-uniform Grid for 2D Convection Diffusion Reaction Equation

By use of the method of dimension reduction, the two-dimensional convection diffusion reaction equation is firstly divided into the sum of two one-dimensional convection diffusion reaction equations. Based on the Taylor progression on non-uniform grid, a high accuracy compact difference for one-dimensional convection diffusion reaction equation is proposed. Finally, we combine the two compact differences for one-dimensional convection diffusion reaction equation to get the high accuracy compact difference for two-dimensional convection diffusion reaction equation. The numerical experiment shows that the present scheme are much more accuracy than that in uniform grid with the same number of grid points.