Abstract: On the steady convection-diffusion equation,a new method is developed for construction of high-order compact finitedifference scheme.First,the two-dimensional equation are transformed into the two equations,which are similar to the form of onedimensional equation,and are subsequently discretized by utilizing compact difference formula proposed for the one-dimensional equation in[6].Then,a compact difference scheme that is O(h⁴+h²k²+k⁴) on the nine-point 2-D stencil for the steady convectiondiffusion equation is established.Finally,numerical example is given to illustrate the present method.

Key words: convection-diffusion equation, high-order accuracy, compact scheme, steady state