Abstract: This paper presents a compact alternate direct implicit difference scheme of high accuracy for solving the two-dimensional constant coefficient reaction-diffusion equations.Firstly,a compact difference scheme is derived by using operator method and an error estimate of O(τ2+h4)is given in detail.Secondly,a compact ADI difference scheme is presented by introducing a variable of intermediate value.Thirdly,the stability and convergence of the ADI scheme are achieved by using Fourier method.Finally,a numercial ...