Summary: A high-order alternating direction implicit (ADI) method for computations of unsteady convection-diffusion equations is proposed. By using fourth-order Padé schemes for the spatial derivatives, the present scheme is fourth-order accurate in space and second-order accurate in time. The solution procedure consists of a number of tridiagonal matrix operations which make the computation cost effective. The method is unconditionally stable, and shows higher accuracy and better phase and amplitude error characteristics than the standard second-order ADI method by D. W. Peaceman
and H. H. Rachford jun.
[J. Soc. Ind. Appl. Math. 3, 28–41 (1955; Zbl 0067.35801
)] and the fourth-order ADI scheme of S. Karaa
and J. Zhang
[J. Comput. Phys. 198, 1–9 (2004; Zbl 1053.65067