A high-order Padé ADI method for unsteady convection–diffusion equations

A high-order alternating direction implicit (ADI) method for computations of unsteady convection–diffusion equations is proposed. By using fourth-order Padé schemes for 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 [D.W. Peaceman, H.H. Rachford Jr., The numerical solution of parabolic and elliptic differential equations, Journal of the Society of Industrial and Applied Mathematics 3 (1959) 28–41] and the fourth-order ADI scheme of Karaa and Zhang [High order ADI method for solving unsteady convection–diffusion problem, Journal of Computational Physics 198 (2004) 1–9].