Journal of Computational Physics
High order difference schemes for unsteady one-dimensional diffusion-convection problems
Journal of Computational Physics
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Summation by parts operators for finite difference approximations of second derivatives
Journal of Computational Physics
A new time-space domain high-order finite-difference method for the acoustic wave equation
Journal of Computational Physics
A high-order exponential scheme for solving 1D unsteady convection-diffusion equations
Journal of Computational and Applied Mathematics
Relaxation method for unsteady convection-diffusion equations
Computers & Mathematics with Applications
Journal of Computational Physics
A new family of (5,5)CC-4OC schemes applicable for unsteady Navier-Stokes equations
Journal of Computational Physics
An efficient fourth-order low dispersive finite difference scheme for a 2-D acoustic wave equation
Journal of Computational and Applied Mathematics
Hi-index | 31.46 |
A high-order alternating direction implicit (ADI) method for computations of unsteady convection-diffusion equations is proposed. By using fourth-order Pade 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].