High order difference schemes for unsteady one-dimensional diffusion-convection problems
Journal of Computational Physics
High order ADI method for solving unsteady convection-diffusion problems
Journal of Computational Physics
Short note: A high-order Padé ADI method for unsteady convection-diffusion equations
Journal of Computational Physics
High-order compact exponential finite difference methods for convection-diffusion type problems
Journal of Computational Physics
A fourth-order compact ADI method for solving two-dimensional unsteady convection-diffusion problems
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
ICIC'11 Proceedings of the 7th international conference on Advanced Intelligent Computing Theories and Applications: with aspects of artificial intelligence
A high-order compact exponential scheme for the fractional convection-diffusion equation
Journal of Computational and Applied Mathematics
Hi-index | 7.30 |
In this paper, a high-order exponential (HOE) scheme is developed for the solution of the unsteady one-dimensional convection-diffusion equation. The present scheme uses the fourth-order compact exponential difference formula for the spatial discretization and the (2,2) Pade approximation for the temporal discretization. The proposed scheme achieves fourth-order accuracy in temporal and spatial variables and is unconditionally stable. Numerical experiments are carried out to demonstrate its accuracy and to compare it with analytic solutions and numerical results established by other methods in the literature. The results show that the present scheme gives highly accurate solutions for all test examples and can get excellent solutions for convection dominated problems.