A higher order alternating direction implicit (ADI) method with completed Richardson extrapolation is proposed for solving unsteady two dimensional convection-diffusion equations. The method has sixth-order accuracy in space and fourth-order accuracy in time. Completed Richardson extrapolation is used to improve the accuracy of the solution obtained from the high-order ADI method in spatial and temporal domains simultaneously. Stability analysis is given to show the influence of Richardson extrapolation on the unconditionally stable ADI method. Numerical experiments are conducted to test its high accuracy and to compare it with Karaa-Zhang's high-order ADI method.
Dai, R., Zhang, J., & Wang, Y. (2016). Higher order ADI method with completed Richardson extrapolation for solving unsteady convection-diffusion equations. Computers and Mathematics with Applications, 71(1), 431–442. https://doi.org/10.1016/j.camwa.2015.12.007