On Accuracy of Alternating Direction Implicit Methods for Parabolic Equations

We study accuracy of alternating direction implicit (ADI) methods for parabolic equations. The original ADI method applied to parabolic equations is a perturbation of the Crank-Nicolson di erence equation and has second-order accuracy both in space and time. The perturbation error is on the same order as the discretization error, in terms of mathematical description. However, we often observe in simulation that the truncation error is one order larger than the discretization error when the solution is moderately or highly oscillatory. This paper presents the observation and strategies recovering the accuracy of the Crank-Nicolson di erence equation.