High Order Alternating Direction Implicit Methods for Wave Equations

Unconditionally stable alternating direction implicit (ADI) methods are useful for wave propagation problems, if the medium contains spatial features that are much smaller than the typical wavelength. In this project, we propose some new high order unconditionally stable ADI methods for the wave equation. Stability properties of the new methods will be studied. The efficiency and accuracy of the new method ares will be illustrated by numerical examples.