Abstract
The Peaceman–Rachford alternating direction implicit (ADI) method is considered for the time-integration of a class of wave-type equations for linear, isotropic materials on a tensorial domain, e.g., a cuboid in 3D or a rectangle in 2D. This method is known to be unconditionally stable and of conventional order two. So far, it has been applied to specific problems and is mostly combined with finite differences in space, where it can be implemented at the cost of an explicit method.
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