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== ADI for parabolic equations ==
Historically, the ADI method was developed to solve the 2D diffusion equation on a square ___domain using finite differences.<ref name=":0" /> Unlike ADI for matrix equations, ADI for parabolic equations does not require the selection of shift parameters, since the shift appearing in each iteration is determined by parameters such as the timestep, diffusion coefficient, and grid spacing. The connection to ADI on matrix equations can be observed when one considers the action of the ADI iteration on the system at steady state.
=== Example: 2D diffusion equation ===
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