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→The method: it is an alternating method between explicit and implicit |
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A disadvantage of the Crank–Nicolson method is that the matrix in the above equation is [[band matrix|banded]] with a band width that is generally quite large. This makes the solution of the equation quite costly.
The idea behind the ADI method is to split the finite difference equations into two, one with the ''x''-derivative taken
: <math>{u_{ij}^{n+1/2}-u_{ij}^n\over \Delta t/2} =
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