Alternating-direction implicit method: Difference between revisions

Revision as of 03:14, 10 March 2011

Revision as of 17:45, 31 May 2011

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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 implicitlyexplicitly and the next with the ''y''-derivative taken implicitly,

: <math>{u_{ij}^{n+1/2}-u_{ij}^n\over \Delta t/2} =