Truncation error of the ADI method

[hermano]

Dear,

Can someone tell me with certainty if the truncation error of the general ADI method is of seconder order in time and space?

 

[Filip Larsen]

If memory serves me right, I think the Douglas ADI has second order spatial truncation error, but only first order temporal error at the sample points. I see in my old thesis that the temporal truncation apparently only can be considered second order at the midpoints between spatial sample points, but I'm not sure what sense that makes for a spatial multi-dimensional solution.

I know this is not "certainty" as you ask for, but you may want to consider that the temporal truncation error in your application of ADI could be first order only.