Can't imagine why ADI w/o mixed derivatives wouldn't work...what was the problem, you remember?A while collaborated with Alex Levin on a HW2-type PDE (no correlation); Long story short, unable to get ADI to work and we went for Marchuck's 1-2-2-1 dimensional splitting method. Maybe someone at some stage could try it for Heston.
http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf
Interesting paper, but what is E in (2.2)? Comes out of thin air, or have I missed something? Also, it's not clear how it would be applied with mixed derivatives present as in Heston. But either way, if someone wants to try different efficient schemes, it should be on other models that don't have semi-analytical solutions (as we did in the paper), which are arguably better than Heston.