Hi all,Has anybody in this forum implemented the ADI technique for solving 2-D PDEs? I could use some guidance! I am following the explanation in PWOQF and have a few queries:Page 919I'm happy with the first discretisation, where we have [ V(i,j,k) - V(i,j,k+0.5) ] / 0.5*delta_t + .... = 0 eqn 1The ifrst term here is -dV/dk which is equal to dV/dt from the definition t = T - k*delta_t However, for the second step (where the explicit and implicit schemes are reversed) this becomes: [ V(i,j,k+1) - V(i,j,k+0.5) ] / 0.5*delta_t + ... = 0 eqn 2My intuition tells me that the derivative wrt 't' in the second expression (eqn 2) is not dV/dt, but -dV/dt.... (again, because in 'reversing the time' we have t= T -k*delta_t and so dt = -dk... So how does the expression hold? Where am I going wrong? Also, on the next page, the text describes the second discretisation as an explicit scheme... Is this a typo? Should it be implicit? Thanks, Sam

Hi,I used a sort of ADI method for multi-asset binomial trees and I followed the implementation found in "implementing derivatives models", but I just diagonalized the system and then as usual.I couldn't understand what follows the diagolalization of the system with the strange (i+0.5) step...bye

Hi audetto,can you please tell me in a nutshell, what is the "ADI"-method ?Thanks a lot,Keanu

I don't know if it is exactly the ADI-method, but:if you use a linear compination of you variables you can have a system of stochastic differential equations with a digonal diffusion matrix, which is more easy to deal with.the square matrix of coefficients of the linear combination is just the transpose of the eigenvectors of the covariance matrix.I think I'm wrong because this is not the ADI method, but peraphs ADI method needs a diagonal system..., but I find diagonalization very useful even alonebyeandrea