QuoteOriginally posted by: AlanQuoteOriginally posted by: CuchulainnI have reduced an elliptic PDE(x,y) to canonical form PDE(v,w) (no mixed derivatives
) . So far, so good.The question is how to 'translate;' the BC(x,y) to BC(v,w).Ex. the Heston PDE BC at v = 0 is fine. But how to formulate the BC in (v,w) world? My concern is you get a modified PDE on a non-rectanguar domain(?) We probably get a rhombus thing.// the transformation is linear; v = ax - y. w = bxMy recollection is that you can transform away the correlation term in the Heston operatorwithout altering the state space from R x R+On the other hand, for some other finance operators, it doesn't necessarily work so nicely or at all.I think there are two issues here:1. Reduction of PDE/quadratic form to canonical form by a homogeneous linear change of variables. This is OK, bug but the new domain is a rhombus.2. Approximating the boundary condition on the transformed boundary. This aspect could to be either or painful depending on the particular problem. We have to find neighbouring nodes on the boundary and corresponding BCs.Life has been made easy with 1 and difficult with 2.