Folks:I am a newbie with very little knowledge of finance, so please bear with me if this has been covered before:While reading thru Wilmott ( Option Pricing (1993)), I couldnt help but wonder why he uses PSOR(Projected Successive Overrelaxation) for solving the tridiagonal system obtained after discretization of the Crank Nicholson method. I mean why not just use the Thomas Algorithm to solve the tridiagonal system, and then impose the constraint (projection) as a separate step. Since Thomas is very efficient (almost the operation count of explicit schemes) wouldnt this be the way to go ?Or is there some reason that the constraint has to be part of the solution of the matrix system and cannot be imposed separately ? I am thinking that perhaps if it is applied separately it will switch on and off repeatedly ?Any and all comments much appreciated.Manatee

Manatee,Not being a mathematician, and thus not knowing the algorithm, could you give us some pseudo code?g

In an explicit scheme, e.g. a simple binomial tree, one has the luxury to apply the constraint after averaging the previously calculated nodes because the only boundary condition is the payoff at expiration. In an implicit scheme, e.g. Crank-Nicolson, one must average AND apply the constraint at the same time because of contributions from the upper and lower boundaries.I think this very error (not using PSOR with an implicit solver) is made in Hull's book, in the section on numerics. I'm not certain how much of an error this is in practice.

Manatee,using Thomas and then applying the constraint loses the quadratic convergence of CN.Q