Hi Edouard,The meshless method is quite cute as an idea, but it doesn't really work in practice. For one thing, nobody uses it in the industry. But one can say the same about FEM (or about wavelets for that matter). The main weakness of the meshless method is that the radial basis function method of interpolation doesn't really work. Sure, you'll find some body of research that claims it actually works, but one thing is to show it works in some cases, quite another to build a robust method that works for a wide class of useful functions. What's the problem with RBF ? Several: 1. in order to interpolate some function you need to solve a large system of equations2. that system becomes more unstable if you use more basis functions3. that means that in practice nobody uses the RBF with more than about 1000 basis functions. In Daniel's book he mentions one result where the author uses 121 basis functions and gets results that are favorable compared to FD. Who would use FD with only 121 points? If I use FD I'm free to use 10000 points; but RBF doesn't work in that case anymore, so the comparison result wouldn't support the author's conclusion ... 4. there is a claim that RBF's are dimension blind. And herein lies their big promise. You would seem to get the best of FD and Monte Carlo in the same package. Unfortunately things are different on paper and in reality. Any decent Monte Carlo scheme needs at least 10000 paths to be worth anything. But this is way beyond the number of points where RBF's are stable. 5. besides, where do you pick the collocation points? you would need to run a MC, which is perfectly fine, except that there is a slight problem: you would get different points at each point in time. Which is again fine, except everything that was written in the literature so far doesn't cover this case. It's still ok, it's not a biggie to implement it yourself, only that now you don't have the Method of Lines anymore; since you change the collocation points, you need to redo the interpolation at each point in time, which means you have to solve that large linear system 6. one of the biggest problems with RBF is that they are not adaptive. Or rather they are, but not in a computationally efficient way. For example, say you realize you need to get more samples in a certain region. You need to resolve that large system again. There is currently no locally adaptive RBF methodology. If you can come up with one, you hit the jackpot; the applications would go far beyond math finance. 7. back to RBF's being dimension blind. They aren't that blind. In particular if you change the unit in one dimension, you change the radial basis functions (because you change the "circles" of the geometry). That means they are not scale invariant. FD are not scale invariant either, but then again, they don't promise to break the curse of dimensionality. Monte Carlo on the other hand is completely scale agnostic. Now this is a fundamental question that none of the proponents of RBF's have bothered to address: how do you choose the units in each dimension? I'll stop here. This is my 2 cents, if anybody had a better experience with RBF's, please share. Best,V.