Appropriate scaling after taking derivatives

[sciml]

Appropriate scaling after taking derivatives

[ChrisRackauckas]

Yes. It's missing the constant. Check the notes on discretizations of the Heat Equation: that operator should have /dx^2 in there. I think that's for the user to handle though, unless you want to add a spot for a scalar (which could be useful in other ways, like diffusion needs D*dt/dx^2)

[dextorious]

The D in the diffusion equation must be left up to the user, obviously, but insofar as we automatically generate finite difference representations of PDEs, we should scale them appropriately, in my opinion. That means dividing any approximation of an nth-order derivative by dx^n.