heat equation with variable material properties about methodoflines.jl HOT 2 CLOSED

Thank you, this has revealed 2 unknown issues, first with the nonlinear handling, second with the heuristic used to match equations to variables to be solved for - this will be important debugging fodder. I will try to get a fix in as soon as possible.

from methodoflines.jl.

@jenri I have a fix for this, check out the branch in the above pull request to see. Tests are failing as they need updating, so should already work. Hopefully this will be merged soon. This is for the auxiliary variable variant, as I realised that we have no special scheme for cases where a registered function wraps the inner derivative.

There are a few adjustments needed to your code to get this to work.
Firstly, please supply boundary conditions at either end of the domain for q.
I noticed that Dx(q(t, x_max)) ~ 0, so you just need to find one for the lower end.
Secondly, please use a solver that can use mass matricies such as Rosenbrock23().

from methodoflines.jl.