Spatial bounds of integration of a PDE using DifferentialEquations

Hi there,
I am solving a PDE over a large domain discretizing with finite difference the RHS and using DifferentialEquations.jl to integrate the ODE system in time. Is there anyway in which I can limit the integration to only nodes in the grid comprised in a certain range. I would basically limit the integration in time to only part of my spatial domain, say comprised between indices l,m (1-d case) or (l,m,n,o) for the 2d case.
This indices might change with times and are successfully computed through callback functions. However, I don’t know how to tell the solver to limit integration only to this part of the spatial domain. Any ideas? Thanks!

Just make the ODE the interior

Thanks for the answer! To be sure I understand, you are suggesting to redefine the ODEproblem with only the interior points?

Yes, that’s generally the easiest way. ModelingToolkit.jl and MethodOfLines.jl do this automatically, but if you’re writing the code by hand then you should do this too.