I am working on a PDE model, the subject has been modeled with ODE's before. The articles usually have a bifurcation diagram, and to be able to validate my model, I want to compare my work with the work of others.
My equation have a time derivative a space derivative, similar to the following:
$$ \partial _t X (y,t)= \nabla ^2 X (y,t) + X (y, t) ^2 $$
So I want to write it as
$$ \partial _t X (t)= X (t) ^2 $$
and perform the bifurcation analysis and say "Hmm it looks reasonable" if it would be logical to use this comparison. I thought maybe it can be used (or it has been used) as a back of the envelope validation.
- Is it reasonable to do this?
- Is there any way for comparison between pde models and ode models?
I googled to see if anyone mentions about this but haven't seen anything similar. So I couldn't come to a conclusion. Any ideas?