What is E in Chapter 9 - Adaptive Time Stepping?

[bradcarman]

I'm assuming $\text{E}$ from here is the residual function value, i.e. $g(u_i) = \text{E}$. Is this correct? And is it scalarized or in vector form?

Does the relative tolerance $\tau_r$ ever take into account the scaling of $u$? For example, a hydraulic problem that has pressure values in the order of 1e7 and valve displacements in the order of 1e-6. If $\text{E}$ is in vector form then is $q$ computed as norm( E ./ (tau_r*u + tau_a) ) ?

[ChrisRackauckas]

No, E is an error estimate between two different methods. It's method-dependent, but generally the difference between two different stepping techniques at different orders.

If is in vector form then is computed as norm( E ./ (tau_r*u + tau_a) ) ?

Yes https://docs.sciml.ai/DiffEqDocs/stable/extras/timestepping/

I'm going to write some notes for the new course that develop this a lot more.