Example logic for auxiliary variables in DIRK stepper

[jmbigman]

Previously all variables were treated as if they have explicit time dependence and were updated by summing over stage derivatives. If $u$ was the time-dependent variable and $\zeta$ an auxiliary variable they would both be replaced by

$$\partial_t u \leftarrow k_u\quad,\quad u \leftarrow g_u + ahk_u$$ $$\partial_t \zeta \leftarrow k_\zeta\quad,\quad \zeta\leftarrow g_\zeta + ahk_\zeta$$

Now the lack of a time derivative on $\zeta$ is identified and they are instead replaced by

$$\partial_t u \leftarrow k_u\quad,\quad u \leftarrow g_u + ahk_u$$ $$\zeta\leftarrow k_\zeta$$

The non-linear solve is still done over $k_u$ , $k_\zeta$ but $k_\zeta$ now represents the value of the auxiliary variable $\zeta$ instead of its stage derivative which is not needed. Only the time-dependent $g_u$ is updated by summing over stage derivatives $k_u$.

[jmbigman]

Introduced based on discussion #116

[ScottMacLachlan]

I'll review this later on, but can you first check on the lint failure that's preventing CI from running fully?