Spectral Deferred Correction

[atb1995]

Pull request to push SDC code to main. Code is in sdc.py and uses external dependency qmat to generate nodes, Q matrices, Qdelta matrices and final update weights. The code has one unified algorithm for Implicit, Explicit and IMEX SDC variants, with labelling of terms defined by the user. Both zero-to-node and node-to-node formulations available, defined when creating the time discretisation. These formulations are:

Node-to-node:
y_m^(k+1) = y_(m-1)^(k+1) + dtau_m*(F(y_(m)^(k+1)) - F(y_(m)^k)) + sum(j=1,M) s_mj*F(y_(m-1)^k)
where s_mj = q_mj - q_(m-1)j for entires q_ik in Q.

Zero-to-node:
y_m^(k+1) = y_n + sum(j=1,M) q'mj*(F(y_j^(k+1)) - F(y_j^k))+ sum(j=1,M) q_mj*F(y(m-1)^k)
for entires q_mj in Q and q'_mj in Q_delta.

The code is tested in integration-tests/model/test_sdc.py.

[atb1995]

[tommbendall]

This looks great! It's well documented and clear. I have only one tiny comment about docstrings.

If you think we will never use SDC with limiters or wrappers, feel free to remove all of that code.

[jshipton]

This looks great, thanks Alex! Only a couple of tiny quibbles about comments...

[jshipton]

Awesome - we're good to go!