Fix IMEX Gear time-integration approach

Issue/feature addressed

The original IMEX Gear time-integration approach is advertised as second-order. However, only the implicit part was second-order, while the explicit part was treated by a first-order approximation resulting in an overall first-order scheme.

Proposed solution

The proposed solution is to consider both the explicit and the implicit terms as second-order. I am not familiar with the IMEX Gear approach, however the proposed approach is also known as "extrapolated Gear" method. (see (p.803) https://www.jstor.org/stable/pdf/2158449.pdf)

Tests

Here is the original convergence rate:

IMEXGear:
1.0048374666093653
1.0024170009943802
1.0012061031178545

Here is the convergence rate of the updated scheme:

IMEXGear:
2.002880533431922
2.0014606941621973
2.000714655758547

Suggested reviewers

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Notes

Please add any other information that could be useful for reviewers.

Checklist

• [ ] Functions and classes, or changes to them, are documented.
• [ ] User guide/documentation is updated.
• Changelog is updated.
• Suitable tests added for new functionality.
• Contributed code is correctly formatted. (See the contributing guidelines).
• [ ] License added to any new files.
• [ ] No extraneous files have been added (e.g. compiler output or test data files).