Merged requested to merge CFD-Xing/nektar:fix/imex-gear-time-integration into master
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.
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)
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
Please suggest any people who would be appropriate to review your code.
Please add any other information that could be useful for reviewers.
[ ] Functions and classes, or changes to them, are documented. [ ] User guide/documentation is updated.
Changelog is updated.
Suitable tests added for new functionality.
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