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Fix CNAB/MCNAB time-integration schemes

Merged Jacques Xing requested to merge CFD-Xing/nektar:fix/CNAB-time-integration into master

Issue/feature addressed

The CNAB/MCNAB time-integration schemes are multi-step IMEX schemes that use previous computed residuals/derivatives to provide a second-order solution in time. As multi-step schemes, CNAB/MCNAB require a startup process. However, as IMEX schemes, the explicit and implicit residuals/derivatives must be stored separately.

Tests

Convergence studies have been performed:

Second-order convergence have been obtained with CNAB

2.001790262556334
2.00086804216596
2.000677507737796

Second-order convergence have been obtained with MCNAB

2.0001811406921695
1.9981824806748891
1.9977267364550606

Suggested reviewers

Please suggest any people who would be appropriate to review your code.

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).
Edited by Jacques Xing