Fix TimeIntegrationDemo.cpp and add ESDIRK tst files to the CI

Issue/feature addressed

The TimeIntegrationDemo.cpp was apparently originally designed to solve the advection-diffusion problem by an explicit discretization of the advection term and a implicit discretization of the diffusion term. Using the Demo for the validation of pure explicit scheme is not adequate. Also, the original code is not suitable for ESDIRK schemes.

Proposed solution

A few flags have been added to the code to properly deal with the various time-integration schemes.

Tests

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Notes

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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).