Added Radau, BDF and LSODA as options for scipy's integration method when using simulate

[joel-martin]

Summary

• Added Radau, BDF and LSODA to option method of dymos.phase.options.SimulateOptionsDictionary .
• Added example for a stiff ODE system.
• Added test for the example.

Related Issues

• Resolves Enable implicit methods of solve_ivp in traj.simulate #674

Backwards incompatibilities

None

New Dependencies

None

[review-notebook-app]

Check out this pull request on 

See visual diffs & provide feedback on Jupyter Notebooks.

---

Powered by ReviewNB

[joel-martin]

https://github.com/joel-martin/dymos/blob/017c5529e85d9cad1ad29baeaffae69aba6b36cb/dymos/examples/robertson_problem/doc/test_doc_robertson_problem.py#L97

This line of code still fails. The relative error rel error 0.00835626525078177 is high, but perhaps acceptable because it is the result at the end of the time integration. The next test could also be a problem.

https://github.com/joel-martin/dymos/blob/017c5529e85d9cad1ad29baeaffae69aba6b36cb/dymos/examples/robertson_problem/doc/test_doc_robertson_problem.py#L98

Should I reduce the tolerances further?

[robfalck]

I'm ok with lowering that tolerance because it's still a small relative error on a very small absolute error, and at this point we're basically testing the accuracy of the integrator in scipy, not the functionality of dymos

[coveralls]

Coverage increased (+0.02%) to 95.369% when pulling 4e2c0c2 on joel-martin:implicit-simulate into 02e4f36 on OpenMDAO:master.

[robfalck]

Thanks for your contribution!