Cubic & Quintic Hermite Spline

[SouthEndMusic]

Fixes #218.

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

I am on a roll hacking around in this repository, so I decided to add the quintic Hermite interpolation as well (:

[ChrisRackauckas]

I like it, but two things.

1. It seems a little odd to have the quintic but not the cubic Hermite, that should probably be added.
2. (u, t, du, ddu) seems like an odd argument order. (ddu, du, u, t) seems more natural

[sathvikbhagavan]

1. Yes, having cubic hermite makes sense.
2. Yes, (ddu, du, u, t) would be better.

[ChrisRackauckas]

BTW, I think you've made significant contributions, and we just happen to be writing an article on DataInterpolations right now. Would you like to a be co-author?

[sathvikbhagavan]

Looks good! Had some minor comments. Also can you add a few tests for checking parameter caches are set properly or not similar to my comment in #274?

[SouthEndMusic]

BTW, I think you've made significant contributions, and we just happen to be writing an article on DataInterpolations right now. Would you like to a be co-author?

That sounds interesting, what would that entail?

[sathvikbhagavan]

We already have a JOSS paper review going on - openjournals/joss-reviews#6917

Can you make a PR adding your name and affiliation in https://github.com/SciML/DataInterpolations.jl/blob/master/joss/paper.md?

[sathvikbhagavan]

Apart from that typo.. LGTM!