Enhanced testing

[AndreyAPopov]

We have a large testing deficiency right now. Here is a non-exhaustive list of tests that need to be added (please add to it!)

• [x] Derivatives need to be verified with finite differences or with automatic differentiation. We can potentially do both.
• [ ] exact solutions need to be verified.
• [ ] alternate RHS need to be tested. Right now they are not. Custom code per problem
• [ ] RHS operator overloading
• [x] test plotting and movies