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Enhanced testing #56

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@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!)

  • 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
  • test plotting and movies

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