Even in fluid dynamics the game is only as hard as you make it for yourself :

https://en.wikipedia.org/wiki/Lattice_Boltzmann_methods

You have well defined operations and conservation laws well behaved by construction.

Don't let Navier & Stokes enter the chat, and you will be fine.

The whole problem of integration is that mathematicians historically introduced new functions, and try to relate them together, in interesting way.

Polynomials are good and well behaved. Algebras too.