to analytical problems
See my coding package.
Every professional will tell you there is a correct tool for every job. This is no different in the programming and computing field. If you want something done as a proof of concept, quick and dirty is the way to go. Want something to be fool-proof and have a streamlined UI? that’s a different game. My toolbox contains several coding languages and paradigms: C++, C# (and other .net languages), Matlab, Mathematica, Python, and Fortran.
Teaching the computer some physics
A computer is basically a glorified abacus, and as the old adage goes - “Garbage in - garbage out”.
The secret to efficient and worthy physical simulations is inserting physical insight into hard and cold calculations. Sometimes moving an equation to a different representation does the trick. Sometimes getting rid of data is actually the right way to go. And at every step of the way, make sure the output conforms to physical reality!