What is Reddit's opinion of Numerical Recipes 3rd Edition: The Art of Scientific Computing?

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You can't just link to some random research paper and hope we'll read through that to understand what you want to do. State "the" equation clearly and also, clearly, what you want to do with it (e. g. the range of parameters you're interested in, the precision you need, &c.).

That being said, Euler's method is very rudimentary and there are much better ones, computationally efficient and with well-studied error estimates and stability. You'll have to dig into some numerical analysis book like Numerical Recipes just to avoid rooky mistakes (and look bad if you publish…).

Last but not least, Python certainly already has canned routines/libraries to integrate differential equations and you'll be better served using them. So dig into that too.

Good luck!

There was a book called "Numerical Recipes". I presume it's still around. Hard to go wrong with that one.

edit:

For C++ programmers... https://www.amazon.com/Numerical-Recipes-3rd-Scientific-Computing/dp/0521880688/

For C programmers... https://www.amazon.com/Numerical-Recipes-Scientific-Computing-Second/dp/0521431085/

For FORTRAN programmers... https://www.amazon.com/Numerical-Recipes-Art-Scientific-Computing/dp/0521308119

There's a field of mathematics called numerical analysis that studies ways to find the best possible approximations. That has been extended to consider finite number representations. There's a chapter in:

Numerical Recipes 3rd Edition: The Art of Scientific Computing by William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery

on numerical integration.

Educate yourself.

Yes there is software.

The first thing I would suggest is to try the Microsoft Excel "Solver" . It is actually a wonderful piece of highly polished numerical analysis code, buried inside a stinky, steaming turd called Excel Spreadsheets. You and Google, working together, can find hundreds of tutorials about this, including

(link 1)

(link 2)

(link 3)

(link 4)

If you prefer to code up the algorithm(s) yourself, so you can incorporate them in other bigger software you've got, I suggest purchasing the encyclopaedic textbook NUMERICAL RECIPES. This tour-de-force textbook / reference book has an entire chapter devoted to optimization, including source code for several different algorithms. I recommend Nelder-Mead "amoeba" but other people recommend other code.

I personnaly like Numerical Recipes The Art of Scientific Computing https://www.amazon.com/Numerical-Recipes-3rd-Scientific-Computing/dp/0521880688