I have a fluid dynamics problem I need to solve. There are 6 equations, and 6 unknowns, but the form of the equations are non-linear. Some unknown variables are not only multiplied by coefficients, but also by other unknown variables. Thus, I can't just do a Gaussian elimination matrix. I'm trying to come up with a way to write a program that uses substitution to solve non-linear algebraic equations. (I'm using Matlab, but I'm also somewhat familiar with Python, if need be). My question is this: is this a topic that has a wealth of information on it? Has it been done before, is it common practice? I need to know if I'm reinventing a wheel. If I am reinventing the wheel that is a substitution-based equation solver, then does anyone know where I can find, say, a sample code that does this?