Dear colleague,

This question is a bit vague. It depends what you want to simulate, what is you approach and the language you are using. For example, if your modeling is simple in the sense that it does not require complex (not predefined) types of variables and you want to simulate a big system, or simulate for a long time, I recommend FORTRAN for build the raw data and R for statistical data-analysis, such as time series analysis and attractor reconstruction.

Would you please give me a little more details?

if you have the algebraic equations available you might try GAMS www.gams.com

As a young engineer you should train yourself in Python programming. Forget about fortran and all the old school stuff.

You might want to explore Julia programming with Jupyter Notebooks. Our group has found success with this combination. I do agree Python and C should also be in programming toolbox. Lastly, I would add Matlab in there for additional analysis. You can use Octave, Scilab or Freemat if your not able to purchase a Matlab license.

If you want to solve nonlinear differential equations (coupled or uncoupled) you can use 'odeint' function in python language. It uses the RK4 method of numerical integration. To use this function you have to define the nonlinear functions f(x,y), g(x,y) etc from the equations dx/dt=f(x,y) and dy/dt=g(x,y) and then supply these to odeint function as arguments. Along with this, you need to define a time range of integration and initial conditions for x and y.

You can start by solving the differential equation of the simple harmonic oscillator by odeint function in python. The system is defined by two coupled 1st order differential equations: dx/dt=y and dy/dt=-w*w*x. Where w is the frequency of the oscillator. Though it is not nonlinear but you can use this method for nonlinear differential equations also.