There must be a problem with your setup. I ran your code with 400,000 equations:
In[10]:= {mSys, mBc} = PrepareEquations[tMin, tMax, 2000, 200];
AbsoluteTiming[ans = SolveEquations[mSys, mBc]; ans // Length]
Out[11]= {1200.81, 402201}
I have a fast machine but it took only 20 minutes. I am using Mathematica 12. I suspect your machine has a physical bottleneck (too little RAM, or some other issue)
Try stepping up to successively larger problems to see where the problem is. For example, When I run this:
{mSys, mBc} = PrepareEquations[tMin, tMax, 1600, 200];
It took 791 seconds for 321,000 equations.
Using
{mSys, mBc} = PrepareEquations[tMin, tMax, 800, 200];
It takes 270 seconds for 161,000 equations
My suggestion is to start with a smaller problem and try various solver options in the documentation here or advanced topics. and time the solve (as above). Find the settings that work best for your problem and then scale back up to the larger problems.
I hope this helps,
Regards,
Neil
