# comparison of stability of two non-linear methods

I have solved a numerical problem using two different sets of non-linear governing equations. I want to get an understanding of the stability of the methods relative to each other. To do so, I solving the problem with each method whilst keeping the time stepping schemes, time step and mesh sizes the same. I then run the code, and observe the largest time step using which stable results are produced or convergence is obtained. I wanted to know whether this makes sense. I know this process does not get definite answer about stability of the methods.

Also what I have found that for this particular problem, stable results are still obtained even with CFL numbers greater than 1 (very large time steps). Do the large time steps I try still need to satisfy CFL?

• I don't understand. First you talk about solving two different sets of equations, which would mean you are solving two different (though perhaps equivalent?) problems. Then in the rest of the question you refer to using two different methods. Do you have two problems or two methods? You'll need to be clearer and include more specifics. – David Ketcheson Sep 20 '15 at 19:32
• I am solving a problem with two different sets of governing equations. (i.e. both sets of equations govern the same problem). I have been advised by a professor to this, I need a second opinion, also comments on CFL please) – melody Sep 20 '15 at 21:14
• Please add a lot more details: which equations precisely (use LaTeX!), which methods? Also, why do you need a second opinion? What's wrong with your professor's? – Christian Clason Sep 20 '15 at 22:31
• This is a general question that could apply to any problem, and I need comments on the CFL. I think the question is pretty clear. I need a second opinion because I am not convinced! I would appreciate some quick hints, replies! – melody Sep 21 '15 at 7:52
• This question makes sense to me, it could be an informal way of comparing stability. It would be good to know the answer from someone experienced. – Hooman Sep 21 '15 at 10:14