stable solution, No convergence at x0
Numerical Bifurcation Analysis Toolbox in Matlab
Brought to you by:
hilmeijer,
willy_govaerts
Hello Matcont team.
I was working on a system of nonlinear equations from my master's thesis when I came up to matcont package. The system of equations is an algebric-differential-integral one. I discritized my system and used matlab "fsolve" and "lsqnonlin" to solve it. However, after changing the initial guess I couldn't find a stable solution (having all eigen values with negative real parts). In one of the articles it was mentioned that "steady-state conditions have been solved using a variable step continuation algorithm". so I started using matcont. I used the unstable solution from fsolve in the time integration from matcont, then I used the final solution as initial value for init_EP_EP. The result was "No convergence at x0".
I have two questions:
1. It seems I cant find a stable solution for the steady state using matlab fsolve and lsqnonlin. Actually, I guess my system has a lot local minimas. Is there a way in matcont I can use to find the stable solution?
2. Should I pass a stable solution to cont algorithm? Or an unstable solution will do the same?
Thanks
Hello,
I am not a member of the Matcont team.
Your description is quite vague: I guess you have rewritten your differential integral algebraic equation as some regular set of ordinary differential equations (or at least a set of n equations in n unknowns (and some parameters)).
If you have found a regular solution (without zero eigenvalues), it should normally work to pass it to MatCont as initial guess and start a continuation. You might have to play around with some continuation settings (initial step size, minimal step seize, ...) Usually it doesn't matter, if your solution is unstable, eigenvalues close to zero are really bad.
You should also take care to properly scale the equations and avoid large numerical rounding errors.
Good luck
Alois
A simple test is that you can check if the derivatives in your system are NNNNN, which means that it is recommended to choose numerical integration (N) and symbolic integration (S) to be prone to the situation you mentioned.