Discussion Forum

Dear users,

I never used COMSOL before, and i would like to understand whether it can be used to solve my problem.
I need to solve a boundary value problem defined by a system of coupled nonlinear PDEs in 2D.

Since i'm not familiar with COMSOL, i started with something easier, namely I would like to solve a single nonlinear PDE in 2D (rectangular domain).

I think I would need to use General Form PDE node in COMSOL. However, my test equation is of the following form:

x*u^2*(2*ux+x*uxx)-uy^2+u*(Cot(y)*uy+uyy)=0

supplied by suitable boundary conditions at the boundaryies (here u=u(x,y) and ux is the first derivative and so on...) The expression itself is not important, since it is just a test, but i stress that I would like to work with PDEs in this form.

Now, i have 2 questions:

1) should I always use the General Form given by COMSOL? Couldn't I just write the PDE in its form above?

2) Accordingly to the Help, the source term "f" in the General Form can "be function of the spatial coordinates, the solution u, and the space derivatives of u". Thus, in principle, I could set Gamma=0 (always in the notation used in General Form) and just have a PDE in the form

f=f(u,ux,uy,uxx,uxy,uyy,...)=0

which is what I would like to have. However, in doing so I get some error (singular matrix).
I also checked this by integrating the Laplace equation.
If i choose Gamma=(ux,uy) and f=0, the program works,
if I choose Gamma=0 and f=uxx+uyy (which should be equivalente, accordingly to the Help) it gives Singular Matrix.

I made a search in the Discussion Forum, but didn't find anything helpful.
Thanks in advance,

Paolo