The most commonly encountered problem when using PDENONLIN occurs by not passing the input arguments correctly.
In an equation such as the following:
-div(c*grad(u))+a*u=f
you can use PDENONLIN as follows:
[U,RES]=PDENONLIN(B,P,E,T,C,A,F)
The B matrix is a boundary matrix, not a geometry matrix. For more information, see the Related Solution at the botom of the page.
P,E,T are the usual quantities when dealing with a PDE. C,A,F in PDENONLIN may be functions of u, and so you can either enter them as scalar quantities or as character arrays.
As an example, to solve the following equation:
-div(grad(u)) + u^3 = 0
you can use the following code:
% this is an example of how to use PDENONLIN
[p,e,t] = initmesh('circleg');
% this defines a unit circle as the surface we simulate the PDE on
% this also has the simple boundary condition u = 0, on the boundary
% you can view the details of the mfile, by typing "edit cricleg.m"
[p,e,t] = refinemesh('circleg',p,e,t);
[p,e,t] = refinemesh('circleg',p,e,t);
% refined the mesh twice (made the elements of FEM smaller)
% we're going to simulate the static problem
% so the equation is: -div(grad(u)) + u^3 = 0
% so the parameters that we will pass to PDENONLIN
% [U,RES]=PDENONLIN(B,P,E,T,C,A,F) solves the nonlinear
% PDE problem -div(c*grad(u))+a*u=f
% so our c = 1, a = u^2 and f = 0;
% you can change these as you wish
[ U, R ] = pdenonlin('circleb1',p,e,t,1,['u.^2'],0,'U0',1);
% Note that we used the function 'circleb1' rather than 'circleg'
% here, this is because we need a boundary matrix b, not a geometry
% this is further explained at the following URL:
% <http://www.mathworks.com/support/solutions/data/1-19DTS.shtml>
% Also, note how we entered a, as a character array, if you simply type
% u.^2 rather than ['u.^2'] you will receive an error
pdeplot(p,e,t,'xydata',u);
% we now plot the solution of the PDE
