non constant PDE toolbox coefficients with second order derivatives.

I need to specify coefficients in PDE tool box. My coefficients are related to the second derivatives not first derivatives. Can I use state.uyy and state.uxx and state.uxy as second derivatives? You can see the code here. Thank you so much.

function amatrix = acoefminsurf(region,state)

n1 = 16;
nr = numel(region.x);
amatrix = zeros(n1,nr);
normrev=-(sqrt( state.uyy(4,:).^2+state.uxx(4,:).^2-2*state.uxy(4,:).^2 ) );
amatrix(2,:) = normrev;
amatrix(7,:) = normrev;
amatrix(12,:) = normrev;

Answer 1

[Alan Weiss]

No, the state structure does not support uxx or uyy, as documented.

I suppose that you might try to increase the number of variables in your equation, such as making a system [u,v] and having v = ux so that uxx = vx. But I make no guarantees that you can really do this successfully. You would have to come up with coefficients and boundary conditions for the system.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[Kaveh Gharibi]

Thank you very much for your response. Actually I tried doing that but it increases the number of PDEs in the system, and it does not converge. Since it is a nonlinear system of PDEs.

[Ravi Kumar]

Could you share your script, and necessary data, for the nonlinear system of PDEs that did not converge?

[Kaveh Gharibi]

I figured it out. My C matrix was wrong. Pay attention when converting the problem to Matlab divergence format.