I have been struggling with trying to solve the vibrating plate equation in polar coordinates with angular dependence (non symmetrical initial condition). That is,
c d2y/dt2 = d4y/dr4
except that d4y/dr4 is just short cut symbolism for the double Laplacian in polar coordinates. I have been successful using a relatively simple explicit finite difference approach for symmetrical initial conditions but the asymmetrical IC's cause a problem. I have been holding off trying to reformulate an implicit finite difference method because there is so much algebraic bookkeeping.
I see that the partial differential solver toolbox does not deal with this problem. Does anyone know about Matlab scripts that deal with this problem?