Recent content by urista

Still not clear Thank you for the replies, but how do I show the degeneracy? Also, how do I show in the case of a square (L=H) wheather the eigenfunctions are orthogonal or not in a two-dimensional sense?

I'm trying to solve the Laplacian in 2D: uxx+uyy=0 in the quarter plane x>0, y>0 using a Fourier sine transform Boundary Conditions: u(x,0)=DiracDelta(x-a) , 0< x < infinity and 0< a< infinity u(0,y)=0, 0< y < infnity I transformed the PDE in x using the definition of the transform with...

I'm solving a Helmholtz equation uxx+uyy+lambda*u=0 in a rectangle: 0<=x<=L, 0<=y<=H with the following boundary conditions: u(x,0)=u(x,H)=0 and ux(0,y)=ux(L,y)=0 I found the eigenvalues to be: lambda(nm)=(n Pi/L)^2+(m Pi/H)^2 and the eigenfunctions to be: u(nm)=Cos(n Pi x/L)*Sin(m Pi...

Thanks HallsofIvy, so I should expand g=Sum form n=0 to infinity(gn sin(n Pi x/L)), and of course the gn coefficients can be found using inner product and the orthogonality of the eigenfunctions, correct?

I have a wave equation Ytt=c^2 Yxx - g where g is a constant. The boundary conditions are Y(0,t)=Y(L,t)=0 with initial conditions Y(x,0)=0 and Yt(x,0)=0 I tried to solve it by Laplace transfoming the PDE in time and everything worked fine until I got to the point where I had to inverse the...

I have a wave equation Ytt=c^2 Yxx - g where g is a constant. The boundary conditions are Y(0,t)=Y(L,t)=0 with initial conditions Y(x,0)=0 and Yt(x,0)=0 I tried to solve it by Laplace transfoming the PDE in time and everything worked fine until I got to the point where I had to inverse the...

Thank you arilando, that was great help. Do you think you might have time later on to give me some input on a 1D wave equation? I won't bother you now!

so with u(r)=1/6 r^2 we'll get du/dr=1/3 r, how could this be equal to zero at r=b?

OK, I got an answer u=b^3/(3*r)-(a^3+2*b^3)/(6*a)+r^2/6 which was completely valid to satisfy the ODE and the boundary conditions. The second part of the question is asking to let the inner radius "a" go to zero in the above solution and to interpret the result. Obviously the limit doesn't...

Thank you; it became evident that the boundary conditions are independent of the angles which means it reduces to an ODE in r. I appreciate your help and let you know what I get for a result.

I have a problem on my homework that is really confusing. I need to solve the partial differential equation in a spherical shell with inner radius = a and outer radius=b: (Laplacian u)=1 in spherical coordinates. The boundary conditions are u=0 on the inner radius r=a, and du/dr=0 on outer...