# partial differential equations

1. ### A How to get a converging solution for a second order PDE?

I have been struggling with a problem for a long time. I need to solve the second order partial differential equation $$\frac{1}{G_{zx}}\frac{\partial ^2\phi (x,y)}{\partial^2 y}+\frac{1}{G_{zy}}\frac{\partial ^2\phi (x,y)}{\partial^2 x}=-2 \theta$$ where $G_{zy}$, $G_{zx}$, $\theta$...
2. ### How to apply the Fourier transform to this problem?

I am struggling to figure out how to approach this problem. I've only solved a homogenous heat equation $$u_t = u_{xx}$$ using a fourier transform, where I can take the fourier transform of both sides then solve the general solution in fourier terms then inverse transform. However, since this...
3. ### A Determine PDE Boundary Condition via Analytical solution

I am trying to determine an outer boundary condition for the following PDE at $r=r_m$: $$\frac{\sigma_I}{r} \frac{\partial}{\partial r} \left(r \frac{\partial z(r,t)}{\partial r} \right)=\rho_D gz(r,t)-p(r,t)-4 \mu_T \frac{\partial^2z(r,t)}{\partial r^2} \frac{\partial z(r,t)}{\partial t}$$...

30. ### Solving this "simple" PDE

Hi guys, I've distilled the 3D Diffusion Equation into the following PDE using Fourier spectral techniques: ∂C(m,n,p,t)/∂t + k(p^2+m^2+n^2)C(m,n,p,t)=0, where C is the Fourier coefficient of the 3D Fourier transform, {m,n,p} are the spatial frequencies, and t is time. I've tried using a...