I am trying to solve the following PDE using finite difference approximations,
$$\frac{1}{r}\frac{\partial}{\partial r}\left(r\frac{\partial T}{\partial r}\right) + \frac{1}{r^2} \frac{\partial^2T}{\partial\theta^2} = 0$$ $$0 ≤ ≤ 1, 0 ≤ ≤ 2$$ $$(1, ) = 100 \sin()$$
Are there any thoughts of how can I discretize this PDE?
New update:
I have tried to simplify the problem into a 2D-plate-like problem, the temperature distribution may look like:
