How to solve a 2D Poisson's equation in cylindrical coordinates using finite difference

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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: enter image description here