Finite Volume Method

Finite volume method is one of the integral method to approximate the partial differential equations (PDEs). The simplicity of calculating the function at each discrete finite volume (or just a 2d box for 2d cases) based on the neighboring cells or volumes.
The best use of this method is, avoiding the problem with singularity.
Imagine FVM like this, the Finite difference is like calculating the function at each nodes or points by seemingly Dirac function like approach, whereas FVM is using an uniform function inside each cells.
(I will add more to this later..)

For now, The Matlab Code solves the heat equation in spherical coordinate assuming the symmetry and the 2d approximation. The code is written poorly and for each boundary condition, you can see I have copy pasted the code with relevant modification so that it is easier to understand the basic essence of how FVM functions. I have also added relevant  comments where ever it is necessary.

Try and change the dt value, may be try to increase it. You will find one of the common criteria required for any numerical computation of PDEs.

Feel  free to contact me in case of confusion or if there is any mistakes.

Cheers

Download the code here
Code