I am learning numerical analysis, and recently I learnt several methods for solving BVPs and PDEs. However, the examples in the textbook is very vague and it uses Matlab code to find the answer. I am wondering if there exist some formulas that we can apply to solve problems by hand for the following methods:
shooting method
collocation
Finite element method
Forward finite difference method (parabolic equations of the heat equation)
Backward finite difference method (parabolic equations of the heat equation)
- Crank Nicolson method
It would be nice if you can provide websites with examples. I am very confused now. Thanks a lot!