1D nonlinear Poisson's equation using Finite Difference Method-Inverse matrix calculation method

In this video we have solved the nonlinear Poisson's equation using finite difference method and we have utilized inverse matrix technique calculation.
First, we linearized Poisson's equation and calculated value of potential at grids altogether.
We will see that, solving of potential at grids altogether using matrix calculation method, convergence speed considerably increase.
Moreover, having a better initial guess have a crucial effect in the convergence of the solution in matrix calculation method, while it is less sensitive to the one-by-one calculation method.
For more videos about numerical methods for solving of PDE's you may find the following channel useful:

00:00 introductory text
00:07 introduction
00:38 Theory and derivation of the matrix calculation method
09:30 Implementing of the MATLAB code
30:58 effect of the initial guess on the stability of the solver in both one-by-one method and matrix calculation method