I am struggling understanding Multi Grid methods. I would like to develop an example of two-grid methods applying to f.e. this equation:
$$-u''(x)+u(x)=x, \qquad u(0)=u(1)=0$$
I am able to create a SLAE for this equation: $$Ax=b$$ and solve it with Jacobi method: $$ x_{i}^{(k+1)}={\frac {1}{a_{ii}}}\left(b_{i}-\sum _{j\neq i}a_{ij}x_{j}^{(k)}\right),\quad i=1,2,\ldots ,n $$
But I can't figure out how to solve it using two-grid approach?