I am solving Boundary value problem using finite difference method from a reference book, but one of the step is not quite clear to me - for more clear view I am sharing a screen shot of that question below.
Can anyone help me how that step comes? I had shown that step with the red marker. Please explain me how that step comes?
The line you marked is: $$16y_{i+1} - 33y_i + 16y_{i-1} = x_i, \quad i = 1,2,3. $$ It comes from the previous line by substituting $$h=1/4, \ \ \ {1\over h^2}=16$$ and then subtracting $y_i$ from both sides of the equation.