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The nonzero elements are given by $$ \begin{align} A_{i,i-1} &= -F_o\\ A_{i,i} &= 1+ 2F_o\\ A_{i,i+1} &= -F_o \end{align} $$
for \( i=1,\ldots,N_x-1 \).
The equations for the boundary points correspond to $$ A_{0,0} = 1,\quad A_{0,1} = 0,\quad A_{N_x,N_x-1} = 0,\quad A_{N_x,N_x} = 1 $$
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