Loading [MathJax]/extensions/TeX/boldsymbol.js
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
\newcommand{\dfc}{\alpha} % diffusion coefficient
Detailed expressions for the matrix entries
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
