Explicit Scheme, general tridiagonal matrix
A more general tridiagonal matrix
\begin{equation*}
\mathbf{A} =\begin{bmatrix}a&b&0& 0 &\dots\\
c&a&b& 0&\dots \\
\dots & \dots & \dots & \dots & b \\
0 & 0 &\dots &c&a\end{bmatrix},
\end{equation*}
has eigenvalues
\mu_i=a+s\sqrt{bc}\cos{(i\pi/n+1)} with
i=1:n .