Loading [MathJax]/extensions/TeX/boldsymbol.js

 

 

 

Explicit Scheme, eigenvalues and stability

We can obtain closed-form expressions for the eigenvalues of \mathbf{A} . To achieve this it is convenient to rewrite the matrix as \begin{equation*} \mathbf{A}=\hat{I}-\alpha\hat{B}, \end{equation*} with \begin{equation*} \hat{B} =\begin{bmatrix}2&-1&0& 0 &\dots\\ -1&2&-1& 0&\dots \\ \dots & \dots & \dots & \dots & -1 \\ 0 & 0 &\dots &-1&2\end{bmatrix}. \end{equation*}