Chapter 11, Problem 3P

The following tridiagonal system must be solved as part of a larger algorithm (Crank-Nicolson) for solving partial differential equations:

$\begin{array}{l}\left[\begin{array}{cccc}2.01475& -0.020875& & \\ -0.020875& 2.01475& -0.020875& \\ & -0.020875& -2.01475& -0.020875\\ & & -0.020875& 2.01475\end{array}\right]\\ \times \left\{\begin{array}{c}{T}_1\\ T_2\\ T_3\\ T_4\end{array}\right\}=\left\{\begin{array}{c}4.175\\ 0\\ 0\\ 2.0875\end{array}\right\}\end{array}$

Use the Thomas algorithm to obtain a solution.