For Couette flow, using the specifications given in the notes, implement the Crank$-$

Nicolson method and, using MATLAB, solve using the automatic matrix inverter

available, i$.$e$.$ use the inv function only. Note the following:

Use $31$ nodes.

Use an $"$E$"$ value equal to $5.$

Plot the computed results at regular intervals and at convergence. Plot $y$ on the

vertical axis and $u$ on the horizontal axis.

Give the number of time steps for convergence. Convergence is said to have

occurred when, for a particular timestep and for all nodes, the following is true:

max

Submit a pdf document showing theory, your MATLAB program, your results,

and conclusions drawn. Write mathlab code for the above question