The temperature distribution of a long, thin copper rod with a length of 15 cm can be determined by solving the one dimensional heat conduction equation

where k = 1.11 cm2/s is the diffusivity constant.

Draw the grid for step sizes of dx = 2 cm and dt = 0.2 seconds with the following initial and boundary conditions:

Obtain the tridiagonal system of linear equations using (a) the Crank-Nicolson implicit finite difference method to determine the temperature distribution at t = 0.2 and t = 0.4 seconds, respectively.
Solve the resulting tridiagonal system of linear equations using Thomas algorithm and provide MATLAB coding to implement all three schemes. 

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