Q$4.$ Use BTCS implicit scheme to solve Q$3$ and write the algorithm and plot the temperature profile at $\backslash (0\mathrm{.}1,0\mathrm{.}2\backslash ),$ and $1$ sec $.(10$ pts $)$:

a$)$ Compare the results with Q$3$ for the two choices of the time steps and discuss the pros and cons of each of the two schemes.

b$)$ Modify the code to admit the zero value Neumann conditions instead the homogenous Dirichlet at the two ends.