Thermal Diffusivity Modeling: Improving Stability with Crank-Nicolson Differencing

[che-4071-hw2]
Part C
1. Express the heat diffusion equation from Part B1 as an algebraic equation via Crank-Nicolson differencing.
2. Using von Neumann stability analysis, show that the Crank-Nicolson differencing scheme is stable regardless of the choice for r=
3. Simulate the time dependent response of a uniform bar initially at 20C after its ends are raised then maintained at 40 and 80C respectively. Discretize the bar with 20 time dependent temperatures and solve the equations from Part C1 using scipy.linalg.solve_banded for r=
=2 over 100 time steps. Plot the simulated results in 10 time step intervals.