Heat Equation solution using Finite Difference and Crank-Nicholson

I rewrote parts of this code so that it used dense (non-sparse) matrices instead of sparse matrices, for demonstration purposes. The code is below:

import numpy as np
import scipy.linalg

# Number of internal points
N = 200

# Calculate Spatial Step-Size
h = 1/(N+1.0)
k = h/2

x = np.linspace(0,1,N+2)
x = x[1:-1] # get rid of the '0' and '1' at each end

# Initial Conditions
u = np.transpose(np.mat(10*np.sin(np.pi*x)))

# second derivative matrix
I2 = -2*np.eye(N)
E = np.diag(np.ones((N-1)), k=1)
D2 = (I2 + E + E.T)/(h**2)

I = np.eye(N)

TFinal = 1
NumOfTimeSteps = int(TFinal/k)

for i in range(NumOfTimeSteps):
   # Solve the System: (I - k/2*D2) u_new = (I + k/2*D2)*u_old
   A = (I - k/2*D2)
   b = np.dot((I + k/2*D2), u)
   u = scipy.linalg.solve(A, b)

Once the code is finished, the last u will have the final values. More detailed code along with the sparse matrix version is here.