Part 2. diffu.Attempt.py.py

import numpy as np
import matplotlib.pyplot as plt
#define input parameters
sigma_a = float(input('enter absorption cross section for the material   '))
sigma_t = int(input('enter total cross section for the material   '))
Q = float(input('enter your value of source for the material   '))
M = int(input('enter length of the slab  ')) # length of slab
n = int(input('enter the number of cells  ')) # number of cells

#define input parameters
D = 1/(3*sigma_t)    # Diffussion coefficient for material
l_t = M +2*D        # extrapolated length
h = l_t/n            # mesh spacing
c = (2*D/h**2) + sigma_a
f = D/ h**2
A = np.zeros([n-1, n-1])
B = np.zeros(n-1)
x = np.linspace(2*h, -l_t+h, 2*n)
for i in range(1,n-2):
    print(i)
    A[i,i-1] = -f
    A[i,i] = c
    A[i,i+1] = -f
    B[i] = Q

# building matrices A and B
A[0,0] = c
A[0,1] = -2*f
A[n-2,n-3] = -f
A[n-2,n-2] = c
B[0] = Q 
B[n-2] = Q 
print (A)
print(B)


guess = np.ones(n-1)

# Let's define our convergence criteria
tol = 10**(-5)
#   Initial guess
mat_x_estimate = guess

# Error
difference = 1.0
#   number of iterations
k = 0

while (difference > tol):
    k = k + 1 # update Number of iteration
    mat_x_ini = 1.0 * mat_x_estimate
    print('iterations:' , k)
    for i in range (len(A)):
         mat_x_estimate[i] = (B[i]- np.dot(A[i], mat_x_estimate)+ A[i,i]*mat_x_estimate[i])/A[i,i]
    # Determine 'Error'
    difference = np.linalg.norm((mat_x_estimate - mat_x_ini)/mat_x_estimate)
    
print (mat_x_estimate)
solution = np.zeros(n)
solution[0:n-1] = mat_x_estimate
print(solution)

mat_y_estimate = np.zeros(2*(n))
for i in range(0,n):
    mat_y_estimate[i]= solution[n-1-i]
    mat_y_estimate[n+i]=solution[i]

print(mat_y_estimate)
print(x)
plt.figure(1)
plt.plot(x,mat_y_estimate)
plt.show()