# case2.py

import numpy as np

k = 0.5                 # W / (cm K)
area = np.pi / 100      # cm^2

def analytical(a, x):
    return 100 * np.cosh(a*x) / np.cosh(a)

def analytical_heat_loss(a):
    return -100*k*area*a*np.tanh(a)

def fdm_array(n, a = 2.75):
    dx = 1/ n 
    kap = 2 + ((a**2)*(dx**2))
    kap_prime = (kap/2)
    
    left_FDM_array = np.zeros((n, n))
    left_FDM_array[0][0:2] = [kap_prime, -1]
    row_FDM = [-1, kap, -1]       
    
    for i in range(1, n-1):
        left_FDM_array[i][i-1:i+2] = row_FDM 
    
    left_FDM_array[n-1][n-2:n] = [-1, kap]
    
    return left_FDM_array

def right_array(n):
    array = [0 for _ in range(n-1)]
    array.append(100)
    return array