AdditionalLab2

import math
import numpy as np

def phi(x):
    return math.exp(x)

def f(x):
    return ((x+2)*math.exp(x) + math.exp(2*x+4) - 1)/(x+2)

def K(x, y):
    return math.exp(x*y)

start = 0
end = 2
n = 10
h = (end - start)/n
xi = [start + h*(i + 1/2) for i in range(n)]
buffer = []
real_sol = np.matrix([[np.float64(phi(xi[i])) for i in range(n)]]).transpose()
_ = real_sol
coeffs = np.matrix([[np.float64(f(xi[i-1])) for i in range(1, n+1)]]).transpose()
for i in range(1, n+1):
    app = []
    for j in range(1, n+1):
        if i == j:
            app.append(np.float64(1 - h*K(xi[i-1], xi[j-1])))
        else:
            app.append(np.float64(-h*K(xi[i-1], xi[j-1])))
    buffer.append(app)
System = np.matrix(buffer)
solution = np.linalg.solve(System, coeffs)
print("------------PHI(X)--------")
print(real_sol)
print("------------~PHI(X)--------")
print(solution)
print("--------------------")
print(max([math.fabs(solution[i][0] - real_sol[i][0]) for i in range(n)]))