NM_Lab9

import numpy as np
import math
import pandas as pd

a, b, c, d, f = 0.3, 0.9, 0.7, 0.5, 0.5
l1, l2 = 1.1, 1.1

eps = 1e-5
n1, n2 = 5, 5

h1 = l1 / n1
h2 = l2 / n2

def u(x, y):
    return a * (x*x - y*y) + b*x*y + c*x + d*y + f

def ux(x, y):
    return 2*a*x + b*y + c


def uy(x, y):
    return -2*a*y + b*x + d


def bx(x, y):
    if x == l1:
        return u(l1, y)
    if x == 0:
        return ux(0, y)
    return 0


def by(x, y):
    if y == l2:
        return uy(x, l2)
    if y == 0:
        return u(x, 0) - uy(x, 0)
    return 0



def norm(A, B):
    sum = 0
    for i in range(n1 + 1):
        for j in range(n2+1):
            sum += (A[i, j] - B[i, j]) ** 2

    return math.sqrt(sum)


def iter(t1, t2, t3, t4):
    c = ((h1 * h2) ** 2) / (2 * ((h1 ** 2) + (h2 ** 2)))
    return c * ((t1 + t3) / (h1 ** 2) + (t2 + t4) / (h2 ** 2))


inp = open("result.txt", "w")

X = [i*h1 for i in range(n1+1)]
Y = [i*h2 for i in range(n2+1)]

M = np.zeros((n1+1, n2+1))
for i in range(n2 + 1):
    M[n1, i] = bx(l1, Y[i])
T = np.copy(M)
k = 0

T1 = [0 for i in range(n1+1)]
T2 = [0 for i in range(n1+1)]
T3 = [0 for i in range(n2+1)]
inp.write("Iteration process:")
while 1:
    k += 1
    T = np.copy(M)
    for i in range(n1 + 1):
        T1[i] = 2 * h2 * by(X[i], 0) + T[i, 1] - 2 * h2 * T[i, 0]
        T2[i] = 2 * h2 * by(X[i], l2) + T[i, n2 - 1]
    for i in range(n2+1):
        T3[i] = -2* h1 * bx(0, Y[i]) + T[1, i]
    M[0,0] = iter(T3[0], T[0, 1], T[1, 0], T1[0])
    M[0, n2] = iter(T3[n2], T2[0], T[1, n2], T[0, n2-1])
    for i in range(1, n1):
        M[i, 0] = iter(T[i-1, 0], T[i, 1], T[i+1, 0], T1[i])
        M[i, n2] = iter(T[i-1, n2], T2[i], T[i+1, n2], T[i, n2 - 1])
    for j in range(1, n2):
        M[0, j] = iter(T3[j], T[0, j+1], T[1, j], T[0, j - 1])
    for i in range(1, n1):
        for j in range(1, n2):
            M[i, j] = iter(M[i-1, j], M[i, j+1], M[i + 1, j], M[i, j - 1])


    norma = norm(M, T)
    inp.write("\ni=" + str(k) + "  Norm = " + str(norma))
    if norma <= eps:
        break

P = np.zeros((n1+1, n2+1))
for i in range(n1+1):
    for j in range(n2+1):
        P[i,j] = u(X[i], Y[j])

E = P - M

P1 = pd.DataFrame(P)
M1 = pd.DataFrame(M)
E1 = pd.DataFrame(E)
writer = pd.ExcelWriter('output.xlsx')
M1.to_excel(writer, 'Метод')
P1.to_excel(writer, 'Точне значення')
E1.to_excel(writer, 'Похибка')
writer.save()
writer.close()

inp.close()