filter

# N(0, 1), N – количество элементов
def NStandart(N):
    xk = np.array([])
    # R(0, 1)
    a1 = RStandart(N)
    time.sleep(3) # pause
    a2 = RStandart(N)

    for i in range(N):
        xk = np.append(xk, np.sqrt(-2 * np.log(a1[i])) * np.cos(2 * np.pi * a2[i]))
    return xk

# Параметры задачи
h = 0.05
t0 = 0
t1 = 10

# разностная схема
yij = np.zeros((4,int((t1-t0)/h)))
xN = NStandart(int((t1 - t0)/h))

for j in range(1,int((t1 - t0)/h)):
    yij[0][j] = yij[0][j-1] + h * yij[1][j-1] + 2 * np.sqrt(2) * np.pi * h * xN[j-1]
    yij[1][j] = -h * yij[0][j-1] + (1 - 2.5 * h) * yij[1][j - 1] + (np.sqrt(6 * np.pi) - 5 * np.sqrt(np.pi)) * np.sqrt(2 * np.pi) * h * xN[j - 1]

# Строим график
t = np.arange(t0, t1, h)
plt.plot(t, yij[1])
plt.grid(True)
plt.show()