diff

import numpy as np
import matplotlib.pyplot as plt

def p(x):
    return np.cos(x)
def q(x):
    return np.cosh(x)
def f(x):
    return np.cos(x)


def methProg(p, q, f, a, b, c1, c2, c, d1, d2, d, n):
    h = (b - a) / n
    u = np.zeros(n + 1)
    v = np.zeros(n + 1)
    x = np.zeros(n + 1)
    y = np.zeros(n + 1)
    alp = np.zeros(n + 1)
    bet = np.zeros(n + 1)
    gam = np.zeros(n + 1)
    phi = np.zeros(n + 1)

    x[0] = a
    i = 1
    u[0] = c * h / (c1 * h - c2)
    v[0] = -c2 / (c1 * h - c2)

    while True:
        x[i] = x[i - 1] + h
        alp[i] = 1 - p(x[i]) * h / 2
        bet[i] = h ** 2 * q(x[i]) - 2
        gam[i] = 1 + p(x[i]) * h / 2
        phi[i] = (h ** 2) * f(x[i])
        v[i] = -gam[i] / (bet[i] + alp[i] * v[i - 1])
        u[i] = (phi[i] - alp[i] * u[i - 1]) / (bet[i] + alp[i] * v[i])
        if i == n - 1:
            break
        i += 1
    x[n] = b
    alp[n] = -d2
    bet[n] = h * d1 + d2
    phi[n] = h * d
    v[n] = 0
    u[n] = (phi[n] - alp[n] * u[n - 1]) / bet[n]
    y[n] = u[n]
    i = n - 1
    while True:
        y[i] = u[i] + y[i + 1] * v[i]
        if i == 0:
            break
        i -= 1
    return {'x': x, 'y': y}
a = -1
b = 1
c1 = 0.1
c2 = 0.4
c = 0
d1 = 0.9
d2 = 0.92
d = 0
n = 500


res = methProg(p, q, f, a, b, c1, c2, c, d1, d2, d, n)
plt.plot(res['x'], res['y'])
plt.show()