Метод хорд

import math

import matplotlib.pyplot as plt

def f(x, y, z):

return -math.cosh(x) * z - 2 * y - 1

def runge_kutta(lambda_):

runge_kutta_y.clear()

runge_kutta_z.clear()

runge_kutta_y.append(y_0)

runge_kutta_z.append(lambda_)

curr_x = a + h

while curr_x <= b:

q0 = f(curr_x, runge_kutta_y[-1], runge_kutta_z[-1])

k0 = runge_kutta_z[-1]

q1 = f(curr_x + h / 2, runge_kutta_y[-1] + k0 * h / 2, runge_kutta_z[-1] + q0 * h /2)

k1 = runge_kutta_z[-1] + q0 * h / 2

q2 = f(curr_x + h / 2, runge_kutta_y[-1] + k1 * h / 2, runge_kutta_z[-1] + q1 * h / 2)

k2 = runge_kutta_z[-1] + q1 * h /2

q3 = f(curr_x + h, runge_kutta_y[-1] + k2 * h, runge_kutta_y[-1] + q2 * h)

k3 = runge_kutta_z[-1] + q2 * h

curr_x += h

runge_kutta_z.append(runge_kutta_z[-1] + h / 6 * (q0 + 2 * q1 + 2 * q2 + q3))

runge_kutta_y.append(runge_kutta_y[-1] + h / 6 * (k0 + 2 * k1 + 2 * k2 + k3))

return runge_kutta_y[-1]

runge_kutta_y = []

runge_kutta_z = []

arr_x = []

a = 0

b = 1

y_0 = 2

y_1 = 2

h = 1e-05

eps = 1e-05

cur_x = a

while cur_x <= b:

arr_x.append(cur_x)

cur_x += h

# метод стрельбы

count = 0

h_lambda = 10

runge_kutta_lambda = 10

prev_y = runge_kutta(runge_kutta_lambda)

runge_kutta_lambda += h_lambda

curr_y = runge_kutta(runge_kutta_lambda)