python-projects/approximation02.py at main · mdoynichenko/python-projects · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
# -*- coding: utf-8 -*-

import matplotlib.pyplot as plt
import numpy as np
import math

def funct(t, y):
    return -t*y + 4*t/y

def approx_f(x, w_i, x_i, n):
    result = 0
    tmp_l = 1
    for i in range(0, n+1):
        tmp_l = 1
        for j in range(0, n+1):
            if i == j:
                continue
            tmp_l *= (x - x_i[j])
            tmp_l /= (x_i[i] - x_i[j])
        result += w_i[i]*tmp_l
    return result


a = 0
b = 1
y_0 = 1
h = 0.1
n = 0
k1 = 0
k2 = 0
k3 = 0
k4 = 0

tmp_t = a
w_i_tr = np.array([y_0])
w_i_h = np.array([y_0])
w_i_st = np.array([y_0])
w_i_rk = np.array([y_0])
x_i = np.array([a])
pl_x = np.array([a])
pl_y = np.array([y_0])

"""
трапеции
"""
while(tmp_t < b):
    w_i_tr = np.append(w_i_tr, w_i_tr[n] + h*(funct(tmp_t, w_i_tr[n]) + funct(tmp_t+h, w_i_tr[n]+ h*funct(tmp_t, w_i_tr[n])))/2)
    n+=1
    tmp_t+=h
    x_i = np.append(x_i, tmp_t)

"""
метод Хойна
"""
tmp_t = a
n = 0

while(tmp_t < b):
    w_i_h = np.append(w_i_h, w_i_h[n] + h*(funct(tmp_t, w_i_h[n]) + 3*funct(tmp_t + 2*h/3, w_i_h[n]+ 2*h*funct(tmp_t, w_i_h[n])/3))/4)
    n+=1
    tmp_t+=h


"""
метод средней точки
"""

tmp_t = a
n = 0

while(tmp_t < b):
    w_i_st = np.append(w_i_st, w_i_st[n] + h*(funct(tmp_t + h/2, w_i_st[n] + h*funct(tmp_t,  w_i_st[n])/2 ) ))
    n+=1
    tmp_t+=h


"""
метод Рунге Кутта четвертого порядка
"""

tmp_t = a
n = 0

while(tmp_t < b):
    k1 = funct(tmp_t, w_i_rk[n])
    k2 = h*funct(tmp_t + h/2, w_i_rk[n] + k1/2)
    k3 = h*funct(tmp_t + h/2, w_i_rk[n] + k2/2)
    k4 = h*funct(tmp_t + h, w_i_rk[n] + k3)

    w_i_rk = np.append(w_i_rk, w_i_rk[n] + (k1 + 2*k2 + 3*k3 + k4)/6)

    n+=1
    tmp_t+=h

lag = 0.01
x = np.arange(a, b, lag)
y_tr = approx_f(x, w_i_tr, x_i, n)
y_h = approx_f(x, w_i_h, x_i, n)
y_st = approx_f(x, w_i_st, x_i, n)
y_rk = approx_f(x, w_i_rk, x_i, n)
y_f = np.array([math.sqrt(4 - 3*math.exp(-x[0]*x[0]))])
tmp_x = a+lag
while tmp_x <= b:
    y_f = np.append(y_f, math.sqrt(4 - 3*math.exp(-tmp_x*tmp_x)))
    tmp_x+=lag


fig, ax = plt.subplots()

ax.plot(x, y_f, linewidth  = 9, color = 'black')
ax.plot(x, y_rk, linewidth  = 7, color = 'blue')
ax.plot(x, y_st, linewidth  = 5, color = 'yellow')
ax.plot(x, y_h, linewidth  = 3, color = 'green')
ax.plot(x, y_tr, linewidth  = 1, color = 'red')

plt.grid(True)

fig.set_figwidth(12)
fig.set_figheight(6)
fig.set_facecolor('linen')
ax.set_facecolor('ivory')

plt.show()

print("метод трапеций")
print(w_i_tr)
print("метод Хойна")
print(w_i_h)
print("метод средней точки")
print(w_i_st)
print("метод Рунге-Кутты")
print(w_i_rk)
print(x_i)