#!/usr/bin/env python3
# -*- coding: utf-8 -*”””
Created on Tue Dec 6 17:06:58 2022
@author: ggor
“””
import numpy as np
from scipy.integrate import solve_bvp
import matplotlib.pyplot as plt
def T_cf(x):
sq = np.sqrt(0.05)
return 200 + 20.4671*np.exp(sq*x) + 79.5329*np.exp(-sq*x)
def fun(x, y):
return np.vstack((y[1], 0.05*(y[0]-200)))
def bc(ya, yb):
return np.array([ya[0]-300, yb[0]-400])
x = np.linspace(0, 10, 11)
y = np.zeros((2, x.size))
res = solve_bvp(fun, bc, x, y)
x_plot = np.linspace(0, 10, 101)
y_cf = T_cf(x_plot)
y_plot = res.sol(x_plot)[0]
fig = plt.figure()
ax = fig.add_subplot()
plt.plot(x_plot, y_cf, linestyle=’–‘, linewidth=4, alpha=0.5,
color=’r’,
label=’Closed form’)
plt.plot(x_plot, y_plot, linestyle=’ ‘, color=’b’, marker=’.’,
label=’Numerical’)
plt.legend()
plt.show()
#!/usr/bin/env python3
# -*- coding: utf-8 -*”””
Created on Tue Dec 6 16:31:22 2022
@author: ggor
“””
import numpy as np
from scipy.integrate import solve_ivp
import matplotlib.pyplot as plt
# y is 2-dimensional
def dydt(t, y):
dy = np.zeros_like(y)
dy[0] = 1.2*y[0] – 0.6*y[0]*y[1]
dy[1] = -0.8*y[1] + 0.3*y[0]*y[1]
return dy
t1 = 0
tf = 20
y0 = [2., 1.] # np.array([2., 1.])
tspan = np.linspace(t1, tf, num=100)
result = solve_ivp(dydt, (t1, tf), y0, t_eval=tspan)
t = result.t
y = result.y
fig = plt.figure()
ax = fig.add_subplot()
ax.plot(t, y[0,:], color=’r’, marker=’.’, linestyle=’-‘,
label=r’$y_1$’)
ax.plot(t, y[1,:], color=’b’, marker=’.’, linestyle=’–‘,
label=r’$y_2$’)
ax.legend()
ax.set_xlabel(r’$t$’)
ax.set_ylabel(r’$y_1, y_2$’)
plt.show()

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