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main.py
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92 lines (76 loc) · 1.99 KB
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import numpy as np
import matplotlib.pyplot as plt
def f(t, y, A, B, C):
x, y, z = y
dxdt = A * y - A * x
dydt = -x * z + B * x - y
dzdt = x * y - C * z
return np.array([dxdt, dydt, dzdt])
def euler_method(f, y0, t0, dt, tmax, *args):
y = [np.array(y0)]
t = t0
while t < tmax:
y_next = y[-1] + dt * f(t, y[-1], *args)
y.append(y_next)
t += dt
return np.array(y)
def midpoint_method(f, y0, t0, dt, tmax, *args):
y = [np.array(y0)]
t = t0
while t < tmax:
k1 = dt * f(t, y[-1], *args)
k2 = dt * f(t + 0.5 * dt, y[-1] + 0.5 * k1, *args)
y_next = y[-1] + k2
y.append(y_next)
t += dt
return np.array(y)
def rk4_method(f, y0, t0, dt, tmax, *args):
y = [np.array(y0)]
t = t0
while t < tmax:
k1 = dt * f(t, y[-1], *args)
k2 = dt * f(t + 0.5 * dt, y[-1] + 0.5 * k1, *args)
k3 = dt * f(t + 0.5 * dt, y[-1] + 0.5 * k2, *args)
k4 = dt * f(t + dt, y[-1] + k3, *args)
y_next = y[-1] + (k1 + 2 * k2 + 2 * k3 + k4) / 6
y.append(y_next)
t += dt
return np.array(y)
y0 = [1, 1, 1]
A = 10
B = 25
C = 8 / 3
t0 = 0
dt = 0.02
tmax = 70
linewidth = 0.7
results_euler = euler_method(f, y0, t0, dt, tmax, A, B, C)
results_midpoint = midpoint_method(f, y0, t0, dt, tmax, A, B, C)
results_rk4 = rk4_method(f, y0, t0, dt, tmax, A, B, C)
x_euler = results_euler[:, 0]
z_euler = results_euler[:, 2]
x_midpoint = results_midpoint[:, 0]
z_midpoint = results_midpoint[:, 2]
x_rk4 = results_rk4[:, 0]
z_rk4 = results_rk4[:, 2]
plt.figure()
plt.plot(x_euler, z_euler, linewidth=linewidth)
plt.xlabel('x')
plt.ylabel('z')
plt.title('Euler Method')
plt.grid(True)
plt.show()
plt.figure()
plt.plot(x_midpoint, z_midpoint, linewidth=linewidth)
plt.xlabel('x')
plt.ylabel('z')
plt.title('Midpoint Method')
plt.grid(True)
plt.show()
plt.figure()
plt.plot(x_rk4, z_rk4, linewidth=linewidth)
plt.xlabel('x')
plt.ylabel('z')
plt.title('RK4 Method')
plt.grid(True)
plt.show()