Question

我对python完全不熟悉，并尝试整合以下ode：

$ \ dot {x} = -2x-y ^ 2 $

$ \ dot {y} = -y-x ^ 2

这会产生一个包含所有0的数组我究竟做错了什么？它主要是复制代码，而另一个，没有耦合的ode，它运行正常。

import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import ode


def fun(t, z):
    """
    Right hand side of the differential equations
      dx/dt = -omega * y
      dy/dt = omega * x
    """
    x, y = z
    f = [-2*x-y**2, -y-x**2]
    return f

# Create an `ode` instance to solve the system of differential
# equations defined by `fun`, and set the solver method to 'dop853'.
solver = ode(fun)
solver.set_integrator('dopri5')

# Set the initial value z(0) = z0.
t0 = 0.0
z0 = [0, 0]
solver.set_initial_value(z0, t0)

# Create the array `t` of time values at which to compute
# the solution, and create an array to hold the solution.
# Put the initial value in the solution array.
t1 = 2.5
N = 75
t = np.linspace(t0, t1, N)
sol = np.empty((N, 2))
sol[0] = z0

# Repeatedly call the `integrate` method to advance the
# solution to time t[k], and save the solution in sol[k].
k = 1
while solver.successful() and solver.t < t1:
    solver.integrate(t[k])
    sol[k] = solver.y
    k += 1

# Plot the solution...
plt.plot(t, sol[:,0], label='x')
plt.plot(t, sol[:,1], label='y')
plt.xlabel('t')
plt.grid(True)
plt.legend()
plt.show()

Answer 1

您的初始状态（z0）为[0,0]。此初始状态的时间导数（fun）也是[0,0]。因此，对于这个初始条件，[0,0]始终是正确的解决方案。

如果您将初始条件更改为其他值，则应该观察到更有趣的结果。

我在Dopri5实现中做错了什么

1 个答案: