错误，尝试使用Euler方法绘制二阶常微分方程解的图

Question

我正在做一个项目，我想使用欧拉方法来显示这个二阶微分方程的解0=y''+y'+9.81y

所以我开始把二阶方程组变成一阶方程组y'=u, u'=f(t,y,u)

具有初始条件y(0)=180, u(0)=0

所以我得到了两个方程式y[n + 1] = y[n] + u[n] * (t[n + 1] - t[n]), u[n + 1] = u[n] + f(u[0], y[n], t[0]) * (t[n + 1] - t[n])

这是我的代码

import numpy as np
import matplotlib.pyplot as plt

def odeEuler(f, y0, u0, t):
y = np.zeros(len(t))
u = np.zeros(len(t))
y[0] = y0
u[0] = u0
for n in range(0, len(t) - 1):
y[n + 1] = y[n] + u[n] * (t[n + 1] - t[n])
u[n + 1] = u[n] + f(u[0], y[n], t[0]) * (t[n + 1] - t[n])
return y, u

t = np.linspace(0, 100)
y0 = 180
u0 = 0
f = lambda u, y, t: -9.81 * y - u
y = odeEuler(f, y0, u0, t)
plt.plot(t, y, 'b.-')
plt.legend(['Euler'])
plt.axis([0, 100, 0, 200])
plt.grid(True)
plt.show()

然而，当我运行代码时，它会给我错误

Traceback (most recent call last):
File "/Users/huangy15/PycharmProjects/Draft/Damped Driven Pendulum/Praying this works.py", line 22, in <module>
plt.plot(t, y, 'b.-')
File "/Users/huangy15/PycharmProjects/Draft/Damped Driven Pendulum/venv/lib/python3.7/site-packages/matplotlib/pyplot.py", line 3021, in plot
**({"data": data} if data is not None else {}), **kwargs)
File "/Users/huangy15/PycharmProjects/Draft/Damped Driven Pendulum/venv/lib/python3.7/site-packages/matplotlib/axes/_axes.py", line 1605, in plot
lines = [*self._get_lines(*args, data=data, **kwargs)]
File "/Users/huangy15/PycharmProjects/Draft/Damped Driven Pendulum/venv/lib/python3.7/site-packages/matplotlib/axes/_base.py", line 315, in __call__
yield from self._plot_args(this, kwargs)
File "/Users/huangy15/PycharmProjects/Draft/Damped Driven Pendulum/venv/lib/python3.7/site-packages/matplotlib/axes/_base.py", line 501, in _plot_args
raise ValueError(f"x and y must have same first dimension, but "
ValueError: x and y must have same first dimension, but have shapes (50,) and (2, 50)

有人能帮我检查一下我的想法是否有效吗？如果无效，我还能采取什么其他方法？谢谢

Answer 1

您的odeEuler函数返回两个变量：y和u，您只需要选择其中一个进行绘图。

将函数的输出存储在两个不同的变量中可以解决问题：

y, u = odeEuler(f, y0, u0, t)