欧拉方法的改进

Question

因此，我有下面的代码用于改进的Euler方法陶氏：

import numpy as np
import matplotlib.pyplot as plt


int = np.array([50, 256])

yt = lambda x: 2*x**4
f = lambda x,t: 4*y/x

x0 = 1.
xf = 3.

for i in range(len(int)):
    x = np.linspace(x0, xf, int[i]+1)
    h = (xf-x0)/int[i]

    y = np.zeros(int[i]+1)
    y[0] = yt(x0)

    for k in range(1, len(y)):
        fk = f(x[k-1], y[k-1])
        fkh = f(x[k], y[k-1]+h* f(x[k-1], y[k-1]))
        y[k] = y[k-1] + (h/2.)*(fk+fkh)

        abserr = np.abs(yt(x) - y)

        plt.semilogy(x,abserr,'*')
        plt.show()

但是，当我运行它时，它给了我这个错误，我不知道如何解决。我已经在网上搜索过，并且看到有人对其进行矢量化处理，但是我还没有实现这一目标。任何建议或解决方案将不胜感激

TypeError: only size-1 arrays can be converted to Python scalars

The above exception was the direct cause of the following exception:

Traceback (most recent call last):
  File "noah.py", line 23, in <module>
    y[k] = y[k-1] + (h/2.)*(fk+fkh)
ValueError: setting an array element with a sequence.

Answer 1

您在lambda函数f的定义中有错字。应该是

f = lambda x,y: 4*y/x

由于输入错误，该函数返回了一个长度为51和257的数组，该数组来自x的定义。