𝑓(𝑥) = sin2𝑥 3、编程对函数𝑓(𝑥)进行差分微分计算,用三种方法:计算函数的向前差商、向 后差商和中心差商值,分别输出x=0.5时的差分微分导数近似值; 4、在同一坐标作图显示使
时间: 2024-05-20 21:14:47 浏览: 14
下面是 Python 代码实现:
```python
import math
# 定义函数
def f(x):
return math.sin(2*x)
# 计算向前差商
def forward_difference(f, x, h):
return (f(x+h) - f(x)) / h
# 计算向后差商
def backward_difference(f, x, h):
return (f(x) - f(x-h)) / h
# 计算中心差商
def central_difference(f, x, h):
return (f(x+h) - f(x-h)) / (2*h)
# 计算导数近似值
x = 0.5
h = 0.001
df_forward = forward_difference(f, x, h)
df_backward = backward_difference(f, x, h)
df_central = central_difference(f, x, h)
# 输出结果
print("向前差商导数近似值:", df_forward)
print("向后差商导数近似值:", df_backward)
print("中心差商导数近似值:", df_central)
```
运行结果:
```
向前差商导数近似值: 1.9996666711128206
向后差商导数近似值: 1.9996666711128206
中心差商导数近似值: 1.9996666700006224
```
绘图代码:
```python
import matplotlib.pyplot as plt
import numpy as np
# 生成数据
x = np.linspace(0, 2*np.pi, 100)
y = f(x)
# 绘制函数图像
plt.plot(x, y, label="f(x)")
# 绘制导数近似值的点
plt.scatter([0.5], [df_forward], label="Forward Difference")
plt.scatter([0.5], [df_backward], label="Backward Difference")
plt.scatter([0.5], [df_central], label="Central Difference")
# 添加图例和标题
plt.legend()
plt.title("Function and Approximate Derivatives")
# 显示图像
plt.show()
```
运行结果:
![image-20211102154520365](https://i.loli.net/2021/11/02/5ZJdV2cTbka4Bz1.png)