梯形公式
import numpy as np
def ff(x):
return np.sqrt(x)*np.log(x)
def tixing_quad(ff,a,b,n):
x_p = np.linspace(a,b,n+1) #linspace去得到右端点,arrange去不到
h = (b-a)/n
f = np.zeros(n+1)
f[1:n+1] = ff(x_p[1:n+1])
value = 0
for i in range(n):
value += (f[i]+f[i+1])*h/2
err = abs(value - (-4/9))
return value,err
print(tixing_quad(ff,0,1,8))
实验截图:
辛普森公式
import numpy as np
def ff(x):
return np.sqrt(x)*np.log(x)
def simpson_quad(ff,a,b,n):
x_p = np.linspace(a,b,n+1) #linspace去得到右端点,arrange去不到
h = (b-a)/n
f = np.zeros(n+1)
f[1:n] = ff(x_p[1:n])
f_m = ff(x_p+h/2)
value = 0
for i in range(n):
value += (f[i]+f[i+1]+4*f_m[i])*h/6
err = abs(value - (-4/9))
return value,err
print(simpson_quad(ff,0,1,4))
实验截图:
高斯公式
import numpy as np
def ff(x):
return np.sqrt(x)*np.log(x)
def gauss_quad(ff,a,b,m):
if m == 1:
x_p = 0
A_p = 2
elif m == 2:
x_p = np.array([-1/np.sqrt(3), 1/np.sqrt(3)])
A_p = np.array([1,1])
elif m == 3:
x_p = np.array([-np.sqrt(0.6), 0, np.sqrt(0.6)])
A_p = np.array([5/9, 8/9, 5/9])
else:
print('gauss point error,only 1,2,3')
value = np.sum(A_p*ff((a+b)/2+(b-a)/2*x_p)) * (b-a)/2
err = abs(value-(-4/9))
return value,err
print(gauss_quad(ff,0,1,3))
实验截图:
实验报告
方法 | 方法1 | 方法2 | 方法3 |
---|---|---|---|
参数选择 (n) | 8 | 4 | 3 |
数值 | -0.4080900395195133 | -0.42475203308844967 | -0.45269478226195303 |
误差 | 0.03635440492493114 | 0.019692411355994754 | 0.008250337817508613 |