梯形公式

import numpy as npdef 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)/nf = np.zeros(n+1)f[1:n+1] = ff(x_p[1:n+1])value = 0for i in range(n):value += (f[i]+f[i+1])*h/2err = abs(value - (-4/9))return value,errprint(tixing_quad(ff,0,1,8))

实验截图：

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辛普森公式

import numpy as npdef 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)/nf = np.zeros(n+1)f[1:n] = ff(x_p[1:n])f_m = ff(x_p+h/2)value = 0for i in range(n):value += (f[i]+f[i+1]+4*f_m[i])*h/6err = abs(value - (-4/9))return value,errprint(simpson_quad(ff,0,1,4))

实验截图：

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高斯公式

import numpy as npdef ff(x):return np.sqrt(x)*np.log(x)def gauss_quad(ff,a,b,m):if m == 1:x_p = 0A_p = 2elif 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)/2err = abs(value-(-4/9))return value,errprint(gauss_quad(ff,0,1,3))

实验截图：

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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