39 lines
1.5 KiB
Python
39 lines
1.5 KiB
Python
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# 复合Newton-Cotes公式 复合牛顿-柯特斯公式
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# n等分参数，x1到x2的区间，type=1表示梯形法，type=2表示辛普生法
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def CompositeNewtonCotes(x_start,x_end,fx,n, type):
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if type == 1:
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h = (x_end - x_start) / n
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result = 0
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for i in range(n):
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result += (fx(x_start + i * h) + fx(x_start + (i + 1) * h))
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result *= (h / 2)
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return result
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elif type == 2:
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h = (x_end - x_start) / n
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result = -fx(x_start) + fx(x_end)
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for i in range(n):
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result += (4 * fx(x_start + (i + 0.5) * h) + 2 * fx(x_start + i * h))
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result *= (h / 6)
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return result
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# 积分原函数 ##############################################################
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def fx(x):
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if x == 0:
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x = 1e-10 # Avoid division by zero #如果x能为0，注释掉这行##############
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pass
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return x/(4+x**2) #把函数改成题干的形式###################
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if __name__ == "__main__":
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##############################################################################################################
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x_start = 3.0 # 积分下限
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x_end = 6.0 # 积分上限
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# 复合梯形公式，点数为n+1
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print("复合梯形公式\n", CompositeNewtonCotes(x_start,x_end,fx,8, 1)) #8等分，1代表是梯形公式####################
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# 复合辛普生公式，点数为2n+1
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print("复合辛普生公式\n", CompositeNewtonCotes(x_start,x_end,fx,4, 2)) #4等分，2代表是辛普生公式###############
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