33 lines
900 B
Python
33 lines
900 B
Python
x1, x2 = 3, 6
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def fx(x):
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return x/(4+x**2)
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# 复合Newton-Cotes公式 复合牛顿-科特斯公式
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# n等分参数，x1到x2的区间，type=1表示梯形法，type=2表示辛普森法
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def CompositeNewtonCotes(n, type):
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if type == 1:
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h = (x2 - x1) / n
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result = 0
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for i in range(n):
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result += (fx(x1 + i * h) + fx(x1 + (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 = (x2 - x1) / n
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result = -fx(x1) + fx(x2)
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for i in range(n):
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result += (4 * fx(x1 + (i + 0.5) * h) + 2 * fx(x1 + i * h))
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result *= (h / 6)
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return result
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if __name__ == "__main__":
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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(8, 1))
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# 复合辛普森公式，点数为2n+1
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print("复合辛普森公式\n", CompositeNewtonCotes(4, 2))
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