返回0的辛普森规则

Question

我为辛普森数值积分规则编写了一个函数。对于n大于或等于34的值，该函数返回0。

这里，n是间隔数，a是起点，b是终点。

import math

def simpsons(f, a,b,n):
    x = []
    h = (b-a)/n
    for i in range(n+1):
        x.append(a+i*h)

    I=0
    for i in range(1,(n/2)+1):

        I+=f(x[2*i-2])+4*f(x[2*i-1])+f(x[2*i])
    return I*(h/3)

def func(x):
    return (x**(3/2))/(math.cosh(x))



x = []
print(simpsons(func,0,100,34))

我不确定为什么会发生这种情况。我还为梯形方法编写了一个函数，即使当n =50时它也不会返回0。这里发生什么事情？

Answer 1

维基百科用Python编写了辛普森规则的代码：

from __future__ import division  # Python 2 compatibility
import math

def simpson(f, a, b, n):
    """Approximates the definite integral of f from a to b by the
    composite Simpson's rule, using n subintervals (with n even)"""

    if n % 2:
        raise ValueError("n must be even (received n=%d)" % n)

    h = (b - a) / n
    s = f(a) + f(b)

    for i in range(1, n, 2):
        s += 4 * f(a + i * h)
    for i in range(2, n-1, 2):
        s += 2 * f(a + i * h)

    return s * h / 3

def func(x):
    return (x**(3/2))/(math.cosh(x))