The Algorithms
The Simpson’s Method
Simpson's Rule is a numerical method that approximates the value of a definite integral by using quadratic functions. This method is named after the English mathematician Thomas Simpson (1710−1761).
Let's check this method for the next function: $$f(x) = ({e^x / 2})*(cos(x)-sin(x))$$ with $\varepsilon = 0.001$
import math
import numpy as np
def simpsone(a, b, n, func):
h = float((b-a)/n)
s = (func(a) + func(b)) * 0.5
for i in np.arange(0, n-1):
xk = a + h*i
xk1 = a + h*(i-1)
s = s + func(xk) + 2*func((xk1+xk)/2)
x = a + h*n
x1 = a + h*(n-1)
s += 2 *func((x1 + x)/2)
return s*h/3.0Some input data
f = lambda x: (math.e**x / 2)*(math.cos(x)-math.sin(x))
n = 10000
a = 2.0
b = 3.0
print("Result: ", simpsone(a, b, n, f))Result: -8.404153016168566
