code for Simpson’s rule

Python code for Simpson’s rule

\PMlinkescapetext{
from math import *
def f(x):
  #function to integrate
  return sin(x)

def simpson_rule(a,b):
  #Approximation by Simpson's rule
  c=(a+b)/2.0
  h=abs(b-a)/2.0
  return h*(f(a)+4.0*f(c)+f(b))/3.0

# Calculates integral of f(x) from 0 to 1
print simpson_rule(0,1)
}

Integrating $\sin x$ from $0$ to $1$ with the previous code gives $0.45986218971\mathrm{\dots }$ whereas the true value is $1-\cos 1=0.459697694131860282599063392557\mathrm{\dots }$.

Title	code for Simpson’s rule
Canonical name	CodeForSimpsonsRule
Date of creation	2013-03-22 14:50:52
Last modified on	2013-03-22 14:50:52
Owner	drini (3)
Last modified by	drini (3)
Numerical id	7
Author	drini (3)
Entry type	Algorithm
Classification	msc 65D32
Related topic	NewtonAndCotesFormulas