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

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 |