Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Trapezoidal, simpsons rule, and higher order approximations

  1. Dec 4, 2009 #1
    hi. i was able to prove the trapezoidal rule and simpsons rule. (basically i used matrices to determine the coefficients m and b for mx+b when proving the trapezoidal rule and a,b,c for ax^2+bx+c such that the points coincide, then i integrated the approximating polynomial) the amount of number-crunching and expanding products of linear terms was probably the most work ive ever done, but i was amazed to see terms cancel out to yeild vastly simplified formulas. but i was wondering, suppose i approximated each step with suppose, a cubic equation. i know how to do this, but after setting up the 4x4 matrix i quickly realized that this would be extremely mundane due to all the algebraic manipulations. so before i try deriving a numerical method that uses cubics to approximate the curve pieces, i wanna know whether it will simplify. will it simplify?
  2. jcsd
  3. Dec 4, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook