1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Simpson method question(numerical analysis)

  1. Jun 25, 2010 #1
    i have been told that simpson with 3 points is a single panel



    a pannel is the distance between to points
    so if we have 3 points then we have 2 panels

  2. jcsd
  3. Jun 25, 2010 #2
    can't view the link clearly and what do you mean by pannel?
  4. Jun 25, 2010 #3


    User Avatar
    Science Advisor

    Simpson's method works by approximating a function by a "piecewise quadratic". If I understand your use of "panel" correctly, it is one of the quadratic pieces.

    Since a quadratic, [itex]y= ax^2+ bx+ c[/itex], has three coefficients to be determined, one quadratic, one panel, requires three points, not two, to determine those three coefficients.

    The "trapezoid method", where we approximate the function by a piecewise linear function, y= ax+ b, requires only two coefficients to be determined and so each "panel" requires two points.
  5. Jun 25, 2010 #4
    so how they use those three points in the formula
    i cant see where they use them on the arrow pointed formula
  6. Jun 25, 2010 #5


    Staff: Mentor

    In the last equation, the three points are (-1, f(-1)), (0, f(0)), and (1, f(1)).

    The equation could be rewritten as
    S1 = (1/3)[f(-1) + 4f(0) + f(1)].
  7. Jun 26, 2010 #6
    so a pannel is not an interval
    a panel in simpsons rule is 3 points (which has two intervals between them)
  8. Jun 26, 2010 #7
    thanks :)
  9. Jun 26, 2010 #8
    i tried to get to your expression by the formula
    if we have three points then we have 2 sub intervals

    you see that it requests 4 points
    and not
    x_0 x_1 x_2

    Last edited: Jun 26, 2010
  10. Jun 26, 2010 #9


    Staff: Mentor

    In Simpson's rule, you divide an interval [a, b] into n subintervals of equal length. In each subinterval you use function values evaluated at three points: the left endpoint, the middle, and the right endpoint.

    Instead of getting lost in the summation symbols, work out for yourself for some simple function and an interval [0, 1] divided into four subintervals. What does Simpson's rule give you for this situation?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook