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Math Help - simpson method question(numerical analysis)

  1. #1
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    simpson method question(numerical analysis)

    i have been told that simpson with 3 points is a single panel

    ??

    why??

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

    http://i48.tinypic.com/nlc4t1.jpg
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by transgalactic View Post
    i have been told that simpson with 3 points is a single panel

    ??

    why??

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

    http://i48.tinypic.com/nlc4t1.jpg
    What do you mean by a single panel?

    CB
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  3. #3
    MHF Contributor

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    Quote Originally Posted by transgalactic View Post
    i have been told that simpson with 3 points is a single panel

    ??

    why??

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

    http://i48.tinypic.com/nlc4t1.jpg
    No, a "panel", in the sense that you are using it here, is the region over which we have a single "piece" of our piecewise quadratic that we are using to approximate the actual function to be integrated.

    In "Riemann sums" we use a "piecewise constant" function between two points and in the "trapezoid method" we use a "piecewise constant" approximation, again between two points because two points determine a line. In both of those case a "panel" is the region between two given points.

    But in "Simpson's rule" we use a "piecewise quadratic" function. A quadratic function is of the form " y= ax^2+ bx+ c" which, because it requires us to determine the three coefficients, a, b, and c, requires three points. For Simpson's rule, a "panel" ranges over three points, not two.
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