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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

    ??

    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
     
  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

    HallsofIvy

    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

    Mark44

    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
    [tex]h=\frac{b-a}{m}=2/2=1[/tex]
    [tex]x_h=a+kh=-1+k[/tex]
    [tex]s(f,h)=\frac{h}{3}(f(a)+f(b)+\frac{2h}{3}\sum_{k=1}^{m}f(x_{2k})+\frac{4h}{3}\sum_{k=1}^{m}f(x_{2k-1})=[/tex]
    [tex]\frac{1}{3}(f(-1)+f(1)+\frac{2}{3}\sum_{k=1}^{m}f(x_{2k})+\frac{4}{3}\sum_{k=1}^{m}f(x_{2k-1})=[/tex]

    [tex]\frac{1}{3}(f(-1)+f(1)+\frac{2}{3}[f(x_2)+f(x_4)]+\frac{4}{3}[f(x_1)+f(x_3)]=
    [/tex]
    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

    Mark44

    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?
     
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