# Math Help - simpson method question(numerical analysis)

1. ## 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

2. Originally Posted by transgalactic
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

3. Originally Posted by transgalactic
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.