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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- Jun 25th 2010, 03:15 AMtransgalacticsimpson 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 - Jun 26th 2010, 05:21 AMCaptainBlack
- Jun 26th 2010, 08:06 AMHallsofIvy
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 "$\displaystyle y= ax^2+ bx+ c$" 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.