Simpson's rule and trapezoidal rule ?'s

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Homework Help Overview

The discussion revolves around the application of Simpson's rule and the trapezoidal rule in numerical integration, focusing on when to use each method and the reasoning behind their respective formulations.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the conditions under which to prefer Simpson's rule over the trapezoidal rule, discussing the smoothness of the curve and the nature of the function being approximated. Questions are raised about the alternating coefficients in Simpson's rule and the implications of error estimates for both methods.

Discussion Status

The conversation is ongoing, with participants sharing their thoughts and uncertainties regarding the effectiveness of each rule for different types of curves. Some guidance on the expected accuracy of Simpson's rule for certain functions has been mentioned, but no consensus has been reached.

Contextual Notes

Participants acknowledge that both methods can be applied to parabolic curves, leading to discussions about the nuances of their effectiveness in various scenarios.

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when do you use simpson's rule over trapezoidal rule?

why does simpsons rule alternate 4 and 2?
 
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ryingling5711 said:
when do you use simpson's rule over trapezoidal rule?

why does simpsons rule alternate 4 and 2?

I think, though I could be wrong, Simpson's rule is used when the curve you are approximating is smooth and "parabolicish." The trap rule, on the other hand, should be used then your curve is not so smooth or not so "parbolicish". Both have some sort of error estimate, right? I might go for the one with the lowest estimate.
 
I'm not really sure about that because i know you can use both for parabolic curves so but maybe your right that the trap rule is better for estimating integrals on less parabolic curves.
 
ryingling5711 said:
I'm not really sure about that because i know you can use both for parabolic curves so but maybe your right that the trap rule is better for estimating integrals on less parabolic curves.

Generally speaking you would expect better approximations for curvy functions with Simpson's rule. One surprising fact about Simpson's rule is that it is exact for cubics even though by design you might expect it would be exact only for second and lower degree polynomials.
 

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