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Simpson's rule for numerical integration

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Simpson's rule for numerical integration

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05 Nov 2009 (Updated )

The Simpson's rule uses parabolic arcs instead of the straight lines used in the trapezoidal rule

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Description

Z = SIMPS(Y) computes an approximation of the integral of Y via the Simpson's method (with unit spacing). To compute the integral for spacing different from one, multiply Z by the spacing increment.
 
Z = SIMPS(X,Y) computes the integral of Y with respect to X using the Simpson's rule.

Z = SIMPS(X,Y,DIM) or SIMPS(Y,DIM) integrates across dimension DIM

SIMPS uses the same syntax as TRAPZ.

Example:
-------
% The integral of sin(x) on [0,pi] is 2
% Let us compare TRAPZ and SIMPS
x = linspace(0,pi,6);
y = sin(x);
trapz(x,y) % returns 1.9338
simps(x,y) % returns 2.0071

Acknowledgements

This file inspired Generation Of Random Variates.

MATLAB release MATLAB 7.10 (R2010a)
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Comments and Ratings (4)
12 Sep 2013 fernando

its very simple,and now i understand the trapz code but then the simps seems to not work on me ..it says
"Undefined function or method 'simps' for input arguments of
type 'double'." how can i fix this?

19 May 2013 Matthew  
18 May 2013 Angelos

That is a very good example for the for understand the Simpson's rule!! Excellent work!

30 Aug 2011 Danny Sale

This is a great extension of Simpson's rule. I find it most valuable that this file works correctly for both even and odd length vectors, and that it can correctly handle arbitrary spacing. Also, the method is fully vectorized so it is very fast. Thank you and excellent work!

Updates
20 Nov 2009

Minor modifications in the descriptions and help texts of the two functions.

17 May 2013

Modifications in the help text

22 May 2013

Modification in the description

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