Simpson's Rule Integration

version 1.6.0.0 (1.71 KB) by Juan Camilo Medina
Computes an integral "I" via Simpson's rule in the interval [a,b] with n+1 equally spaced points

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Updated Fri, 29 Apr 2011 17:16:16 +0000

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This function computes the integral "I" via Simpson's rule in the interval [a,b] with n+1 equally spaced points

Syntax: I = simpsons(f,a,b,n)

Where,
f= can either be an anonymous function (e.g. f=@(x) sin(x)) or a vector containing equally spaced values of the function to be integrated
a= Initial point of interval
b= Last point of interval
n= # of sub-intervals (panels), must be integer

Written by Juan Camilo Medina - The University of Notre Dame
09/2010 (copyright Dr. Simpson)

Example 1:

Suppose you want to integrate a function f(x) in the interval [-1,1].
You also want 3 integration points (2 panels) evenly distributed through the
domain (you can select more point for better accuracy).
Thus:
f=@(x) ((x-1).*x./2).*((x-1).*x./2);
I=simpsons(f,-1,1,2)

Example 2:

Suppose you want to integrate a function f(x) in the interval [-1,1].
You know some values of the function f(x) between the given interval,
those are fi= {1,0.518,0.230,0.078,0.014,0,0.006,0.014,0.014,0.006,0}
Thus:
fi= [1 0.518 0.230 0.078 0.014 0 0.006 0.014 0.014 0.006 0];
I=simpsons(fi,-1,1,[])
note that there is no need to provide the number of intervals (panels) "n",
since they are implicitly specified by the number of elements in the vector fi

Cite As

Juan Camilo Medina (2022). Simpson's Rule Integration (https://www.mathworks.com/matlabcentral/fileexchange/28726-simpson-s-rule-integration), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2010a
Compatible with any release
Platform Compatibility
Windows macOS Linux
Acknowledgements

Inspired: simpsonQuadrature, Simpson's 1/3 and 3/8 rules

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