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Simpson's rule for numerical integration

version 1.5 (2.48 KB) by

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



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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.

% 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

Comments and Ratings (7)

Excellent job, I hope Matlab will include this as a built-in function in future releases :)


I am confused on how to use this I'm having the same problem as fernando


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



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

Danny Sale

Danny Sale (view profile)

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!



Modification in the description


Modifications in the help text


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

MATLAB Release
MATLAB 7.10 (R2010a)

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