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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

Updated

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

Amin Mohammed

### Amin Mohammed (view profile)

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

David MERCIER

Nicholas Tavares

### Nicholas Tavares (view profile)

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

fernando

### fernando (view profile)

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?

Matthew

Angelos

### Angelos (view profile)

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!