MATLAB: Looking for good example of where numerical integration beats symbolic integration

cumtrapznumerical integrationsymbolic

Hi,

I'm looking for a good example of where numerical integration beats symbolic integration to show a group of students why they should match their method to the problem. Aside from 'real world' lab data which can't be approximated by an equation, are there equations for which Matlab can't produce a nice integral solution using the Symbolic Math Toolbox, but can be well approximated using cumtrapz?

Best Answer

voxynn,

how about a RLC circuit? You could start with the linear DE, show that the DE can be solved symbolically and numerically, and then add a small non-linearity to the DE. Let me know if you need code and I can point you to it.

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MATLAB: Is there a function in Matlab that is similar to “cumtrapz” but uses a more accurate method of array integration (such as Simpson’s rule)

You COULD use a spline interpolant, then integrating the spline. That would be a higher order integration. (Pchip MAY be a better choice than spline, although spline will be theoretically a higher order as an integration tool here.)

Or you could use a Simpsons rule. Note that it is easy to think you are doing a better job, because the integration rule is of a "higher" polynomial order. In fact, it is trivial to give you a set of points that will cause a simple high order integration to fail miserably.

MATLAB: Numerical Integration of Equally Spaced Data

hi David,

I think using trapz integrator with the x/t axis gives good result, in the mean wile try to interpolate your data to get better accuracy , as this example :

 t=0:1/100:pi/2;
 y=sin(t);
 f=trapz(t,y);
 t2=interp(t,4);
 y2=sin(t2);
 f2=trapz(t2,y2)      %  Df=1.0064-0.9992=0.0072

Best Answer

Related Solutions

MATLAB: Is there a function in Matlab that is similar to “cumtrapz” but uses a more accurate method of array integration (such as Simpson’s rule)

MATLAB: Numerical Integration of Equally Spaced Data

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