Double & Triple Integration with tabular data

Hi

The function dblquad(fun, xmin, xmax, ymin, ymax, tol) can be used for double integration over x and y if the function is known, Similarly for 3D integration the function triplequad(..) can be used.

If, however, I have the x and y data in tabular form (eg. experimental points), what are the MATLAB functions for the double and triple integrations ?

Thanks in advance

Answer 1

[Roger Stafford]

You can use Matlab's 'trapz' successively for this purpose. The easiest case is integrating over a rectangular region in (x,y) - that is, where the tabular data, T(x,y), is defined over a rectangular mesh of (x,y) values. Let x and y be vectors of the (x,y) values along the two edges of the rectangular table.

   [X,Y] = meshgrid(x,y);
   T = (The array of tabular values corresponding to X and Y)
   I = trapz(y,trapz(x,T,2));  % <-- The double integral

You should realize that the accuracy of this method is limited by how closely-spaced the x and y values are in the rectangle. For higher order integration than the trapezoidal method there are some algorithms given in the MatLab File Exchange.

[Sreedhar]

Roger Thank you for the answer. In this formula I = trapz(y,trapz(x,T,2)); % <-- The double integral

can y and x be interchanged ? In the case of a triple integral what is the formula ?

Can you post some examples ?

TIA