MATLAB Mathematics - SERC - Index of

Numerical Integration (Quadrature)
To perform the integration, two functions are available in the funfun directory.
The first, dblquad, is called directly from the command line. This M-file
evaluates the outer loop using quad. At each iteration, quad calls the second
helper function that evaluates the inner loop.
To evaluate the double integral, use
result = dblquad(@integrnd,xmin,xmax,ymin,ymax);
The first argument is a string with the name of the integrand function. The
second to fifth arguments are
xmin
xmax
ymin
ymax
Lower limit of inner integral
Upper limit of the inner integral
Lower limit of outer integral
Upper limit of the outer integral
Here is a numeric example that illustrates the use of dblquad.
xmin = pi;
xmax = 2*pi;
ymin = 0;
ymax = pi;
result = dblquad(@integrnd,xmin,xmax,ymin,ymax)
The result is -9.8698.
By default, dblquad calls quad. To integrate the previous example using quadl
(with the default values for the tolerance argument), use
result = dblquad(@integrnd,xmin,xmax,ymin,ymax,[],@quadl);
Alternatively, you can pass any user-defined quadrature function name to
dblquad as long as the quadrature function has the same calling and return
arguments as quad.
4-29