Example for Adaptive Integration

The program adaptintegr.f90 implements adaptive integration based on the trapezoid rule. As an example, the function |sin(x)|1/2 is integrated from 2.5 to 3.5. Note that this function is not smooth at x=pi. The plot below shows the points which the adaptive algorithm selects for the integration.

The graph below shows for several input values of the desired error the actual error and the number of integration points given by the algorithm.

Note that the actual error behaves in the same way as for a smooth function and the trapezoid rule, i.e., C·(number of integration points)-2
Tobias von Petersdorff , tvp@math.umd.edu
Last modified: Sun Apr 6 17:06:03 EDT 1997