ABSTRACT
The numerical integration of oscillating functions shows serious difficulties if we automatically apply one of the usual approximate integration procedures. The problems essentially arise from the following facts:
During the calculation of alternating functions many positive and negative values have to be added together. In a large proportion of instances, the sum of the positive values is nearly equal to the absolute value of the sum of the negative values. The resulting cancellation is attended by instabilities and a significant loss of accuracy.
For oscillating functions, the absolute values of certain derivatives often increase considerably as the degree of differentiation increases. Thus, the growth of the derivatives in remainder terms causes slow convergence.
