The problem of the numerical computation of integrals has been investigated for many centuries, yet there are still some cases for which no satisfactory results are known.
One is the case where the integrand possesses strong oscillations. Some progress has been made in recent years, but there are still open problems. Hascelik’s paper is very useful because it fills one of the remaining gaps. Specifically, an accurate algorithm is provided for integrals of the form ∫01 tα f(t) sin (ω / tr) dt, where ω and r are positive real numbers and α + r > -1, and for the corresponding integral where the sine function is replaced by a cosine.
The author not only constructs the algorithms in a theoretical way, but also investigates their properties, provides a stable method for the practical computation of the required coefficients, and gives some impressive numerical examples demonstrating the accuracy that can be achieved.
The topic of the paper is highly specialized; therefore, it is probably only of interest to a rather limited group, but they will find the paper most helpful.
