On a differential-delay equation arising in number theory Original Research Article

We use the Tau Method to approximate Buchstabʹs function which is defined by the differential-delay equation (uw(u))′ = w(u − 1) for u ≥ 2 and w(u) = 1/u for 1 ≤ u ≤ 2. This equation has been treated by other authors using different numerical techniques. The errors in the Tau Method case are found to be lower than those obtained using power series expansions.