Difference equations, Euler’s summation formula and Hyers–Ulam stability

Abstract

In connection with the difference equation of the spiral of Theodorus (square root spiral) we develop an approach of Herbert Kociemba who gave an approximation of this spiral using Euler's summation formula (see [7]). We use Hyers-Ulam stability to obtain estimates about the distance between the approximative soution and the exact solution (the normal solution) of the considered difference equation. The presented method can be applied to the general difference equation f (x + 1) = f (x) + c(x).